- List of Steel beam posts-part -1.
- Steel beams and types of buckling.
- An easy approach to Compact and non-compact section.
- An Easy Introduction to Plastic Theory for Beams.
- An Easy Introduction to Plastic Theory for Beams.
- Solved problem 4-3 for the elastic and plastic section moduli.
- A Solved problem 5-1 for Sx & Zx-elastic-plastic moduli.
- Solved problem 5-2 for Sx&Zx and shape factor.
- Local buckling parameters for steel beams.
- How to make an analysis of steel beams? Solved problems.
- Solved problem-7-4-1 how to design a steel beam?
- Step by step guide to Lateral-torsional buckling

**List of Steel beam posts-part -1**.

### S**teel beams and types of buckling.**

This is the first post of the Steel beams Posts which includes:

1-Definition of steel beams. Sketch showing the different parts of a frame.

2- Causes of failure for beams. The beams can fail while reaching the plastic moment. Or one of the three causes which are LFB-Local flange buckling, LWB Local web buckling, and LTB lateral-torsional buckling. Detailed description for the different three cases is given with sketches with a given resource to view.

This is the link to the first post: S**teel beams**** and types of buckling.**

**An easy approach to Compact and non-compact section.**

This is the second post of the Steel beams Posts which includes:

1-Definition of compact section.

2-The value of Mp-Fy*Zx.

3- AISC Table B4.1 for the width-to-section ratio for compression elements, members subject to bending.

The next slide is one of the slide images included in the post.

This is a link to post 2: An Easy Approach to Compact and Non-compact section.

### **An Easy Introduction to Plastic Theory for Beams.**

This is the third post of the Steel beams Posts which includes an introduction to the plastic theory, the stress-strain curve for steel, a review of the allowable stress design ASDM, the definition of a plastic hinge, and an analysis of a rectangular section for any shape.

The next slide is one of the slide images included in the post.

This is a link to post 3: An Easy Introduction to Plastic Theory for Beams.

** An Easy Introduction to Plastic Theory for Beams.**

The post includes three terms, The section modulus Sx and how to estimate. When we have a rectangular section (b*h) under a moment, the stress at the upper fiber has reached yield. The section modulus Sx equals My/Fy, where My is the yielding moment and Fy is the yield stress and can be found to be equal to b*d^2/6 for a rectangular section.

The plastic section modulus is termed Zx and equals Mp/Fy, where Mp is the plastic moment and Fy is the yield stress, for a rectangle Zx equals b*d^2/4. the third item is the shape factor which is Zx/Sx. More details for any shape on how to estimate Sx and zx values are given.

The next slide is one of the slide images included in the post.

This is a link to post 3a: **An Easy Introduction to Plastic Theory for Be**ams.

**Solved problem 4-3 for the elastic and plastic section moduli.**

**Solved problem 4-3 for the elastic and plastic section moduli.*** *This is the 5th post of the Steel beams Posts which includes a solved Example 4-3, quoted from the structural engineering reference manual.

Determine the plastic section modulus and the shape factor for the steel section shown. Assume that the section is compact and adequately braced. To get the shape factor, we need to find the elastic section modulus Sx. Sx can be estimated as equal to Ix/Sx. There are two ways to get the value of Ix.

To get Zx, find the plastic axis that divides the T section into equal areas. Zx=(At/2)*(y1+Y2). The shape factor equals Zx/Sx.

The next slide is one of the slide images included in the post.

This is a link to post 4: solved problem 4-3 for the elastic and plastic section moduli.

**A Solved problem 5-1 for Sx & Zx-elastic-plastic moduli.**

**A Solved problem 5-1 for Sx & Zx-elastic-plastic moduli.**

This is the 6th post of the list of Steel beams Posts which includes, A solved problem from Prof. William T Segui‘s book.

Example 5.1 For the built-up shape shown in Figure 5.6, determine (a) the elastic section modulus S and the yield moment My and (b) The plastic section modulus Z and the plastic moment Mp. Bending is about the x-axis, and the steel is A572 Grade 50.

This problem is similar to solved problem 4-3 included in the previous post. The only added step is to multiply Zx by Fy to get the plastic moment value.

The next slide is one of the slide images included in the post.

Part (b) Find the plastic section modulus Z and the plastic moment Mp. Bending is about the x-axis, and the steel is A572 Grade 50.

This is a link to post 5: **A Solved problem 5-1 for Sx & Zx-elastic-plastic moduli.**

** **Solved problem 5-2 for Sx&Zx and shape factor.

This is the 7th post of the Steel beams posts which has A solved problem from Prof. William T Segui‘s book.

Example 5.2 Compute the plastic moment, Mp, for a W10 × 60 of A992 steel. Two methods are used for the solution. The first method is to consider the W section as composed of several plates.

The second method is using Table 1-1 to get the relevant data. The complete details to find Sx, Zx, and Plastic moment are explained in the post.

This is a link to post 6: Solved problem 5-2 for Sx&Zx and shape factor.

### Local buckling parameters for steel beams.

This is the 8th post of the Steel beams Posts which includes lambda λp and λr values for compact and non-compact flange and web for The W section, what are the stiffened and the unstiffened elements? How to get the Fcr value? A more detailed illustration of Local buckling parameters is given. A discussion of the AISC table B 4.1B is presented.

This is a link to post 7: Local buckling parameters for steel beams.

### How to make an analysis of steel beams? Solved problems.

This is the 9th post of the Steel beams Posts which includes a Solved problem from Prof. William T Segui‘s book, Example 5-3. The beam shown in Figure 5.11 is a W16 × 31 of A992 steel. It supports a reinforced concrete floor slab that provides continuous lateral support of the compression flange. The service dead load is 450 lb/ ft.

This load is superimposed on the beam; it does not include the weight of the beam itself. The service live load is 550 lb/ ft. Does this beam have adequate moment strength?

This load is superimposed on the beam; it does not include the weight of the beam itself. The service live load is 550 lb/ ft. Does this beam have adequate moment strength?

The second solved problem is from Eng Lindeburg ‘s book. Establish whether the W21x55 beam of A992 is compact with given four options to check the correct one.

This is a link to post 8: How to make an analysis of steel beams? Solved problems.

sis of steel beam-Solved problems.

### Solved problem-7-4-1 how to design a steel beam?

* *This is the 10th post* *of the Steel beams Posts *which includes a * Solved problem *From Prof. Charles G Salmon’s book.*

Solved problem 7-4-1 Select the lightest W or M section to carry a uniformly distributed dead load of 0.2 kip/ft superimposed (i.e., in addition to the beam weight) and 0.8 kips/ft live load.

The simply supported span (Fig. 7.4.2) is 20 ft. The compression flange of the beam is fully supported against lateral movement. Use Load and Resistance Factor Design, and select the following steels: A36; A992; and A572 Grade 65.

This is a link to post 9: Solved problem-7-4-1 how to design a steel beam.

**Step by step guide to Lateral-torsional buckling**

This is the 11th post of the Steel beams Posts. A new subject is the *Lateral- torsional buckling* of beams. A torsion will occur for a beam accompanied by a lateral movement, which refers to the definition from Schaum’s book, structural steel design. Introduction to the coefficient of bending CB.

This is a link to post 10: Step-by-step guide to Lateral-torsional buckling

For the second post, **Lis**t of steel beam posts-part 2, this is the link.

A very useful external resource is **A Beginner’s Guide to Structural Engineering**.