# How do you calculate the maximum bending stress in a beam with different thickness along different parts on the beam?

Here is a practise question that I am working on. The beam has different thickness due to the supports in the middle. I would expect the maximum bending stress be away from the middle due to the support? But that is not what I got.

Also I am very confuse with the moving pointload. Do we have different induced maximum external moment (due to pointload) at different location along the beam(due to the thickness)? For example, the maximum moment at the thinner beam would be $$(-1m \times 20kN)$$? But the maximum moment at the thicker beam would be $$(-2m \times 20kN)$$? (As the pointload moves)

What you have is a box beam with a different second moment of inertia at the segment without or with the cover plate, $$I_1, I_2$$, respectively. Note that the varying stiffness does not affect the distribution of shear force and moment along the span; so without guessing, you can compare the resulting bending stresses obtained from 1) place the concentrated loads at the mid-span, and 2) place the concentrated load at where the section change occurs (point "a").
ADD: A cross-section is said to be symmetrical when the mirror image exists on the centroidal axis. In the graph below, the cross-section on the upperrow is said to be "doubly symmetrical", while the cross-sections in the lower row are said to be "singularity symmetrical about y-axis", for which, the equation for $$I_x$$ in the sketch is not applicable without modification.
• Just to make sure the centroidal distance of the cross section with the plates is $\frac{0.122}{2}= 0.061m$? Mar 6, 2022 at 4:30