# "Engineering Oasis" > " Civil Engineering data" ## Posts - [7- A guide to Local buckling parameters for steel beams.](https://magedkamel.com/7-local-buckling-parameters/): Local buckling parameters for members that are subjected to flexure. A discussion is extended to cover the difference between stiffened and un-stiffened elements. - [4b- Easy to introduce the definition of IRR-NPV.](https://magedkamel.com/4b-what-is-the-definition-of-irr/): What is the Npv, net present value? What is the IRR or the internal rate of return? Solved problem is given to illustrate the subject. - [6-Solved problem 5-2 for the plastic moment value for W10x60.](https://magedkamel.com/6-solved-problem-5-2-for-plastic-moment/): A solved problem 5-2 for the plastic moment value for section W10x60, two methods are used to estimate the value. - [4a- Easy illustration for MARR, WACC definitions](https://magedkamel.com/4a-definition-of-marr-wacc/): The post includes two definitions, MARR and WACC.MARR is the minimum rate of attractive rate of return.WACC is the weighted average cost of capital. - [4-Fixed-point iteration and how to use it?](https://magedkamel.com/4-fixed-point-iteration/): In numerical analysis, fixed-point iteration is a method of computing the roots of a function by changing the typical f(x)=y form to another form which is x= g(x). - [5- A Solved problem 5-1 for Sx & Zx-elastic-plastic moduli](https://magedkamel.com/5-solved-problem-5-1-for-sx-zx/): Solved problem 5-1 how to estimate elastic, plastic section moduli, and shape factor for a given I section? - [4-A Solved problem 4-3 for elastic and plastic sections.](https://magedkamel.com/4-problem-4-3-elastic-plastic-section/): Solved problem 4-3 for determining the elastic section modulus, plastic section modulus, and shape factor for a given T section, several methods are used. - [4- Easy illustration for Cash flow in and out diagram.](https://magedkamel.com/4-cash-flow-in-and-out-diagram/): The difference between cash flow in and out diagram. how to draw the cash in and out from different perspectives? A solved problem is given. - [3a- Simple and compound interest part 2.](https://magedkamel.com/3a-compound-interest-part-2/): In this post, simple and compound interest part 2, an additional solved problem is included to show the difference between simple and compound interest. - [3b-Elastic and plastic section moduli for any shape.](https://magedkamel.com/elastic-and-plastic-section-moduli/): How to find the Elastic and plastic section moduli for any shape? - [3- Simple and compound interest part 1.](https://magedkamel.com/3-compound-interest-part-1/): What is the difference between simple interest and compound interest? Solved problems are given for illustration. How to use excel for interest estimation? - [3a- Elastic and plastic section moduli for a rectangle.](https://magedkamel.com/3a-elastic-and-plastic-section-moduli/): A step by step guide to estimate elastic section modulus and plastic section modulus and shape factor for a rectangle. - [3- An Easy Introduction to Plastic Theory for Beams.](https://magedkamel.com/3-introduction-to-plastic-theory/): A simplified approach to plastic theory, step by step illustration for the basis of the plastic theory. - [3- Quick start to False position method for roots finding.](https://magedkamel.com/3-false-position-method/): The false position method is another numerical method for roots finding, The same Solved problem will be used to get the root for f(x) by false position. - [2- An easy approach to Compact and non-compact sections.](https://magedkamel.com/2-compact-and-non-compact-sections-for-beams/): Introduction to the compact and non-compact sections for the steel beams, what are the major differences between both. - [1- Understanding the Definition of matrix, matrices properties.](https://magedkamel.com/1-definition-of-matrix/): Definition of matrix, introduction to matrices, how to construct a matrix from a set of equations? What is the augmented matrix? - [2A- Guide to two solved problems for Economic equivalence.](https://magedkamel.com/2a-solved-problems-for-economic-equivalence/): The post includes solved problems for economic equivalence. Example 1.3 sets a lot of statements and it is required to get the correct one. - [2- Easy introduction to Economic Equivalence.](https://magedkamel.com/2-economic-equivalence/): The post includes two solved problems for deposited money in banks. The major item is the economic equivalence and how to estimate? - [15- Solved problem 6-19-4 for local buckling of column-2010.](https://magedkamel.com/15-solved-problem-6-19-4/): A solved problem 6-19-4 for local buckling is From prof. Salmon handbook. The steel section is a Built-up section. - [14-Solved problem 6-8 for local buckling of columns-CM#14](https://magedkamel.com/14-solved-problem-6-8-for-local-buckling/): Solved problem 6-8 For Local Buckling. The column is a rectangle hollow section, determine the axial compressive design strength and factored strength. - [13-A Solved problem 5-3 for local buckling of columns-CM#14](https://magedkamel.com/13-a-solved-problem-5-3-for-local-buckling/): A Solved problem 5-3 For Local Buckling, it is required to estimate Φc*Pn and Pn/Ωc, with the appropriate AISC equations for a square hollow steel section. - [12- Solved problem 5-2 for local buckling of columns.](https://magedkamel.com/12-solved-problem-5-2-for-local-buckling/): A Solved problem 5-2 For Local Buckling, for which it is required to estimate the LRFD value Φ* Pn and the ASD allowable strength P/Ωc, for a column. - [1- Easy approach to steel beams and types of buckling.](https://magedkamel.com/1-steel-beams-and-types-of-buckling/): Introduction to steel beams under flexure, study the definition between the local flange buckling and web buckling, the Compactness of steel beam. - [11- Local Buckling for stiffened and un-stiffened elements.](https://magedkamel.com/11-local-buckling-for-stiffened-and-un-stiffened/): Local buckling for stiffened and un-stiffened elements. A discussion is made for Limiting Kl/r based on the different Fy values and the coefficients Qa and Qs. - [10a- Easy study of Local Buckling-part-2.](https://magedkamel.com/10a-local-buckling-part-2/): Introduction to Local buckling-part-2 for columns, derive the expression for the Qa and Qs coefficients. - [10- Best Introduction to Local Buckling-part-1](https://magedkamel.com/10-introduction-to-local-buckling-part-1/): Introduction to Local Buckling-part-1 for columns, how to derive the equations relating to the local buckling? - [1- Step-by-step guidance for the Engineering Economy.](https://magedkamel.com/1-introduction-to-engineering-economy/): Introduction to the Engineering economy. What is the economical study? What is the difference between borrower and investor? Solved problems are included. - [9-Two Solved Problems for steel column analysis-FE Exam](https://magedkamel.com/9-solved-problems-for-column-analysis/): 2 Solved Problems For column analysis. First solved problem for finding the compressive strength. The second solved problem is for the service Live load. - [8-Solved Problem 13-28 For Compression Members-FE Exam.](https://magedkamel.com/8-solved-problem-13-28/): Solved Problem 13-28 for compression members, from Prof Iqbal handbook, for which the available compression member is to be selected. - [7- Solved problem 7-1 for alignment chart for columns.](https://magedkamel.com/7-solved-problem-7-1-for-alignment-chart/): Solved problem 7-1 for alignment chart for columns, it is a practical example to show how to use the alignment chart to get the K value for a frame. - [List of Steel beams Posts-part-1.](https://magedkamel.com/list-of-steel-beams-posts-part-1/): List of Steel beams Posts-part -1 for all the different items for the structural steel beams included and solved problems. - [6- Alignment charts for columns- easy approach.](https://magedkamel.com/6-alignment-charts-for-columns/): Alignment charts for columns. There 2 alignment charts, one is for the braced columns and the other is for the un-braced columns. The assumptions are included. - [5-A Solved Problem 4-9 For available compressive strength.](https://magedkamel.com/5-problem-4-9-for-compressive-strength/): A Solved Problem 4-9 For available compressive strength. How to decide the controlling axis for deflection, major or minor axis? - [4-How to compute critical stress-Table 4-22 & Table 4-1?](https://magedkamel.com/4-compute-critical-stress-table-4-22/): Compute Critical Stress-Table 4-22 & Table 4-1 for the available strength of W14x74. - [3a-Solved problem 4-2-how to find design compressive strength?](https://magedkamel.com/solved-problem-4-2/): Solved problem 4-2 for estimating the design compressive strength for the W section under compression load. An Introduction to ratio λ^2 is illustrated. - [3- Column compressive strength by the general equation](https://magedkamel.com/3-column-compressive-strength/): Column compressive strength for general buckling and how to differentiate between long columns and short columns? - [2- Easy introduction to Bisection method for roots findings.](https://magedkamel.com/2-bisection-method/): The bisection method can be done by taking the average value of the horizontal distance between points of brackets, and then substitute it in the function. - [1- Introduction to structural steel.](https://magedkamel.com/1-introduction-to-structural-steel/): This post includes an introduction to structural steel. The advantages and disadvantages of structural steel are discussed. - [2a-Introduction to Buckling for columns-part 2.](https://magedkamel.com/2a-buckling-for-columns-part-2/): The post title is buckling for columns-part 2 includes solved problems for major and minor axis which govern the buckling? - [2-Buckling for columns-effective length factors.](https://magedkamel.com/2-buckling-for-columns-effective-length-factors/): The post includes definition of buckling for columns. The second point is effective length factors based on the end conditions of columns. - [1a-Steel columns and Euler's formula-part 2](https://magedkamel.com/1a-steel-columns-and-eulers-formula-part-2/): In the post steel columns and Euler's formula-part 2. The discussion includes the different shapes of steel columns & how to derive Euler's formula. - [1- Easy approach to Steel columns and Euler's formula 1/2.](https://magedkamel.com/1-steel-columns-eulers-formula-part-1/): Steel columns are crucial elements. Euler's formula gives a relation between the load-carrying capacity of these columns and their slenderness ratio. - [1-Introduction to the moment of inertia.](https://magedkamel.com/1-introduction-to-moment-of-inertia/): This post includes an introduction to the moment of inertia and what is the difference between the second moment of area and mass moment of inertia? - [List of Compression Member Posts-part 1.](https://magedkamel.com/list-of-compression-member-posts-part-1/): Check out Compression Member Posts-part 1, which includes a detailed list of posts 1 to 10 along with their descriptions and relevant links. - [1a-What