Statement: A fixed-end beam under uniform load has the maximum shear at the supports.

Statement: A fixed-end beam under uniform load has the maximum shear at the supports.

• A. True
• B. False
• C. Only at midspan
• D. Only at quarter-span

Answer: (A)

Vertical shear in a fixed-end beam under a uniform load is highest at the ends. The end reactions balance the total load, and by symmetry each end carries half of the total load, so R_A = R_B = wL/2. The internal shear at a section a distance x from the left is V(x) = R_A − w x. With R_A = wL/2, this becomes V(x) = wL/2 − w x, a linear function that starts at V(0) = wL/2 at the left support and ends at V(L) = −wL/2 at the right support, crossing zero at midspan. Thus the maximum magnitude of shear occurs at the supports, equal to wL/2. The statement is true because the shear is largest at the ends and zero at midspan.

Vertical shear in a fixed-end beam under a uniform load is highest at the ends. The end reactions balance the total load, and by symmetry each end carries half of the total load, so R_A = R_B = wL/2. The internal shear at a section a distance x from the left is V(x) = R_A − w x. With R_A = wL/2, this becomes V(x) = wL/2 − w x, a linear function that starts at V(0) = wL/2 at the left support and ends at V(L) = −wL/2 at the right support, crossing zero at midspan. Thus the maximum magnitude of shear occurs at the supports, equal to wL/2. The statement is true because the shear is largest at the ends and zero at midspan.