A shear force diagram is a right-angled triangle: zero at the free (right) end and rising linearly to wl at the fixed (left) support. It belongs to:

Asked in SSC JE 04/03/2017 (Morning)

Detailed Explanation

A linearly varying SFD means a constant load intensity (dV/dx = w). Zero at one end and maximum at the other, with only one support, means a cantilever.

Why “a cantilever with a uniformly distributed load” Is Correct

A SS beam with UDL would give a line from +wl/2 to −wl/2; a cantilever with an end load would give a rectangle. Only a cantilever with a UDL gives a triangle from 0 to wl — option (d).

Cantilever of length l with UDL w. The shear grows linearly from zero at the free end to wl at the fixed end (a triangle); the bending moment grows as a quadratic parabola to wl²/2 (hogging) at the fixed end.

Why the Other Options Are Wrong

A. a simply supported beam with an isolated central load: A central load on a SS beam gives two rectangles (+W/2 and −W/2).
B. a simply supported beam with a uniformly distributed load: A SS beam with UDL gives a line crossing zero at mid-span.
C. a cantilever with an isolated load at the free end: An end load on a cantilever gives a rectangle of height W.

Key Point

Cantilever + UDL: triangular SFD (0 → wl), parabolic BMD (0 → wl²/2).

Key Concepts for Students

Shape of SFD identifies the loading: rectangle = point loads, triangle = UDL.
The steepness of the SFD equals the load intensity.
A triangular load would give a curved (parabolic) SFD.

Practice more: this is question 47 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.