is synthetic division? Numerical Analysis-part 2](https://magedkamel.com/1a-what-is-synthetic-division/): Numerical analysis-part 2-What is synthetic division? Solved problems for synthetic divisions are included. - [1-Introduction To Numerical Analysis-part 1](https://magedkamel.com/1-introduction-to-numerical-analysis/): Introduction to numerical analysis, the difference between numerical and analytical methods, roots findings. review of the synthetic division. - [3-Estimation of max and min-moment of inertia for a section.](https://magedkamel.com/3-max-and-min-moment-of-inertia/): Estimation of max and min-Moment of inertia for a section. How to derive the The expression for max and min-moment of inertia. The equation of principal angle θp - [2-First moment of area and product of inertia at the CG.](https://magedkamel.com/2-first-moment-of-area-at-the-cg/): Derivation of the expression for the first moment of area at the Cg and the expression for the product of inertia at the CG. - [1- Easy illustration of the theory of pure bending.](https://magedkamel.com/1-the-theory-of-pure-bending/): Introduction to the Theory of Pure bending, the various assumption to be made and the resulting formula due that assumptions. - [3-How to determine y bar for a right angle-case-1?](https://magedkamel.com/3-y-bar-for-a-right-angle-case-1/): How to estimate y bar for a right angle triangle case-1 by using a horizontal strip? There are detailed steps to get the expression for the y bar. - [5-Solved problems for the net area estimation.](https://magedkamel.com/5-solved-problems-for-the-net-area-estimation/): Two Solved problems 3-4-2& 3-5 are explained. In both solved problems net area is to be estimated, first for an equal angle and second for the C channel. - [2-Definition of Integers solved problems](https://magedkamel.com/2-definition-of-integers-solved-problems/): The post includes the definition of integers and 5 solved problems to review the previous information for the whole number and the Integers. - [6-Solved problem 10-1-how to get Bearing value-LRFD? 2-3.](https://magedkamel.com/6-bearing-value-lrfd/): The post includes the second part of the solved problem 10-1. It is required to estimate bearing value-lrfd for a given connection. - [2a- X bar for a right angle-case-1-using vertical strip.](https://magedkamel.com/2a-x-bar-for-a-right-angle-case-1/): How to estimate X bar for a right angle-case-1 by using a vertical strip? step by step guide to get the final expression. - [31-Collapse load for a simply supported beam.](https://magedkamel.com/31-collapse-load-for-a-beam/): How to estimate the collapse load for a simply supported beam under a concentrated load?A given solved problem for a W18x76 simple beam of 32 feet long. - [15-Product of inertia Ixy-for the triangle.](https://magedkamel.com/15-product-of-inertia-ixy-for-the-triangle/): How to estimate the product of inertia Ixy for a triangle? the procedure considered the triangle as composed of two right-angle triangles. - [4- Workable Gauge Lines distances for an angle.](https://magedkamel.com/4-workable-gauge-lines/): What are workable gauge lines distances for an angle?table 1-7a for gages.How do we estimate the g distance between bolts for angles? - [14a-How to get of Moment of inertia Iy-at Cg for a triangle?](https://magedkamel.com/14a-moment-of-inertia-iy-at-cg/): How to estimate the moment of inertia Iy-at Cg for a triangle? using the value of Iy of a triangle we can get the inertia Iy-at Cg. - [2-How to determine x bar for a right angle-case-1?](https://magedkamel.com/2-x-bar-for-a-right-angle-case-1/): How to estimate x bar for a right angle triangle case-1 by using a horizontal strip? What is the difference between Case 1 and 2? - [5- A solved problem 10-1-for bearing connection-1-3.](https://magedkamel.com/5-solved-problem-10-1-for-bearing/): The post includes the first part of the solved problem 10-1-for bearing. It is required to estimate the shear force that can be applied on a given connection. - [7- Approach to Uniform series of compound interest-1/2.](https://magedkamel.com/7-uniform-series-of-compound-interest-2/): Introduction to the uniform series of compound interest, how we can develop an expression for the uniform series of compound interest with Solved problems - [30-Introduction to design of continuous beam, problem 4-15.](https://magedkamel.com/30-design-of-continuous-beam/): Design of continuous beam. We have a Detailed design solved problem 4-15 for which it is required to find the lightest W10 for beam after moment redistribution. - [1- Easy definition of Sets, set braces, and notations.](https://magedkamel.com/1-definition-of-sets-set-braces-and-notations/): The post includes an introduction to sets, what are set braces? The notations used for an expression of a set, whole number and natural number. - [14-The Moment of inertia Iy for a triangle.](https://magedkamel.com/14-moment-of-inertia-iy-for-a-triangle/): A full estimate of the moment of inertia Iy for any given triangle? the procedure considered the triangle as composed of two right-angle triangles. - [3- Solved problem 3-1-Nominal strength of a plate.](https://magedkamel.com/3-solved-problem-3-1-for-nominal-strength/): Solved problem 3-1 for nominal strength, how to estimate the LRFD and ASD tensile nominal strength?two cases will be considered yielding and rupture. - [2- Easy approach to solved problems for net area estimation.](https://magedkamel.com/2-solved-problems-for-net-area-estimation/): How to estimate the net area for plate members? solved problems 3-1& 3-2 for plate members, and how to consider the zigzag line of fasteners? - [List of Tension Member's Posts-part 1A](https://magedkamel.com/list-of-tension-members-posts-part-1a/): List of Tension Member's Posts-part 1A from post 2 to post 6. The list includes strength estimation, workable gauge lines and effective net area estimate. - [List of Tension Member's Posts-part 1.](https://magedkamel.com/list-of-tension-members-posts-part-1-2/): List of Tension Member's Posts-part 1 from post 1 to post 1c. The list includes an introduction to tension members and a review to AISC tables 2-4&2-5. - [22-Modification to Alignment Chart for Braced Frame.](https://magedkamel.com/22-modification-to-alignment-chart/): Modification to Alignment chart for the braced frame, the three cases for m modified for the braced frames. - [5A- Second solved problem-LU decomposition-3x3 matrix](https://magedkamel.com/5a-second-solved-problem-lu-decomposition/): The second solved problem-LU decomposition for the 3x3 matrices, how to get x,y,z values for three simultaneous equations? - [29- Moment redistribution for Continuous steel beams.](https://magedkamel.com/29-moment-redistribution-for-continuous-beams/): Introduction to the moment redistribution For Continuous Steel Beams. What are the value of moment values before and after redistribution? - [21-Solved problem 4-16 for k value using the French equation.](https://magedkamel.com/21-solved-problem-4-16/): Solved Problem 4-16 For K Factor,by-using-french-equation for the unbraced frame with different end conditions, and how to estimate the k values? - [5- First solved problem-LU decomposition for the 3x3 matrix](https://magedkamel.com/5-first-solved-problem-lu-decomposition/): This post illustrates the first solved problem-LU decomposition for the 3x3 matrix. Step by step guide to solve 3 simultaneous equations by the LU method? - [1C- Best and Full illustration of AISC Table 2-4.](https://magedkamel.com/introduction-to-table-2-4/): AISC Table 2-4 for various steel- shapes The main difference in Table 2-4 between CM#14 and CM#15. - [4- Easy Introduction to Matrix operations-part-2.](https://magedkamel.com/4-matrix-operations-part-2/): A discussion of matrix operations-part-2 The operations are powers of matrix & multiplication of 3x3 matrices. Review of the properties of matrix addition. - [1B-Review of AISC table 2-5 for plates.](https://magedkamel.com/1b-review-of-aisc-table-2-5-for-plates/): A review of AISC table 2-5 for plates including the differences between CM#14 and CM #15 and a review of table 1-7a for Workable gauges for angles. - [20-Solved problem 4-16 for k factor for a portal frame.](https://magedkamel.com/20-solved-problem-4-16-for-k-factor/): Solved Problem 4-16-part -1 For K Factor, for un-braced frame with different end conditions, and how to estimate the k values for two columns? - [4-Derive the expression for L-U values for-3x3 matrix.](https://magedkamel.com/4-the-expression-for-l-u-values/): Step-by-step guide on how to derive the expression for L-U values for-3x3 matrix using Doolittle's method? - [1-What is the First moment of area?](https://magedkamel.com/1-what-is-the-first-moment-of-area/): The lecture includes definitions for the area, Cg of an area, and the first moment of area, Moment of inertia, and product of inertia. - [4-Nominal shear strength and bearing- tear out made simple.](https://magedkamel.com/4-nominal-shear-strength-for-bolts/): The relation between the nominal shear strength of bolts, and their ultimate strength. The discussion is about bearing and tear out in more detail. - [28- Part 4/4 of the Solved problem 9-9-6 How To Find LL?](https://magedkamel.com/28-part-4-4-of-the-solved-problem-9-9-6/): Part 4/4 of the solved problem 9-9-6, which includes the estimation of Cb for a simply supported beam under uniform load. - [1A- Easy introduction to Tension members-part-2.](https://magedkamel.com/1a-easy-introduction-to-tension-members/): Introduction to Tension members-part 2, how to estimate net area. The definition of net area, net effective area. - [3-How to solve for x-y by L-U Decomposition?](https://magedkamel.com/3-solve-for-x-y-by-l-u-decomposition/): How to solve for x-y by L-U Decomposition? Illustration by Gauss elimination for L and U matrices. - [1- A step-by-step introduction to tension members.](https://magedkamel.com/1-introduction-to-tension-members/): Introduction to tension members. What are the various types of fracture of tension members? The damage due to the punching of a hole. - [19-Modification to the alignment chart for an un-braced frame.](https://magedkamel.com/19-modification-to-chart-un-braced-columns/): Modification To the Alignment Chart, introduction to modification factor m, and how these factors were derived? - [27- Part 3/4 of the Solved problem 9-9-6, how to find LL?](https://magedkamel.com/27-solved-problem-9-9-6-part-3-4/): Part 3/4 of the solved problem 9-9-6, this part includes the estimation of Lp value and Lr value for the built-up beam under lateral-torsional buckling. - [2- Easy illustration for LU decomposition for 2x2 matrix](https://magedkamel.com/2-lu-decomposition/): How to use the Lu decomposition method for a 2x2 matrix? A step-by-step guide to find L and U values? - [13- Easy approach to Moment of inertia Ix-for a triangle.](https://magedkamel.com/13-moment-of-inertia-ix-for-a-triangle/): How do we estimate the moment of inertia Ix -for a triangle and the radius of gyration about x? Estimate the value Ix at center of gravity cg . - [18A-Analysis of portal