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

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

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

### 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.

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

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.

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.

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.

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

3- From table 1-1 get the Sx value, ry for the selected section, and apply 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.

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.

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.

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. 