Question

For a simply supported beam, here does the maximum shear stress occur?

A) at the section of maximum moment
B) at the top fibers
C) at the bottom fibers
D) at the supports

Answer 1

The maximum shear stress for a simply supported beam occurs at the supports due to the force being most concentrated at this point. Shear stress is related to forces acting parallel to the cross-sectional area and aims to cause sliding between material parts.

Step-by-step explanation:

For a simply supported beam, the maximum shear stress occurs at the supports. While at the section of maximum moment, the normal stresses due to bending are the greatest, the shear stress reaches its peak value where the shear force is the largest—which is typically at the supports. Unlike normal stress, which can be distributed either as tensile at the bottom fibers or compressive at the top fibers of a beam under load, shear stress acts parallel to the cross-sectional area and is concerned with forces that cause one part of a material to slide past another.

Considering the examples provided, a container or a beam under load will experience maximum shear at the areas that resist the tendency of the material to shear or slide - in the case of the fluid container, it is the bottom that holds all the fluid, for the beam it would be at the supports if that's where the load is applied or transferred. Thinking about the forces involved, they are perpendicular to the length of the beam (L0) and act across the cross-sectional area (A), and these forces create what we deem as shear stress, dictated by the shear modulus (S).

Answer 2

For a simply supported beam, the maximum shear stress occurs at the supports (D).

Step-by-step explanation:

In a simply supported beam, the shear stress distribution is triangular, reaching its maximum value at the supports. This occurs because the shear force is zero at the supports, and as we move towards the center of the beam, the shear force increases linearly.

According to shear stress distribution, the maximum shear stress will be at the supports where the shear force is at its highest.

At the section of maximum moment (Option A), the bending stress is maximum, not the shear stress. The top fibers (Option B) experience tension, and the bottom fibers (Option C) experience compression, but the maximum shear stress is concentrated at the supports. Understanding the distribution of forces in different sections of a beam is crucial for designing and analyzing structures to ensure they can withstand the applied loads.