frame-fixed supports at base.](https://magedkamel.com/18a-portal-frame-fixed-supports-at-base/): A review of portal frame-fixed supports at base, how to derive the internal forces for portal frame-fixed supports at base, - [26-Part-2-4 of the Solved problem 9-9-6, How To Find LL?](https://magedkamel.com/26-part-2-4-for-solved-problem-9-9-6/): Part-2-4 of the solved problem 9-9-6 from Prof. Charles salmon's book, how to get the service LL for a welded section. Values for Sx and Mn were estimated. - [25-Part 1-4 Solved problem 9-9-6, how to find service LL?](https://magedkamel.com/25-part-1-4-solved-problem-9-9-6-1-4/): Part 1 of the solved problem 9-9-6 from Prof. Charles G salmon's book, How to check whether the Flange and web are compact or non-compact sections. - [12-Product of inertia Ixy for the right angle-case-2.](https://magedkamel.com/12-product-of-inertia-ixy-for-right-angle/): The post includes the product of inertia Ixy for the triangular section case -2. Two alternative methods were used. A full description is introduced. - [24b- Easy approach to solved problem-5-1-part 2.](https://magedkamel.com/24b-solved-problem-5-1-part-2/): In our post, we continue solving the Solved problem-5-1-part 2-2 in which the design of steel beam is governed by deflection. - [24a- Easy approach to the solved problem-5-1-part 1-2](https://magedkamel.com/24a-solved-problem-5-1-part-1-2/): In our post we will introduce a solved problem-5-1-part 1-2 in which the design of steel beam is governed by deflection. - [18-A Review of portal frames-pin supports at base.](https://magedkamel.com/18-a-review-of-portal-frames/): A review of portal frames subject, how to derive the internal forces for the portal frame with hinged supports at the base? - [11-Moment of inertia Iy-Case-2 for a right-angle triangle.](https://magedkamel.com/11-inertia-for-right-angle-iy-case-2/): How to get the moment of inertia for a right-angle triangle -Iy-case-2?The procedure is done by using a vertical strip. How to find polar moment of inertia Jo? - [24- Easy approach to deflection of steel beams.](https://magedkamel.com/24-deflection-of-steel-beams/): Deflection of steel beams, what are the disadvantages. What are the parameters controlling the deflection of steel beams? - [10-Ix-the moment of inertia for a right-angle-Case-2.](https://magedkamel.com/10-ix-the-moment-of-inertia/): How to get Ix-the moment of inertia for the right-angle triangle-Case-2? by using a horizontal strip, and the other method is to use a vertical strip. - [17-Alignment chart-part 2 for the unbraced frames.](https://magedkamel.com/17-alignment-chart-part-2/): Alignment chart-part 2, discussion about the conditions from which the alignment chart was developed and an introduction to the portal frame. - [9- Easy approach to Ixy for-right-angle -Case-1.](https://magedkamel.com/9-product-of-inertia-ixy-right-angle/): How to estimate the product of inertia Ixy for a right-angle triangle case No.1 at the external axis? step-by-step illustration by using integration. - [23S- Solved problem 10-2, Table 3-2 for shear value.](https://magedkamel.com/23-solved-problem-10-2-table-3-2-for-shear-value/): A solved problem 10-2 indicates how to check the adequacy of shear using table 3-2. the second part is the relation between h/tw and Vn-CM#15. - [16a- Solved Problem 5-10 with more iterations-Fcr value.](https://magedkamel.com/16a-solved-problem-5-10-with-more-iterations/): A Solved Problem 5-10 with more iterations For the Available Strength Of A Column w16x26 which is a slender column. - [3-Bearing Type connections-part-2.](https://magedkamel.com/3-bearing-type-connections-part-2/): This is bearing Type connections-part-2. The topics include the nominal tensile strength of a bolt. Edge spacing and bolts spacing. - [22S-Step-by-step guide to the solved problem 10-2 for beam.](https://magedkamel.com/22-solved-problem-10-2-for-beam-adequacy/): A solved problem 10-2 indicates how to check the adequacy of shear for a given W section beam? The relation between h/tw and vn for CM#14. - [21S- Solved problem 2-22 for shear stress estimation-part 2](https://magedkamel.com/21-solved-problem-2-22-shear-stress/): A solved problem 2-22 that includes three different shapes and the shear stresses-for each shape to be evaluated and drawn. - [20S- A guide to solved problem 2-22 for shear stress-part-A](https://magedkamel.com/20-a-solved-problem-2-22-for-shear-stress/): A solved problem 2-22 for shear stress, it is required to estimate in part-a, the shear stress for a rectangle with given force and dimension in inches. - [19S- Review of shear stresses for steel beams.](https://magedkamel.com/19-review-of-shear-stresses/): Review of shear stresses for beams, The relation between horizontal stresses and vertical stresses, and how to derive the shear stress for a rectangle. - [16-A Solved Problem 5-10-Available Strength for slender column.](https://magedkamel.com/16-problem-5-10-for-available-strength/): A Solved Problem 5-10 For the Available Strength of A Column w16x26 which is a slender column. - [8-Moment of inertia-Iy for right-angle triangle case-1.](https://magedkamel.com/8-inertia-iy-for-right-angle-triangle/): How to estimate the moment of inertia-Iy for right-angle triangle -case-1? This is done by using a vertical strip, Iy at Cg is also estimated. - [18C-CB value bracing at third points of a beam-U load](https://magedkamel.com/18c-cb-value-bracing-at-third-points/): The post includes how to get Cb value bracing at third points of a beam-uniform load. - [6b-Introduction to a solved problem for compound interest](https://magedkamel.com/6b-solved-problem-for-compound-interest/): A Solved problem for compound interest. Different options are given, it is required to estimate the least value deposit as of today for $10,000 after 4 years. - [18b-Cb value-bracing at the midpoint of a beam-uniform load](https://magedkamel.com/18b-cb-value-bracing-at-the-midpoint/): The post includes how to get Cb value-bracing at the midpoint of the beam-for uniform loads for two cases which are simple beam and fixed end beam. - [6a- Types of frequencies of compounding.](https://magedkamel.com/6a-frequencies-of-compounding/): The post includes The various types of frequencies of compounding . Starting by semi-annual, followed by quarterly, monthly, and daily. - [18a-Old Cb Coefficient of bending for steel beams](https://magedkamel.com/18a-old-cb-coefficient-of-bending-for-steel-beams/): Old Cb Coefficient of bending for steel beams. A review of the old cb coefficient with solved problems. - [6- Easy approach to compounding technique.](https://magedkamel.com/6-compounding-technique/): Approach to compounding technique. How to convert a simple interest to a compound interest? A given example is included with a given interest rate. - [18-Cb-The coefficient of bending part 2 for steel beams.](https://magedkamel.com/18-cb-the-coefficient-of-bending-part-2/): The post includes the CB the coefficient of bending for beams and how to get the value of CB for a simply supported beam under two concentrated loads? - [1- Easy introduction to the Inverse of a Matrix-2x2 matrix.](https://magedkamel.com/1-introduction-to-inverse-of-a-matrix/): How to get the inverse of a matrix by creating an identity matrix. A solved example is given for the inverse of a 2x2 matrix. - [3- Matrix Operations-Part-1: A Simple Guide to Basics.](https://magedkamel.com/3-matrix-operations-part-1/): The post includes matrix operations-part-1, Definition of the scalar matrix, and addition &subtraction, and multiplication of matrices. - [7-Moment of inertia for right-angle-Ix-Case-1.](https://magedkamel.com/7-inertia-for-right-angle-ix-for-case-1/): How to estimate the moment of inertia for right-angle-Ix - case No.1? two methods are used a horizontal strip and a vertical strip. - [2- Easy introduction to bearing type connections-part-1.](https://magedkamel.com/2-bearing-type-connections-part-1/): This is bearing Type connections-part-1. The points of discussion are about. What are the types of bearing connections and also include the types of failures? - [17- Introduction to Cb-Bending coefficient part-1 for steel](https://magedkamel.com/17-cb-bending-coefficient-1-3/): Introduction to cb-bending coefficient or moment gradient factor Cb for beams. Two examples for evaluation for CB were included with step by step. procedures. - [1- Easy introduction to bolted connections.](https://magedkamel.com/introduction-to-bolted-connections/): Introduction to bolted connections, the difference between low carbon steel and high tensile steel bolts, the different components of a bolt, categories of High- strength bolts, learn about snug-tight bolt - [6-Solved problems for the estimation of Moment of inertia.](https://magedkamel.com/6-solved-problems-for-moment-of-inertia/): Two solved problems for practice, the first solved problem is for the inertia of a given rectangular section, it is required to estimate Ix&Iy,kx, and Ky. - [9-Maximum deflection distance by Newton-Raphson method.](https://magedkamel.com/9-maximum-deflection-distance-numerically/): Maximum deflection distance for a simply supported beam under triangular load numerically. How to use the Newton-Raphson method for root findings? - [5-Step-by-step illustration of solved problems for P-F value](https://magedkamel.com/5-solved-problems-for-p-f-value/): The post includes solved problems for P-F Value. The first problem 3.5 includes h how to get F in terms of P,t, and i%? another problem is also included. - [16-Solved problem 4-7-Design using Table 3-10 when Lb>Lr](https://magedkamel.com/16-problem-4-7-design-using-table-3-10/): Solved problem 4-7, this a design problem for which lb>lr, the solution is made by using a design chart, table3-10, a discussion about the use of table 3-2, and why is table 3-10 is better in that case. - [8- Structural analysis numerically by Newton-Raphson method.](https://magedkamel.com/8-structural-analysis-numerically/): Perform structural analysis using the Newton-Raphson method for a beam under uniformly distributed load and get the maximum deflection point location. - [7A-Solved problem-8 by Modified Newton-Raphson method](https://magedkamel.com/7a-solved-problem-8-by-modified-newton/): A solved problem-8 by modified newton Raphson Method. A step-by-step guide comparison is made between the newton method and the modified Newton Raphson method. - [2- Types of Matrices: An Easy Introduction to Their Forms.](https://magedkamel.com/2-types-of-matrices/): The post includes different types of matrices, the scalar matrix, identity matrix, symmetric matrix , skew symmetric matrix, Unit matrix. - [15- Step-by-step How to design a beam using design chart?](https://magedkamel.com/15-design-a-beam-using-design-chart/): How to design a beam using design chart 3-10? For a given Mult & bracing length,cb=1, a steel beam can be designed by design chart 3-10. - [5- Easy approach for Product of inertia Ixy for a rectangle](https://magedkamel.com/5-product-of-inertia-ixy-for-rectangular/): The Product of inertia Ixy for a rectangle Two alternative methods to