Brief content of steel beam post 11.

11-Solved problem 4-5-How to design a steel beam?

Solved Problem 4-5-How To Design A Steel Beam?

Brief content of the video.

For the solved Solved problem 4-5. A Simply supported beam of grade 50 steel is laterally braced at 4 Ft intervals, the length of the beam was not given, and the bracings are indicated by X marks as an indication of lateral bracings.

If the beam is subjected to a uniform factored bending moment of 270 Ft-kips (LRFD), this moment is the Ultimate load estimated already as LRFD, or 180 Ft-kips -ASD, allowable strength design, the given Cb value =1.

Determine (a) the lightest adequate W shape. That was a part of the video with a subtitle and a closed caption in English.

You can click on any picture to enlarge, then press the small arrow at the right to review all the other images as a slide show.

A Solved problem 4-5.

A solved problem 4-5 from Prof. Alan Williams‘s Structural Engineering Reference Manual.

Design of beam according to LRFD for part a.

Part a includes the lightest adequate W section for design. We have to identify which region That w section is located according to bracing. This is a design problem for which, the distance between bracing for a beam is Lb < Lp. After the design, we will get the Lb value from the next step 3.

Solved problem 4-5, it is required to determine the lightest W section.

For the LRFD design: 
 1-Estimate the preliminary Zx value by considering that φb*Mn=Mult, since Mn=Zx*Fy.

We can get the plastic section modulus Zx= Mult /(φb*Fy). We go to table 3-2, where sections are sorted by Zx, and select the first bold section which Zx > Zx.

Check the bracing length required at the plastic stage Lp from the table.

2- from table 3-2, we get the section W16x 40, that has Zx =73.0 inch3 >72.0 inch3, which is the preliminary value for Zx. 
We can get the bracing length required from table 3-2 at the plastic stage Lp and lr value.

The nominal moment formula and the values of plastic bracing length based on the ASTM.

This is a reminder of the Graph of Mn and the bracing distance and the different zones.

            If we wish to check Lp value.  Lp can be estimated from the relevant formula  Lp=ry* (300/sqrt(Fy)), but we need to have ry value.

Estimate the value of φ*Mn of the selected section and check against the estimated Ultimate moment Mult.

3- From table 1-1 get the Sx value, ry for the selected section, and apply at the equation of LP=ry*300/sqrt(fy) or from table 3-2 for Fyis equal to 50 ksi.

4- Since the given bracing length Lb is smaller than Lp, the section is compact,  φb*Mn= φb*Zx*Fy, to be divided by 12 to get the value in Ft-kips-LRFD. we get the φb*Mn=274 ft.kips.

Estimate the value of φ*Mn of the selected section from the table.

The same value φb*Mn can be obtained from Table 3-2, as we can see from the next slide.

Design of beam according to ASD for part a.

The ASD calculation is shown in the next slide, here are the following steps to implement:
1-Get a preliminary Zx value by considering that (1//Ω)*Mn=Mtotal, since Mn=Zx*Fy.

We can get Zx= Mtotal /(1/Ω)*Fy). 2-From table 3-2, select the lightest w section, that gives Zx>Zx preliminary.
The selected W section is W16x40, Zx of the selected section=73.00 inch3, which is >72.144 inch3 as per requirement.

2- From table 3-2, we get the section W16x 40 that has Zx =73.0 inch3 >72.0 inch3, the preliminary value for Zx. 

We can get the bracing length required from table 3-2 at the plastic stage Lp. Lp can be estimated from the relevant formula  Lp=ry* (300/sqrt(Fy)), but we need to have ry value.     

Estimate the value of (1/ Ω)*Mn of the selected section

3- From table 1-1 get the Sx value, ry for the selected section, and apply at the equation of LP=ry*300/sqrt(fy), or from table 3-2.

4- Since the given bracing length Lb is smaller than Lp, the section is compact,  (1/ Ω)*Mn = (1/ Ω)*Zx*Fy, to be divided by 12 to get the value in Ft-kips-ASD.
5- Check that the estimate (1/ Ω)*Mn is >=total moment Mt.

Estimate the value of (1/ Ω)*Mn

The same value (1/ Ω)*Mn can be obtained from table 3-2, as we can see from the next slide.

Design of beam according to LRFD for part b.

This is part b, W shape with minimum depth,  as per LRFD.

Estimate the value of φ*Mn of the selected section

For the selection is based on the minimum depth.
We will select W10x60 since the depth is smaller < depth of W 16×40 as shown in the next slide, then check that the φb*Mn> Mult.

Design of beam according to ASD for part b.

Estimate the value of 1/ Ω)*Mn of the selected section

This is part b, W shape with minimum depth,  as per ASD,  for the selection based on the minimum depth.
We will select W10x60 since the depth is smaller < depth of W 16×40 as shown in the next slide, then check that the (1/ Ω)*Mn > Mt.

This is the pdf file used for the illustration of this post.

For a useful external source, please follow this link. Lateral Torsional Buckling Limit State.


For the next post, review the Information of Lp, Lr. This post is an introduction to the different terms of the Lp and lr for a steel beam.

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