Question

The following statements are related to bending of beams:

I. The slope of the bending moment diagram is equal to the shear force.
II. The slope of the shear force diagram is equal to the load intensity.
III. The slope of the curvature is equal to the flexural rotation.
IV. The second derivative of the deflection is equal to the curvature.

The only FALSE statement is

• A. I
• B. II
• C. III
• D. IV

Answer 1

The correct option is C III

$\frac{dM}{dx}=V$

$\frac{dV}{dx}=w$

$\left\{\begin{array}{c}M\to Bendingmoment\\ V\to Shearforce\\ w\to Loadingintensity\\ k\to Curvature\\ \theta \to Slopeofdeflectioncurve\\ EI\to FlexuralRigidity\\ y\to Deflection\end{array}\right\}$

Curvature,

$k=\frac{d\theta }{dx}$

Slope, $\theta$ = $\frac{dy}{dx}$

Slope of curvature $=\frac{dk}{dx}$ = $\frac{d^2\theta }{d{x}^2}$ $\ne$ $\theta$

$\frac{d\theta }{dx}$ = $\frac{d^{2}y}{d{x}^2}=k=$$\frac{M}{EI}$