estimate.The first method is by dividing the rectangle into 4 sections of equal area. - [14- Find the Flexture Strength: Analysis Problem 9-7-lb>lr.](https://magedkamel.com/14-find-the-flexture-strength/): Find the flexure strength-solved problem 9- 7-Lb is bigger than Lr. A step-by-step guide to detrmine the flexture strength Fcr and Mrx. - [7- An Easy Guide to Modified Newton-Raphson method.](https://magedkamel.com/7-modified-newton-raphson-method/): The Modified Newton-Raphson method is another method for root finding. A simple modification to the previous method of Newton -Raphson was introduced. - [6a- Two Solved problems for Newton-Raphson method.](https://magedkamel.com/6a-solved-problems-for-newton-raphson/): Two solved problems for Newton-Raphson method for root extraction or roots finding are presented in this post. - [6- Newton-Raphson method-Easy approach](https://magedkamel.com/6-newton-raphson-method/): Newton-Raphson method. is another method for roots finding. The derivation of this method is based on the linear approximation method. - [13-Solved problem 4-6-how to find the available flexure strength?](https://magedkamel.com/13-solved-problem-4-6-for-flexure-analysis/): Solved problem 4-6- how to get the available flexure strength for a beam? this is an analysis problem, bracings distances are >Lp but less than Lr. - [12- Easy introduction to plastic bracing length Lp, Lr, Fcr.](https://magedkamel.com/12-review-of-the-information-of-lp-lr-fcr/): Review of the information of Lp, Lr, Fcr, what are the relating equation for each item? a practice example is given for illustration of the subject. - [4-Moment of inertia Iy for the rectangular section](https://magedkamel.com/4-inertia-iy-for-the-rectangular-section/): How to estimate the Moment of inertia Iy for the rectangular section about axis y? What will be the Iyg value at the Cg? - [11-Solved problem 4-5-Design a steel beam-(lb less than lp)](https://magedkamel.com/11-solved-problem-4-5-how-to-design-beam/): Download the worked solution for Problem 4‑5: Design a steel beam with lb < lp. Includes assumptions, AISC checks, limit states, and final sizing in a detailed PDF. - [3- Easy introduction to Ix for the rectangular section](https://magedkamel.com/3-inertia-ix-for-the-rectangular-section/): How to estimate the Moment of inertia Ix for the rectangular section using a horizontal strip about axis x? What will be the Ixg value and radii of gyration? - [5A-Practice problems with linear approximation](https://magedkamel.com/practice-problems-with-linear-approximation/): In this post, there are practice problems with linear approximation. these pr practice problems are using step-by-step illustration. - [10a-Regions for Lateral-torsional buckling for beams -2/2.](https://magedkamel.com/regions-for-lateral-torsional-buckling/): We have three Regions for Lateral-torsional buckling for beams. A new item is discussed which is moment gradient cb. - [10-Step by step guide to Lateral-torsional buckling.](https://magedkamel.com/10-lateral-torsional-buckling-for-beams/): Lateral-torsional buckling is the overall instability of a beam, includes twisting of the member and lateral buckling of the compression flange. - [2-Parallel axes theorem for Iy, polar moment of inertia.](https://magedkamel.com/2-parallel-axes-theorem-iy-polar-of-inertia/): Introduction to the parallel axes theorem for Iy and polar moment of inertia. and how to get the values of radius of gyrations kx and Ky. - [9A-Solved problem-7-4-1-part 2.](https://magedkamel.com/9a-solved-problem-7-4-1-part-2/): Solved problem-7-4-1-part 2. In this part we will deign a Wsection for a steel beam with span of 20 feet based on steel A572. - [5- What is the Linear Approximation method?](https://magedkamel.com/5-linear-approximation-method/): Introduction to linear approximation, what is a linear approximation equation? - [9-How to design a steel beam? Solved problem-7-4-1.](https://magedkamel.com/9-problem-7-4-1-design-a-steel-beam/): How to design a steel beam?-Solved problem-4-7-1. two cases for the design of a steel beam, first case for Fy=36 ksi and the second is for Fy=50 ksi. - [8- How to make an analysis of steel beams? Solved problems.](https://magedkamel.com/8-how-to-make-an-analysis-of-steel-beams/): How to make an analysis of steel beam of ? The first problem for analysis of a given beam W16x31, the second problem for checking section compactness. - [4-Easy introduction to Mohr's Circle of inertia part-1.](https://magedkamel.com/4-mohrs-circle-of-inertia-part-1/): This is an introduction to Mohr's circle of inertia. This is the case of ix is bigger than Iy. How to locate point D of(ix',Ix'y'? - [5-How to find the area and Cg for a circular segment?](https://magedkamel.com/5-area-and-cg-for-a-circular-segment/): How do you determine the area and Cg for a circular segment? We will deduct the area of two triangles from the area of the circular sector. - [4-How to find the area and Cg for a circular sector?](https://magedkamel.com/4-area-and-cg-for-a-circular-sector/): How do you determine the area and Cg for a circular sector? Use the integration of small area dA to get the value of the area and the Cg distance. - [3-How to find the area and Cg for a semi-circle?](https://magedkamel.com/3-area-and-cg-for-a-semi-circle/): How do you determine the area and Cg for a semi-circle? Use the integration of small area dA to get the value of the area and the Cg distance. - [2- How to find the area and Cg for a circular shaft?](https://magedkamel.com/2-how-to-find-the-area-and-cg-for-a-circular-shaft/): How to determine the area and Cg for a circular shaft? Use the integration of small area dA to get the value of the area and the Cg distance. - [22- Easy illustration of Iy for the Trapezium.](https://magedkamel.com/22-inertia-iy-for-the-trapezium/): Moment of inertia Iy for the Trapezium, How to get the Iy value for the trapezium? and how to get the polar of inertia? - [7- Easy introduction to row echelon form.](https://magedkamel.com/7-row-echelon-form/): Introduction to row echelon form and reduced row echelon form and their components. what is gauss- Jordan's elimination? - [1- How to find the area and Cg for a circle?](https://magedkamel.com/1-area-and-cg-for-a-circle/): How to determine the area and Cg for a circle? Use the integration of small area dA to get the value of the area and the Cg distance. - [14- A solved problem-inertia value for a given direction.](https://magedkamel.com/14-solved-problem-inertia-value/): A solved problem-inertia value for a given direction. how to get Ix', Iy'and Ix'y' about new axes that have 30 degrees rotation clockwise. two methods are used/ - [13- A solved problem for Mohr's circle of inertia case 4.](https://magedkamel.com/13-solved-problem-for-mohrs-circle-of-inertia/): A solved problem for Mohr’s circle of inertia case 4. This post will introduce a solved problem for Mohr’s circle of inertia case 4. The moment of inertia about the X-axis, Ix, is less than the moment of inertia about the Y-axis, Iy, and the product of inertia, Ixy, is negative. The given solved problem is for the unequal angle of dimension 3 inches by 2 inches, and the thickness of the steel angle is (1/4) inch. It is required to determine the principal moment of inertia. We will use Mohr’s circle of inertia to get the directions of the principal ... Read more - [12- Easy Approach to Mohr's circle of inertia-fourth case.](https://magedkamel.com/12-mohr-circle-of-inertia-fourth-case/): The post includes Mohr's circle of inertia-fourth case. How to find the principal two axes' orientation and the maximum and minimum values of inertia? - [11- A Solved problem-case-3-Mohr's circle of inertia.](https://magedkamel.com/11-solved-problem-case-3/): The post includes Solved problem-case-3-Mohr's circle of inertia. Ix is bigger than Iy and the product of inertia has a negative value. - [10A-Mohr's circle of inertia-third case-part 2](https://magedkamel.com/10a-mohrs-circle-of-inertia-third-case-part-2/): The post includes Mohr's circle of inertia-third case-part 2. The steps used to draw Mohr's circle of inertia-third case, find principal axes and their directions. - [10- Easy Approach to Mohr's circle of inertia-third case.](https://magedkamel.com/10-mohrs-circle-of-inertia-third-case/): The post includes Mohr's circle of inertia-third case. How do we find the principal two axes' orientation and the maximum and minimum values of inertia? - [9- A Solved problem-case-2-Mohr's circle of inertia.](https://magedkamel.com/9-solved-problem-case-2/): The post includes Solved problem-case-2-Mohr's circle of inertia. Ix is less than Iy and the product of inertia has a positive value. - [8- Easy Approach to Mohr's circle of inertia-second case](https://magedkamel.com/8-mohr-circle-of-inertia-second-case/): The post includes Mohr's circle of inertia-second case. How to find the principal two axes' orientation and the maximum and minimum values of inertia? - [7- A Solved problem-case-1-Mohr's circle of inertia.](https://magedkamel.com/7-solved-problem-case-1/): The post includes Solved problem-case-1-Mohr's circle of inertia. A solved problem is for a right-angle where the height is bigger than the base. - [6- Easy Approach to Mohr's circle of inertia-First case.](https://magedkamel.com/6-mohr-circle-of-inertia-first-case/): The post includes Mohr's circle of inertia-first case. How to find the principal two axes' orientation and the maximum and minimum values of inertia? - [6- Introduction to types of linear systems-Two variables.](https://magedkamel.com/types-of-linear-systems/): Introduction to types of linear systems-Two variables. what are the row operations? solved problems are included. - [13-Solved problems, Deposit value for uniform series.](https://magedkamel.com/deposit-value-for-uniform-series/): Two solved problems, How to find deposit value for uniform series? detailed illustrations for the solved problems are given. - [12-Solved problem-Future value for uniform series deposits.](https://magedkamel.com/future-value-for-uniform-series-deposits/): A solved problem, How to find Future value for uniform series deposits? three different methods are used, Cash flow moments, interest table, Excel function. - [11a- Derive the P and F relation as cash flow moment.](https://magedkamel.com/p-and-f-relation-as-cash-flow-moment/): In this post, we will derive Derive the P and F relation as cash flow moment. Two Solved problems are given to illustrate the idea. - [11- What is the similarity between cash flows and forces?](https://magedkamel.com/similarity-between-cash-flows-and-forces/): A step-by-step guide to illustrating the similarity between cash flows and forces How to find positive or negative moments? - [5- Step by step guide to Transpose of a Matrix-definitions](https://magedkamel.com/5-transpose-of-a-matrix/): A step by step guide to the transpose of a matrix. A discussion of properties with solved problems included. - [4a- Solved problem for matrix operations.](https://magedkamel.com/4a-solved-problem-for-matrix-operations/): A discussion of the three properties