Question

Problem 1: Circle the right answer 1. Shear force at a point on a flexural member indicates (5 points) a) Slope of bending moment diagram b) Slope of loading diagram c) Area under the bending moment diagram d) All of the above e) None of the above 2. Typically, maximum bending stress occurs at the of the cross section a) Neutral axis b) Extreme edge c) Point where thickness is the maximum d) Flange e) None of the above 3. Neutral axis always passes through a) Middle of the cross sectio b) Center of gravity of the cross section c) The point of application of load d) One third of the height of a cross section e) All of the above 4. Area under shear force diagram indicates a) Intensity of loading b) Shear modulus c) Bending moment d) All of the above e) None of the above 5. Typically, shear stress in a beamn is at the neutral axis a) Maximum b) Minimum c) Zero d) All of the above e) None of the above

Answer 1

(1)

The rate of change of the bending moment with respect to length of the beam is equal to the shearing force, or the slope of the moment diagram at the given point is the shear force at that point.

Hence option (a) is correct.

(2)

Typically maximum bending stress occurs at extreme edge, Because

$\sigma _{max}=\frac{My_{max}}{I}$

y is maximum at either top or bottom of cross section

Hence option (b) is correct.

(3)

Neutral axis always passes through center of gravity of the cross section.

Option (b) is correct

(4)

Area under shear force diagram indicates Bending moment.

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

OR

$\int dM = \int Vdx$

Hence option (c) is correct.

(5)

Typically, shear stress in a beam is maximum at the neutral axis.

Shear stress is given by

$\tau =\frac{VQ}{It}$

Where V = shear force

Q = First moment of area above the point where shear stress is to be calculated.

Typically, First moment of area is maximum at neautral axis.

Hence option (a) is correct.