Determine the internal bending moment and bending stress. Please help

Question

The cross-sectional dimensions of a beam are shown. Assume b_f=1.875 in., t_f=t_w=0.375 in. and d=4.75 in.

(a) If the bending stress at point K is 2350 psi (T), determine the internal bending moment M_z acting about the z centroidal axis of the beam. What is the M_z in lb-ft?

(b) Determine the bending stress σHσH at point H (positive if tension, negative if compression). (in psi)

Answer 1

Isaac:

I will outline the procedure and summarize my results in the following steps…

1. Calculate composite section properties.  I usually set up a table or spreadsheet for finding area, moment of inertia, and neutral axis for the composite section. My calculated values were…

(A)tot = 2.3438in²

(z)bar = 1.8499in…measured from the bottom of the section

(I)tot = 5.0413in⁴

2. Calculate the section modulus using “(S)z = (I)tot / c”.  My governing value is (S)z = 1.8625in³.

3. Calculate the bending moment using “σ = M/S,” substituting the given stress value at Point K and the calculated value (S)z in Item2.  Solve for moment M.  My calculated value was M = 4377in-lb = 364.7ft-lb. Always watch units carefully.

4. Under elastic bending, the stress block is linear across the depth of the section.  Draw a elevation diagram of the stress block across the section with the given value (σ)k = +2350psi labeled, 0psi through the neutral axis, and by similar triangles, calculate (σ)h.  My calculated value was (σ)h = -1499psi (compression).

Should you need a more detailed explanation, contact me and we can walk through the steps more closely including the table for calculating section properties and review diagrams.