Commutative, associative and distributive properties. The post also includes a solved problem for matrix operations. - [7A- Solved problem 12-1-part 2-Find connection nominal load.](https://magedkamel.com/7a-solved-problem-12-1-part-2/): solved problem 12-1-part 2. How to use Table 7-4 to calculate the bearing nominal load? What will be the final factored nominal load? - [2d-Solved problems for Newton-divided differences.](https://magedkamel.com/2d-solved-problems-for-newton-divided-differences/): Two Solved problems for Newton-divided differences are given for more information about the method. - [2c- What is Newton-divided difference interpolation?](https://magedkamel.com/2c-newton-divided-difference-interpolation/): Learn about deriving the expression of Newton-Divided difference interpolation function and how to derive the expression. - [5-A solved problem for Load combination.](https://magedkamel.com/5-a-solved-problem-for-load-combination/): We have a solved problem for load combination. In which Dead load& floor live load & roof live load and snow load are given, Find the nominal strength. - [4- Easy introduction to structural loads-LRFD and ASD.](https://magedkamel.com/4-introduction-to-structural-loads/): A discussion of the various types of structural loads is introduced. An introduction to LRFD and ASD design is given. - [3-Structural steel sections-an easy approach.](https://magedkamel.com/3-structural-steel-sections-an-easy-approach/): The post includes a discussion about the structural steel sections, the symbols used for each section, and the main differences in-between. - [2- Easy approach to Stress strain relationship.](https://magedkamel.com/2-stress-strain-relationship/): This post includes a discussion of the stress strain relationship in structural steel. A full illustration steel grades for structural steel including graphs. - [5- Easy introduction to Mohr's Circle of inertia part-2.](https://magedkamel.com/5-mohrs-circle-of-inertia-part-2/): The post includes Mohr's circle of inertia part-2. the post shows how to derive the expression for the values of Iy' and Ix'y'. - [List of compression Member Posts-part 3.](https://magedkamel.com/list-of-compression-member-posts-part-3/): This is the list of compression Member Posts-part 3, with their relevant links with summary information. - [List of Steel beam posts-part-2.](https://magedkamel.com/list-of-steel-beam-posts-part-2-2/): List of Steel beam Posts-part-2 for all the different items for the structural steel beams included and solved problems. - [List of compression Member Posts-part 2.](https://magedkamel.com/list-of-compression-member-posts-part-2/): This is the compression member posts-part 2. A detailed description of each post is included their relevant links are included - [14-Solved problem 5-7 for block shear.](https://magedkamel.com/14-a-solved-problem-5-7-for-block-shear/): A Solved problem 5-7 for block shear for which several modes of failures are inspected and the final block shear strength will give the least value. - [13-The relation between Block shear and coped beams.](https://magedkamel.com/13-block-shear-and-coped-beams/): Introduction to block shear and coped beams, why do we need to use coped beams? what are the different names for the cut in a coped beam, the cases for UBS? - [12a-Solved problem 4-6-block shear for a C-Channel-2/2.](https://magedkamel.com/12a-block-shear-for-a-c-channel-2-2/): Block shear for a C-Channel-2/2. In the post, we continue to estimate the gross areas for shear and finally get the ultimate load. - [12-Solved problem 4-6-block shear for a C-Channel-1/2.](https://magedkamel.com/12-solved-problem-4-6-p-ult-with-block-shear/): A Solved problem 4-6-P-ult with block shear. It is required to check the adequacy of a given C channel bolted to a plate against a given ultimate load. - [11-A Solved problem 4-4, Pult without block shear.](https://magedkamel.com/11-solved-problem-4-4-without-block-shear/): Solved problem 4-4, how to check the adequacy of a channel connected to a gusset plate under a given Ultimate tension load? first case neglecting block shear. - [2b- Solved problems for quadratic interpolation](https://magedkamel.com/2b-solved-problems-for-quadratic-interpolation/): Solved problems for quadratic interpolation. In both two solved problems three points, are given and used to get the quadratic interpolation function. - [8-Complements of a set, Cumulative, associative of sets.](https://magedkamel.com/8-complement-of-a-set/): The complement of a set, cumulative, associative distributive properties of sets, What are the ordered pairs? solved examples are included. - [10-Depreciation, useful life, Per annum, book value.](https://magedkamel.com/10-depreciation-book-value/): In this post, we continue discussing additional terms, Depreciation, and salvage value. what are the book value and per annum use? - [10- Quickstart to the introduction to block shear resistance.](https://magedkamel.com/10-introduction-to-block-shear/): Introduction to block shear and how to derive the expression? What is the recommended L/r slenderness ration? - [37a- Solved problem-8-34 for a nominal uniform load.](https://magedkamel.com/37a-solved-problem-8-34/): Solved problem-8-34, how to determine the plastic Nominal uniform load acting on a continuous steel beam? with different loading& span conditions. - [2a- Easy introduction to quadratic interpolation.](https://magedkamel.com/2a-quadratic-interpolation/): Quadratic interpolation, how to derive the expression of it? The Vandermonde matrix and how to get its inverse value and determinant value? - [7-Universal set Subsets of sets.](https://magedkamel.com/7-subsets-of-sets-universal-set/): What are the subsets of sets and the universal set?solved problems are given for these items. - [9- Easy approach to Area and Cg for a Parallelogram.](https://magedkamel.com/9-area-and-cg-for-a-parallelogram/): The post includes the steps needed to get the area and Cg for a Parallelogram. This is done by getting the first moments of areas about two external axes. - [List of Tension Member's Posts-part 2.](https://magedkamel.com/tension-members-posts-part-2/): In this post there is a list of Tension Member's Posts-part 2, the list starts from post 7 till post 9d. For shear lag factor and several practice problems. - [9b- Easy approach to Assets for Economy-part 3.](https://magedkamel.com/9b-assets-for-economy/): The different types of assets for economy-part-3. Definition of supplies, inventory, and rent accounting. - [1- Easy introduction to the definition of Interpolation.](https://magedkamel.com/1-what-is-linear-interpolation/): An introduction to interpolation and linear interpolation, what are polynomials, and how can be used as a tool to make a linear interpolation? - [8- Easy illustration for Area and Cg of a Trapezium](https://magedkamel.com/8-area-and-cg-of-a-trapezium/): The post includes the steps needed to get the area and CG of a Trapezium. This is done by getting the first moments of areas about two external axes. - [9d- Effective area for a staggered bolted angle.](https://magedkamel.com/9d-effective-area-for-a-staggered-bolted-angle/): Two solved problems, the first problem includes how to get an Effective area for a staggered bolted angle. Second includes how to find service load capacity . - [6- Easy approach what is Roster notation for sets?](https://magedkamel.com/6-what-is-roster-notation-for-sets/): Introduction to Roster notation. the symbols that are used with given solved examples. - [9c- Practice problem-longitudinal weld of a c section](https://magedkamel.com/9c-longitudinal-weld-of-a-c-section/): Practice problem-longitudinal weld of a C section. It is required to estimate the LRFD and ASD value for a given plate section. - [7- Easy approach to find Area and Cg for a rectangle](https://magedkamel.com/7-area-and-cg-for-a-rectangle/): How to determine the area and Cg for a rectangle? The rectangle area and GC values are obtained by integration of infinitesimal area about external axes. - [37-Solved problem 8-33 for Plastic nominal Uniform Load.](https://magedkamel.com/37-solved-problem-8-33/): Solved problem 8-33, how to determine the plastic Nominal uniform load acting on continuous steel beam? with different loading& span conditions. - [27-Solved problem 4-14-effective length factor-Part 1.](https://magedkamel.com/27-solved-problem-4-14/): Solved problem 4-14-effective length factor-Part 1. Determine the effective length factor with respect to x-axis for member AB. - [9b- Practice problem-longitudinal weld of a plate section](https://magedkamel.com/9b-longitudinal-weld-of-a-plate-section/): Practice problem-longitudinal weld of a plate section. It is required to estimate the LRFD and ASD value for a given plate section. - [21- How to find Moment of Inertia Iy for Parallelogram?](https://magedkamel.com/21-moment-of-inertia-iy-for-parallelogram/): How to find Moment of Inertia Iy for Parallelogram? A step-by-step guide to finding the inertia at the Cg and the radius of gyration. - [5- 3 Solved Quizzes for rounding numbers-easy approach.](https://magedkamel.com/5-solved-quizzes/): Three solved quizzes for a round of numbers. The post cover rounding for hundredth, decimal points and for significant figures. - [36a-Plastic Nominal Uniform load for partially loaded beam](https://magedkamel.com/36a-plastic-nominal-uniform-load/): Plastic Nominal Uniform load for partially loaded beam. The load occupies half of the span from the left.two methods are used,Lower and upper bound methods. - [9A- Practice problem-transverse weld of a WT section](https://magedkamel.com/9a-transverse-weld-of-a-wt-section/): Practice problem-transverse weld of a WT section. It is required to estimate the LRFD and ASD value for a given welded WT section. - [36-Solved problem 8-32 for plastic nominal Uniform load.](https://magedkamel.com/36-solved-problem-for-nominal-uniform-load/): Solved problem 8-32, how to determine the plastic Nominal uniform load? The uniform load is partial, two methods are user, the lower and upper bounds. - [9-Two Solved problems for an estimate of effective net area.](https://magedkamel.com/9-2-solved-problems-for-net-area/): Two solved problems for a single angle connected to a gusset plate, first by bolts and second problem by welds. How to determine the effective net area? - [35A-Solved problem 8-22-for Plastic nominal load( 2/2).](https://magedkamel.com/35a-solved-problem-8-22/): Solved problem 8-22 second part, we will verify the nominal load for the fixed end beam by MASTAN2 and verify the loads for first and second plastic hinges. - [35-Solved problem 8-22-for Plastic nominal load( 1/2).](https://magedkamel.com/35-solved-problem-for-plastic-nominal-load/): Solved problem 8-22, find the plastic Nominal load acting on two Fixed ends beam? Use lower and upper bounds. Find the loads for first and second plastic hinges. - [9a- Easy approach to types of assets-part-2.](https://magedkamel.com/9a-types-of-assets-part-2/): The different types of assets-part-2. like Accounts receivable, notes receivable Marketable securities. Definition