LOADING
Question
A cantilever beam of span L carries a concentrated load 'W' at the free end. If the width 'b' of the beam is constant throughout the span, then for the beam to have uniform strength, the depth 'd' at the free end should be
A.
B.
C.
D.
Answer ( Option D)

Solution

For a beam of uniform strength, the bending stress (f) remains constant

throughout the beam length, even though the bending moment varies - this is

achieved by varying the depth (d) while keeping width (b) constant.

Bending stress relation: 

f M/Z (where Z = section modulus = bd²/6 (for rectangular section))

At the fixed end (x = L from free end), the bending moment is maximum:

Mmax = WL

At this section, depth = d (maximum depth, occurring at the fixed end for a cantilever of

uniform strength since M = 0 at the free end, the theoretical depth there is zero).

Applying the bending equation at the fixed end:

 

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