Question

A beam is supported at two points with a uniform load across its length. The type of bending moment diagram this beam will have is

• A. Linearly increasing
• B. Parabolic
• C. Constant
• D. Hyperbolic

Hint:

Load, Shear, Moment Relationships. Constant Load \(\rightarrow\) Linear Shear \(\rightarrow\) Parabolic Moment. Linear Load \(\rightarrow\) Parabolic Shear \(\rightarrow\) Cubic Moment. Point Load \(\rightarrow\) Constant Shear (between loads) \(\rightarrow\) Linear Moment (between loads).

Answer 1

The Correct Option is B

Consider a beam supported at two points (e.
g.
, a simply supported beam) subjected to a uniformly distributed load (UDL) of intensity \(w\) across its length.
The relationships between load (\(w\)), shear force (\(V\)), and bending moment (\(M\)) are: $$ \frac{dV}{dx} = -w $$ $$ \frac{dM}{dx} = V $$ Integrating the load distribution: Since \(w\) is constant, the shear force \(V\) will be a linear function of \(x\) (\(V = -wx + C_1\)).
Integrating the shear force: Since \(V\) is linear, the bending moment \(M\) will be a quadratic (parabolic) function of \(x\) (\(M = -\frac{1}{2}wx^2 + C_1 x + C_2\)).
Therefore, for a beam under a uniform load, the bending moment diagram is parabolic.