of materials. - [6- Easy steps to find the area and Cg of a Triangle.](https://magedkamel.com/6-area-and-cg-of-a-triangle/): How to determine the area and Cg of a triangle? Divide Triangle into two right-angle triangles and use to find get X bar and y bar for the triangle. - [26-Solved problem 4-13 to estimate stiffness reduction τb.](https://magedkamel.com/26-problem-4-13-stiffness-reduction/): A solved problem 4-13 from Prof. Segui's book. we are going to estimate the reduction stress factor τb, for a column that is an inelastic column. - [20-How to get a moment of Inertia Ix for Parallelogram?](https://magedkamel.com/20-inertia-ix-for-parallelogram/): How to get a moment of Inertia Ix for Parallelogram? A step-by-step guide to find the inertia and the radius of gyration about the x-axis. - [8- Solved problem 4-2 for shear Lag factor U.](https://magedkamel.com/8-a-solved-problem-4-2-for-shear-lag/): Solved problem 4-2 for shear lag factor U, for a welded angle to a gusset plate, Weld details, and section of angle is given. - [5-Y bar for a right angle case-2](https://magedkamel.com/5-y-bar-for-a-right-angle-case-2/): How to estimate y bar for a right angle case-2 by using a horizontal and a vertical strip? the process includes area estimation. - [25a-Stiffness reduction factor for inelastic columns-part 2.](https://magedkamel.com/25a-reduction-factor-for-inelastic-columns/): In this post we will discuss the Stiffness Stiffness reduction factor for inelastic columns-part 2. and how to get the expression for τb the inelastic column. - [19- Discovering Ix for the Trapezium: A Step-by-Step Guide.](https://magedkamel.com/19-ix-for-the-trapezium/): Moment of inertia Ix for the Trapezium, step by step procedure to get the Ix value for the trapezium by dividing it into two triangles and one rectangle. - [4- How to round numbers to Decimal points? perfect guide](https://magedkamel.com/how-to-round-numbers/): How to round numbers, what are the different types of rounding? rounding decimals, round to significant figures, round to nearest whole numbers. - [9- Easy introduction to the different types of Assets.](https://magedkamel.com/9-types-of-assets/): The different types of assets, the difference, and current assets. Other items were included like depreciation, useful life, Salvage value, per annum. - [7- A solved problem 12-1 for bearing connections.](https://magedkamel.com/7-solved-problem-12-1-for-bearing-connections/): Solved problem 12-1. it is required to estimate the design strength of a bearing type connection. All the values of nominal loads due to failure modes are estimated. - [7- Solved problem for design strength of tension member.](https://magedkamel.com/7-solved-problem-for-design-strength/): A solved problem 3-6 for determining the LRFD and ASD tensile design strength for W section, the shear lag is discussed through the solved problem 3-6. - [25-Stiffness reduction factor for inelastic columns.](https://magedkamel.com/25-stiffness-reduction-factor/): Stiffness Reduction Factor for inelastic columns, step-by-step explanation, and introduction to the Tangent modulus of elasticity. - [34- Easy approach to the Plastic moment for continuous beam](https://magedkamel.com/34-plastic-moment-for-continuous-beams/): How to estimate the plastic moment for Continuous beam of three equal spans? The first method is by using the Lower bound theorem. - [8c-Arithmetic Gradient-part 2 in the Economy.](https://magedkamel.com/8c-arithmetic-gradient-part-2/): In the post, arithmetic gradient-part 2, there is a solved problem 4-8 where it is required to find in terms of I%,n, G. - [33a- Location of plastic hinges and effect on lambda value](https://magedkamel.com/33a-location-of-plastic-hinges/): Location of plastic hinges and effect on lambda value. we will select different plastic hinge locations and determine lambda value. - [6a-Solved problem 10-1-how to get Bearing value-ASD?3-3.](https://magedkamel.com/6a-bearing-value-asd/): The post includes the second part of the solved problem 10-1. It is required to estimate bearing value-ASD for a given connection. - [8b-A solved problem for EAW/ Equivalent Annual Worth.](https://magedkamel.com/8b-a-solved-problem-for-eaw/): In this post, we will introduce a definition of EAB-EAC-EAW. A solved problem for EAW or the Equivalent Annual Worth. - [18-Product of inertia Ixy for an isosceles triangle.](https://magedkamel.com/18-product-of-inertia-ixy-for-an-isosceles-2/): The estimation of the product of inertia Ixy for an isosceles triangle. The Product of inertia Ixy for an isosceles at the CG is estimated. - [8A-What is Capital Recovery in the Economy?](https://magedkamel.com/8a-what-is-capital-recovery/): In this post, we discuss a new term which is Capital recovery, and the different terms for Capital recovery, the related general equation. - [33- Easy introduction to upper bound and Lower bounds.](https://magedkamel.com/33-upper-bound-definition/): Definitions of the upper bound, lower bound, and the Uniqueness theorem, what are the main differences between all of these theorems? - [4- Easy steps for X bar for a right angle case-2.](https://magedkamel.com/4-x-bar-for-a-right-angle-case-2/): How to estimate x bar for a right angle case-2 by using a horizontal and a vertical strip? Detailed steps are included in the post. - [24-Solved problem 7-2-frame K value 3/3.](https://magedkamel.com/solved-problem-7-2-frame-k-value-3-3/): Solved problem 7-2-frame K value 3/3. For K Factor, for the braced frame with different end conditions. Application of French equation to geet k values. - [8- Easy Illustration of the Arithmetic Gradient.](https://magedkamel.com/8-arithmetic-gradient/): Introduction to the arithmetic gradient, how we can develop an expression for the arithmetic gradient, and the various terms used. - [6-Definition of the effective area for tension members.](https://magedkamel.com/6-definition-of-the-effective-area/): Definition of the effective area for tension members, and why we use it for estimation of the net area? what is shear lag and how we estimate the factor U? - [3- Definition of absolute value, rational numbers, fraction.](https://magedkamel.com/3-absolute-value-rational/): Definition of the absolute value of a number.what is fraction? factoring against product and irrational number. - [3a- Y bar for a right angle-case-1-using vertical strip.](https://magedkamel.com/3a-y-bar-for-a-right-angle-case-1/): How to estimate Y bar for a right angle-case-1-using vertical strip? using the integration to get area and Cg distance. - [17-Moment of inertia for an isosceles triangle-Ix,Iy.](https://magedkamel.com/17-moment-of-inertia-for-an-isosceles-ix-iy/): A guide to estimating the moment of inertia for an isosceles triangle-Ix, Iy. An isosceles triangle is a special case of a triangle. - [7a- Uniform series of compound interest-2/2 in the Economy.](https://magedkamel.com/7a-compound-interest-2-2/): A discussion of uniform series of compound interest-2/2 in economy is presented through two solved examples. - [32- Easy illustration for collapse load for indeterminate beam.](https://magedkamel.com/32-collapse-load-for-indeterminate-beam/): Collapse load for indeterminate beam by using of two methods, the first method is a statical method and the second method is a kinetic method. - [23a-Solved problem 7-2 for k value for frame 2/3.](https://magedkamel.com/solved-problem-7-2-for-k-value-for-frame-2-2/): Solved problem 7-2 for k value for frame 2/3. This post is the second part, how to find K value for a frame with different bracing conditions? - [16-Simple approach to Polar Moment of Inertia J for the triangle](https://magedkamel.com/16-polar-moment-of-inertia-j-for-the-triangle/): The polar moment of inertia j for a triangle. Two methods are used to get the polar moment of inertia for a triangle and the CG polar moment of inertia. - [23-Solved problem 7-2 for k value for columns in frame 1/3](https://magedkamel.com/23-solved-problem-7-2-for-k-value/): Solved problem 7-2 for k value for columns in frame 1/3 -the frame has two parts, braced and unbraced. This post is the first part. - [List of Tension Member's Posts-part 3.](https://magedkamel.com/tension-members-posts-part-3/): In this post there is a list of Tension Member's Posts-part 3. The list includes posts from post 10 till post 16. - [19-Solutions for Block Shear-Coped Beam Problem](https://magedkamel.com/19-block-shear-coped-beam-problems/): The post includes A solved problem for block shear-coped beam. The solved problem includes full data for both LRFD and ASD when Ubs equals 1. - [42s-Nominal shear strength for M10x7.50.](https://magedkamel.com/42s-nominal-shear-strength-for-m10x7-50/): Find the Nominal shear strength for M10x7.50. The estimation is based on CM#15 and specification 2016. An excel plot is included between h/tw and Vn. - [41-Practice problem 5-6-1-What is the available strength for W12x65?](https://magedkamel.com/what-is-the-available-strength-for-w12x65/): Practice problem 5-6-1-What is the Available strength for W12x65? The post explains how to deal with non-compact W section and get the available strength value. - [14a-Problem-6-8 for local buckling-CM#15 For HSS section](https://magedkamel.com/14a-problem-6-8-local-buckling-hss-section/): Problem-6-8 for local buckling-CM#15 For HSS section.The HSS section is a slender column, determine the available strength. - [16b-Available Strength for slender W section-CM#15.](https://magedkamel.com/16b-available-strength-for-slender-w-section/): Available Strength for slender W section-bsdrf on CM#15. A step by step guide to find the factored strength. - [41s-Nominal shear strength for S41x121.](https://magedkamel.com/41s-nominal-shear-strength-for-s41x121/): Find the Nominal shear strength for S41x121. The estimation is based on Cm#14 and specification 2010. An excel plot is included between h/tw and Vn. - [List of Steel Beam posts-part-2a](https://magedkamel.com/list-of-steel-beam-posts-part-2a/): List of Steel beam Posts-part-2a for subject of Cb or the gradient coefficient for steel beams. - [Easy approach to Structural steel design.](https://magedkamel.com/easy-approach-structural-steel-design/): Discover an easy approach to structural steel design, essential topics in tension, compression, beams, and connections for steel items. - [40- Easy Design of steel section for continuous beam-4-4](https://magedkamel.com/40-steel-section-for-continuous-beam-4-4/): The steel section for continuous beam is based on the maximum value of the moments according to the 0.90 rule. The design is made according to the ASD. - [39-Solved problem 10-1-use three-moment equations 3/4](https://magedkamel.com/39-three-moment-equations-3-4/): The three-moment equations for steel continuous beams to estimate the moment values at the different support joints A, B, C, D . - [38a-Solved problem 10-1-design of steel continuous beam-2-4.](https://magedkamel.com/38a-design-of-steel-continuous-beam-2-4/): Design of steel continuous beam-2-4 using Plastic theory, the upper bound theorem is used to get the required w -section for a continuous