Last Updated on September 24, 2026 by Maged kamel
CB-The coefficient of bending part 2 for steel beams.
You can view the summary of the content of Post 18 in the next slide image.
CB- coefficient of bending values for a supported Beam under two concentrated loads.
We will now cover a new topic: how to determine Cb and calculate it for different loading and bracing.
Another example concerns a supported Beam acted upon by two concentrated loads, with a PultValuee for each.
According to the Table, the Beam has four bracings: two at both ends and two at one-third of the span. The CB at the middle third is 1.00, while the CB Value for the first 1/3 of the span and the last third is 1.67. We want to prove that Value
Determine the reactions at A and B, then estimate the bending Moment for Beam AB. The Moment at a’=Moment at ‘=Pu*L/3. Please refer to the image on the next slide for more details.
Assume we have 4 bracings at A, A’, B’, and B as shown in the sketch. We will estimate the Value of the bending moments at A, A ‘, B ‘, and B and multiply these values by the coefficients. The numerator has a 12.50 factor.
Cb Value for parts A-A’ and B-B’.
The Moment at A’=P*L/3 is a positive Value for the Bending Moment diagram. And the exact Value of mome t=P*L/3 is at Point B’.
The Bending Moment values are equal, and the points A’ and B’ form a straight line. For the part from A to A’, we will enlarge the bending Moment values and divide that part into four quarters.
The span length is L/3; after dividing it into 4 quarters, each distance equals L/12.
Since the Moment at A’ = Pu*L/3, and the bending Moment is linear, we can find the Moment at each quarter.
The Moment values are M1=Pu*L/12 at 1& M2=Pu*L/6, while at 3, M3=P*L/4. Refer back to the CB equation. M-max is still Pu*L/3.
Ap ly the CB equations:: 12.50 max equals 50/12*Pu*L. Find the sum of 3*M1+2.5*Mm x+4*M2 and 3*M3. the sum value equals 30* Pu*L*30/12.
The Cb Value equals 50 Pu*L/12/30*Pu*L*30/12= equals 1.67. The CB Value is for parts A-A’ and B-B ‘.
CB Value for parts A’ -B’.
Consider the middle part, from A’ to B’. The bending Moment is a constant Value = Pu*L/3.
Again, divided into four quarters. All Moment values are the s me=Pu*L/3,
The final Value of Cb for the middle part A’-B’ will be equal to 12.50/12.50=1.0.
Old Equation to Estimate CB, Coefficient Of Bending Value.
The old equation states that the CB is equal to (1.75+1.05*(M1/M2)+0.30*(M1/M2)^2)<=2.30, where M1<M2, M1 is the smaller Moment at the end of the unbraced length of the member. M2 is the larger Moment at the end of the unbraced length of the member. If M1 rotates in the same direction as M2, then M1/M2 is considered positive.
But if M1 and M2 rotate against each other, then M1/M2 is considered negative; this changes the coefficient of g. sincethe sign of M1/M2 is important.
I quote: if M1 is the smaller and M2 is the larger end Moment for the unbraced segment of the Beam under consideration, and the rotations due to end moments M1 and M2 are in opposite directions, then M1/M2 is negative (clockwise against anticlockwise); otherwise, M1/M2 is positive. The Value of the CB- the coefficient of bending equals 1.
The next slide image shows the plot of cb versus the ratio of M1/M2 for different values of M1/M2.
You can view and download the PDF from the following file.
The discussion of Cb will continue in the next posts.
As an external resource: A Beginner’s Guide to Structural Engineering, Chapter 8: Bending Members, 14th edition.
As an external resource –A Beginner’s Guide to Structural Engineering–Chapter 8 – Bending Members- 15th edition
As an external resource –A Beginner’s Guide to Structural Engineering–Chapter 8 – Bending Members- 16th edition.
This is the complete List of all posts related to Cb:
1-Introduction to Cb-Bending coefficient part 1 for the steel Post 17-previous Post.
2- Cb-The coefficient of bending part 2 for steel beams-post 18-this Post.
3-Cb-The coefficient of bending part -3 for steel beams-Post 18a-next Post.
4-Cb value-bracing at the Midpoint of a beam-uniform load-Post 18b.
55-C V-value bracing at the third Point of the beam-uniform load-Post 18C8C.