beam. - [20-AISC Tables 9-3a,b, and C for Block shear-coped beam.](https://magedkamel.com/20-use-of-aisc-tables-9-3a-b-and-c/): AISC Tables 9-3a,b, and C for the block shear-coped beam. Table 9-3a is for Tensile rupture. Table 9-3b is for Shear yielding and 9-3c is for Shear rupture. - [38- Solved problem-10-1-design of steel continuous beam-1-4.](https://magedkamel.com/38-solved-problem-10-1-design-of-beam/): solved problem-10-1 using Plastic theory, the upper bound theorem is used to get the required w -section for a continuous beam. - [10-Two solved problems for 3x3 matrix by Crout's LU-option 1.](https://magedkamel.com/10-solved-problems-for-3x3-matrix/): Two solved problems for 3x3 matrix by Crout's LU decomposition. Option 1 is used for which the matrix is converted to a lower matrix. - [9A- A Second option for Crout's LU decomposition-3x3 matrix](https://magedkamel.com/9a-second-option-for-crouts-lu-decomposition/): A Second option for Crout's LU decomposition-3x3 matrix. How to covert the A matrix to an upper matrix? How to get the values of L and U matrices? - [9d-Practice problem 5-5-8-Compute Mn.](https://magedkamel.com/9d-practice-problem-5-5-8/): Practice problem 5-5-8 A W18 x 71 is used as a beam with an unbraced length of 9 feet. Use Fy=65 ksi and Cb = 1 and compute the nominal flexural strength. - [9c-Practice problem 5-5-6-Compute Lp and Lr and φb*Mn.](https://magedkamel.com/9c-practice-problem-5-5-6/): Practice problem 5-5-6 A W12 x 30 of A992 steel has an unbraced length of 10 feet. Using Cb = 1.0, a. Compute Lp and Lr. Find φb*Mn and Mn/Ωb for lb=10 feet. - [9b-Practice problem 5-4-1-Check compactness for Fy=60 ksi.](https://magedkamel.com/9b-practice-problem-5-4-1/): Practice problem 5-4-1-Check compactness when the yield stress Fy=60 ksi. for W,M and S shapes - [6d-Practice problem 6-17-11-Find Sx and ZX for WT5x22.50](https://magedkamel.com/6d-practice-problem-6-17-11/): Practice problem 6-17-11-find Sx and ZX for WT5x22.50. It is required to model WT5x22.5 into two rectangles and find elastic and plastic section modului. - [6c-Practice problem 6-17-5-find Sx and ZX for W18x35.](https://magedkamel.com/6c-practice-problem-6-17-5/): Practice problem 6-17-5-find Sx and ZX for W18x35. it is required to model W18x35 into three rectangles and find elastic and plastic section modului. - [27-Two Practice problems for Ixy for a trapezium.](https://magedkamel.com/27-two-practice-problems-for-ixy-for-a-trapezium/): The post includes 27-Two Practice problems for Ixy for a trapezium. The first problem is for Ixy about an external axis, while the second is for Ixy at the CG. - [26-Two Practice problems for polar of inertia for trapezium.](https://magedkamel.com/26-two-practice-problems-for-polar-of-inertia/): Two Practice problems for polar of inertia for trapezium. The first problem is for Jo and Ko at an external axis, The second is for Jo and Ko at the CG. - [25-Two Practice problems for inertia for trapezium.](https://magedkamel.com/25-two-practice-problems-for-inertia/): We have two practice problems for inertia and radius of gyration for a given trapezium. A step-by-step guide to get Ix and kx. - [List of Steel Beam Posts-part-4a.](https://magedkamel.com/list-of-steel-beam-posts-part-4a/): Steel beam posts-part-4a. from steel beam post 38 to post 40. For all different subjects for the steel beams and solved problems. - [List of Steel Beam Posts-part-4.](https://magedkamel.com/list-of-steel-beam-posts-part-4/): Steel beam posts-part-4. from steel beam post 29 to post 37. How to use plastic theories to get the nominal loads? - [List of steel Beam Posts-part-3b.](https://magedkamel.com/list-of-steel-beam-posts-part-3b/): Steel beam posts-part-3b, posts are from 24 to post 28. The main subject is the deflection, there are solved problems for deflaction and design of built up beam. - [List of steel Beam Posts-part-3a.](https://magedkamel.com/list-of-steel-beam-posts-part-3a/): Steel beam posts-part-3a includes the posts from post 19 to post 21. Solved problems are included for Block shear for beams. - [List of Steel Beam Posts-part-3.](https://magedkamel.com/list-of-steel-beam-posts-part-3/): Steel beam posts-part-3 includes the posts from post 19S to post 23S. these posts include shear equations based on AISC and practice problems. - [5a-Part 2 of Practice problem-7-38](https://magedkamel.com/5a-part-2-of-practice-problem-7-38/): part 2 of Practice problem-7-38-Discontinuity Functions. Find expressions for W(x),V(x) and M(x).Draw shear and moment diagrams and use excel if then function. - [5-Part 1 of Practice problem-7-38 Discontinuity Functions](https://magedkamel.com/5-part-1-of-practice-problem-7-38/): part 1 of Practice problem-7-38-Discontinuity Functions. W(x),V(x) and M(x) for a beam are included. Shear values and moment values are estimated. - [4a-Part 2 of Practice problem-7-35 Discontinuity Functions](https://magedkamel.com/4a-part-2-of-practice-problem-7-35/): part 2 of Practice problem-7-35-Discontinuity Functions. How to draw shear and moment diagrams and use excel if then function? - [4-Part 1 of Practice problem-7-35 Discontinuity Functions](https://magedkamel.com/4-part-1-of-practice-problem-7-35/): part 1 of Practice problem-7-35-Discontinuity Functions. How to get the expressions for W(x),V(x) and M(x) for a beam? - [3a-Part 2 of Practice problem-7-32 Discontinuity Functions](https://magedkamel.com/3a-part-2-of-practice-problem-7-32/): part 2 of Practice problem-7-32-Discontinuity Functions. How to draw shear and moment diagrams and use excel if then function? - [3-Part 1 of Practice problem-7-32 Discontinuity Functions](https://magedkamel.com/3-part-1-of-practice-problem-7-32/): part 1 of Practice problem-7-32-Discontinuity Functions. How to get the expressions for W(x),V(x) and M(x) for a beam? - [2-Discontinuity Functions Table.](https://magedkamel.com/2-discontinuity-functions-table/): Discontinuity Functions table, how to use these tables to derive an expression for load, shear and moment functions? - [Video for practice problem P7-38-Use discontinuity Function.](https://magedkamel.com/video-for-practice-problem-p7-38/): A Video for practice problem P7-38-Use discontinuity Function.to develop expressions for load ,shear and moment functions and draw shear and moment diagrams. - [9- Crout's LU decomposition for a 3x3 matrix-Option 1](https://magedkamel.com/9-crouts-lu-decomposition-for-a-3x3-matrix/): How to drive Crout's LU decomposition for a 3x3 matrix-option-1? Step-by-step introduction to Crout's LU decomposition for a 3x3 matrix. - [Video for practice problem P7-35-Use discontinuity Function](https://magedkamel.com/video-for-practice-problem-p7-35/): A Video for practice problem P7-35-Use discontinuity Function.to develop expressions for load ,shear and moment functions and draw shear and moment diagrams. - [Video for practice problem P7-32-Use discontinuity Function](https://magedkamel.com/video-for-practice-problem-p7-32/): A Video for practice problem P7-32-Use discontinuity Function.to develop expressions for load ,shear and moment functions and draw shear and moment diagrams. - [Video for Discontinuity Functions Table for loads, shear.](https://magedkamel.com/video-for-discontinuity-functions-table/): A Video for Discontinuity functions table for loads, shear and moment expressions. How to derive the Discontinuity functions table?. - [23-Video for Ixy for an isosceles triangle.](https://magedkamel.com/video-for-ixy-for-an-isosceles-triangle/): Video for Ixy for an isosceles triangle. how to find Ixy value at the left corner and at the CG? - [22-Video for Ix and Iy for an isosceles triangle.](https://magedkamel.com/video-for-ix-and-iy-for-an-isosceles-triangle/): Video for Ix and Iy for an isosceles triangle at the left corner. What are the values of Ix and Iy at the Cg? - [21-Video for Ixy for a triangle.](https://magedkamel.com/video-for-ixy-for-a-triangle/): Video for Ixy for a triangle. How to determine the Ixy for a triangle on the left corner and discover the Ixy value at the CG? - [20-Video for Iy at the Cg for a triangle.](https://magedkamel.com/video-for-iy-at-the-cg-for-a-triangle/): Video for Iy at the Cg for a Triangle. Determine the Iy at the Cg for a triangle by deducting the product of the Area by the x bar^2 from Iy value. - [19-Video for Iy for a triangle.](https://magedkamel.com/video-for-iy-for-a-triangle/): Video for Iy for a Triangle. By adding the Iy values from case 1 and case 2 for right angles. How to find ix at the Cg? - [18-Video for Ix for a triangle.](https://magedkamel.com/video-for-ix-for-a-triangle/): Video for Ix for a Triangle. By adding the Ix values from case 1 and case 2 for right angles. How to find ix at the Cg? - [17-Video for Ixy at CG-right-angle case 2.](https://magedkamel.com/video-for-ixy-at-cg-right-angle-case-2/): Video for Ixy at CG-right-angle case 2. using the parallel axes theorem we can derive an expression for Ixy at the Cg. - [16-Video for a product of inertia-right-angle case 2.](https://magedkamel.com/video-for-a-product-of-inertia-right-angle-case-2/): Video for a product of inertia-right-angle case 2. two methods are used to find the product of inertia for right-angle case 2. - [15-Video-Iy and polar moment of inertia-right angle-case 2.](https://magedkamel.com/video-iy-and-polar-moment-of-inertia/): Video-Iy and polar moment of inertia-right angle-case 2. Detailed calculations to find the value of Iy at the Cg and also the polar moment of inertia. - [14-Video-Use a vl strip to get Iy for right-angle case-2.](https://magedkamel.com/video-use-a-vl-strip-to-get-iy/): Video-Use a vl strip to get Iy for right-angle case-2. Derive the value for iy for y-axis is at the left and for the Y axis at the right. - [13-Video-Use a vl strip to get Ix for right-angle case-2.](https://magedkamel.com/video-use-a-vl-strip-to-get-ix/): Video-Use a vl strip to get Ix for right-angle case-2. Derive the expression for Ix at the Cg and estimate the radius of gyration. - [12-Video for Ix for a right-angle case -2-Use Hl strip.](https://magedkamel.com/video-for-ix-for-a-right-angle/): Video for Ix for a right-angle triangle case 2. By Using a horizontal strip we can obtain ix at the left corner and Ix at the Cg. - [10-Video for Iy for a right-angle triangle case 1.](https://magedkamel.com/video-for-iy-for-a-right-angle-triangle-case-1/): Video for Iy for a right-angle triangle case 1. Derive the expression of Iy by using two alternative methods, a horizontal strip and a vertical strip. - [11-Video for Ixy for a right-angle triangle case 1.](https://magedkamel.com/video-for-ixy-for-a-right-angle-triangle/): Video for Ixy for a right-angle triangle case 1. How to estimate the product of inertia Ixy for a right-angle triangle case No.1 at the external axis and at the Cg? - [8-Introduction to Crout's LU decomposition for a 2x2 matrix.](https://magedkamel.com/8-crouts-lu-decomposition-for-a-2x2-matrix-2/): How to drive Crout's LU decomposition for a 2x2 matrix? Step-by-step introduction to Crout's LU decomposition with a solved problem. - [9-Video for Ix for a right-angle triangle case 1.](https://magedkamel.com/video-for-ix-for-a-right-angle-triangle-case-1/): Video for Ix for a right-angle triangle case 1. Derive the expression of Ix by using two alternative methods, a horizontal strip and a vertical strip. - [8-Video for practice problem-2 for the moment of inertia.](https://magedkamel.com/video-for-practice-problem-2/): A Video for practice problem-2 for the moment of inertia. It required to find the Ix and Ixy for L -shaped section. - [7-Video for practice problem-1 for the moment of inertia.](https://magedkamel.com/video-for-practice-problem-1/): A Video for practice problem-1 for the moment of inertia. it required to find the Ix and Kx, Iy and Ky. for a rectangle section. - [6-Video for Polar moment of inertia for a rectangle section](https://magedkamel.com/video-for-polar-moment-of-inertia-for-a-rectangle/): A Video for Polar moment of inertia for a rectangle section. A third method for product of inertia for a rectangle section is added. - [5-Video for Ixy for a rectangle section.](https://magedkamel.com/video-for-ixy-for-a-rectangle/): A Video for Ixy for a rectangle section. Two different methods are shown to get the value of Ixy at the Cg and at a left corner. - [4-Video for Iy for a rectangle section.](https://magedkamel.com/video-for-iy-for-a-rectangle-section/): A Video for Iy for a rectangle section. different methods are shown to get the value of Iy and The radius of Gyration. - [3-Video for Ix for a rectangle section.](https://magedkamel.com/video-for-ix-for-a-rectangle-section/): A Video for Ix for a rectangle section. different methods are shown to get the value of Ix and The radius of Gyration. - [2-Video for Parallel axes theory for the moment of inertia](https://magedkamel.com/video-for-parallel-axes-theory/): A Video for Parallel axes theory for the moment of inertia.Parallel axes theorem proof for Iy. and ixy are also included. - [1-Video for the introduction to the moment of inertia.](https://magedkamel.com/video-for-the-introduction-to-the-moment-of-inertia/): A Video for the introduction to the moment of inertia. How can we estimate the moment of inertia? What is the product of inertia? - [Video for the Introduction to Macaulay's function.](https://magedkamel.com/video-for-the-introduction-to-macaulays-function/): A Video for the introduction to Macaulay's function, that is a mathematical tool used to define a piecewise function. - [7-A Solved problem 9-5 LU decomposition.](https://magedkamel.com/7-solved-problem-9-5-lu-decomposition/): Solved problem 9-5 LU decomposition from reference book Numerical methods for engineers. We will verify our solution with the author's solution. - [9-Video for Mohr's circle of inertia case-3.](https://magedkamel.com/video-for-mohrs-circle-of-inertia-case-3/): Video for Mohr's circle of inertia case-3. Where Ix>Iy and the product of inertia Ixy is negative. How to draw Mohr's circle of inertia? - [8-Video for solved problem Mohr's circle-case-2-inertia](https://magedkamel.com/solved-problem-mohrs-circle-case-2-inertia/): Explore our 8-video tutorial for solved problem Mohr's circle-case-2-inertia, featuring a detailed guide on principal moments of inertia and angles. - [7-Video for Mohr's circle of inertia case-2.](https://magedkamel.com/video-for-mohrs-circle-of-inertia-case-2/): Video for Mohr's circle of inertia case-2. Where Ix - [6-Video of a solved problem-Mohr's circle of inertia case-1.](https://magedkamel.com/video-of-a-solved-problem/): Video of a solved problem for Mohr's circle of inertia case 1. A given triangle , use Mohr's circle of inertia for maximum and minimum moments of inertia . - [5-Video for Mohr's circle of inertia case-1.](https://magedkamel.com/video-for-mohrs-circle-of-inertia-case-1/): Video for Mohr's circle of inertia case-1. step by step guide to draw Mohr's circle of inertia and get Imax and Imin values and directions. - [4-An introduction video for Mohr's Circle of Inertia.](https://magedkamel.com/video-for-mohrs-circle-of-inertia/): The video is An introduction video for Mohr's Circle of Inertia. Mohr circle of inertia is a graphical tool used to estimate the maximum and minimum value of inertia. - [3-A Video for deriving expressions for min and max Inertia.](https://magedkamel.com/a-video-for-deriving-expressions/): This is A Video for deriving expressions for min and max Inertia. what are the directions of the major and minor principal axes? - [2-A Video about Pure bending expressions.](https://magedkamel.com/a-video-about-the-first-moment-of-area/): This is A Video about the First moment of area. In theory of pure bending the sum of the first moment of area equals zero. - [1-A Video about pure bending.](https://magedkamel.com/a-video-about-pure-bending/): This is A Video about pure bending. whar are the cases for pure bending and the relevant assumptions? - [6a- Easy approach to permutation matrix-Part 2](https://magedkamel.com/6a-permutation-matrix-part-2/): In the Permutation matrix-part 2, we continue the discussion about the various types of Permutation matrices. - [6- Easy introduction to permutation matrix](https://magedkamel.com/6-introduction-to-permutation-matrix/): The post includes an introduction to the permutation matrix for both 2x2 and 3x3 matrices. How to change the arrangement of rows and columns for matrices? - [5c- Solved problem for x-y-z values by LU decomposition.](https://magedkamel.com/5c-solved-problem-for-x-y-z/): The solved problem for x-y-z values by using the LU decomposition. for three simultaneous equations. Step by step illustration is explained. - [5b-Find the three unknowns for Second solved problem](https://magedkamel.com/5b-find-the-three-unknowns/): Find the three unknowns for the Second solved problem. Two method to be used to solve for x1, x2 and x3. - [1-Macaulay's function and singularity functions.](https://magedkamel.com/macaulays-function-and-singularity-function/): Macaulay's function and singularity functions are important concepts in mathematical analysis. Macaulay's function is a mathematical tool used to define a piecewise function. - [6b-Practice problem 5-2-3-verify Zx for W18x50](https://magedkamel.com/6b-practice-problem-5-2-3/): Practice problem 5-2-3-verify Zx for W18x50.We convert the W section into two Wt9x25 and get the required Zx value. - [6A-Practice problem 5-2-2 Find y bar, Zx, and Zy.](https://magedkamel.com/6a-practice-problem-5-2-2/): Practice problem 5-2-2. For an un-symmetric section find y bar, plastic moment about P.N.axis, the plastic moment and plastic section modulus about the minor axis. - [8A- Solved problem 5-part 2 for design shear strength.](https://magedkamel.com/8a-solved-problem-5-part-2-for-design/): Solved problem 5-part 2 for design shear strength. It is required to find the design shear strength for A 490-N and A 490-X bolts for different types of bolts. - [8- Solved problem 5-part 1 for design shear strength for bolts](https://magedkamel.com/8-solved-problem-5-part-1-for-design/): Solved problem 5-part 1 for design shear strength. It is required to find the design shear strength for different types of bolts with different diameters. - [21- Case 2 for block Shear-Coped Beam Problem.](https://magedkamel.com/21-case-2-for-block-shear-coped-beam/): Case 2 for block Shear-Coped Beam -UBS=1/2. A step-by-step guide to finding the values of shear yielding shear rupture and tension rupture. - [6- Practice problem 5-8. Find the centroid for the shaded area](https://magedkamel.com/6-find-the-centroid/): Practice problem 5-8. Find the centroid for the shaded area. using integration we will find the x bar and y bar of the centroid for a composite shape. - [10- Practice problem for the x and y coordinates of a trapezoid](https://magedkamel.com/10-practice-problem-for-the-x-and-y-2/): Practice problem for the x and y coordinates of a trapezoid. A step by step guide is given by using two options - [24- Ix for the Trapezium second option](https://magedkamel.com/24-ix-for-the-trapezium-second-option/): Ix for the Trapezium second option, we will use a horizontal strip and integrate it to get the final expression for Ix . - [28-Solved problem 4-14 part 2 for effective length factor](https://magedkamel.com/28-solved-problem-4-14-part-2/): Solved problem 4-14 part 2 for effective length factor. the detailed calculation for both LRFD and ASD designs. - [23- Product of inertia Ixy for the parallelogram](https://magedkamel.com/23-ixy-for-the-parallelogram/): Product of inertia Ixy for the parallelogram. Step-by-step guide for the estimation for the radius of gyration for the product of inertia. - [18-The Effective Area for a Built-Up Section.](https://magedkamel.com/18-effective-area-for-a-built-up-section/): How to estimate the effective Area for a Built-Up Section? A solved problem 3-19 is used to explain how to find the effective area for a built up section. - [17-Problem 3-4-3 for MC section-LRFD and ASD value-2/2.](https://magedkamel.com/17-mc-section-lrfd-and-asd-value/): This is the second part, of problem 3-4-3 MC section-LRFD and ASD value. We will estimate the effective area. Finally, we can get the strength values. - [16-Problem 3-4-3 for staggered bolts-tension members-1/2.](https://magedkamel.com/16-problem-3-4-3-for-staggered-bolts/): Problem 3-4-3 for staggered bolts-tension members. It is required to get the factored design strength for a given MC section with staggered bolts. - [15A-Solved problem 3-8-1 for staggered Bolts.](https://magedkamel.com/15a-solved-problem-3-8-1-for-staggered-bolts/): Solved problem 3-8-1 for staggered Bolts. estimate the net area for the different routes under tension force and modify these values due to load transfer. - [15- Solved problem 3-7 for staggered bolts-tension members](https://magedkamel.com/15-problem-3-7-for-staggered-bolts/): Problem 3-7 for staggered bolts-tension members. It is required to get the factored design strength for a given unequal angle with staggered bolts. - [9- How to Use a matrix for the quadratic polynomial function?](https://magedkamel.com/9-matrix-for-the-quadratic/): How to Use a matrix for the quadratic function? Three practice problems are used to find the quadratic functions by using a matrix. - [8-Practice problem for reduced echelon form.](https://magedkamel.com/8-practice-problem-for-reduced-echelon/): Practice problem for reduced echelon form. How to determine whether the given matrix is in R echelon form or not? - [7b- Practice problems for Gauss Jordan elimination.](https://magedkamel.com/7b-practice-problems-for-gauss-jordan-elimination/): Practice problems for Gauss Jordan elimination are introduced. Step by step guide for solving these problems. - [7a- Practice problems for back substitution: Easy approach.](https://magedkamel.com/7a-problems-for-back-substitution/): Practice problems for back substitution for matrices. Step by step illustration of the process of back substitution. ## Pages - [Contact me](https://magedkamel.com/contact-me/): If you have questions about any tutorial, need clarification, or want to suggest a topic, feel free to reach out. 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