Theory of Pure Bending

Q. For a square-sectioned beam bent as shown in the given figure, the exaggerated view of the deformed cross - section is

1. 
2. 
3. 
4. 

Q. A steel beam is replaced by a corresponding aluminium beam of same cross-sectional shape and dimensions, and is subjected to same loading. The maximum bending stress will

1. be unaltered
2. increase
3. decrease
4. vary in proportion to their modulus of elasticity

Q. A structural beam subjected to sagging bending has a cross-section which is an unsymmetrical I-section. The overall depth of the beam is 300 mm. The flange stresses in the beam are:
${\sigma }_{top}=200N/m{m}^2$
${\sigma }_{bottom}=50N/m{m}^2$

What is the height in mm of the neutral axis above the bottom flange?

1. 240 mm
2. 60 mm
3. 180 mm
4. 120 mm

Q. Consider the following statement for a beam based on theory of bending:
1. Strain developed in any fibre is directly proportional to the distance of fibre from neutral surface.
2. For flexural loading and linearly elastic action the neutral axis passes through the centroid of cross-section.
3. The assumption of the plane cross-section remaining plane will not hold good during inelastic action.
4. Instances in which the neutral axis does not pass through the centroid of a cross-section include a homogenous symmetrical beam (with respect to axis) and subjected to inelastic action.

Which of these statements are correct ?

1. 1, 2, 3 and 4
2. 1, 2 and 4
3. 3 and 4
4. 1 and 2

Q. A square section as shown in the figure below is subjected to bending moment M.

What is the maximum bending stress?

1. ${\sigma }_{bc}={\sigma }_{bt}=\frac{12M}{h^3}$
2. ${\sigma }_{bc}={\sigma }_{bt}=\frac{6M}{h^3}$
3. ${\sigma }_{bc}={\sigma }_{bt}=\frac{9M}{2h^3}$
4. ${\sigma }_{bc}={\sigma }_{bt}=\frac{9M}{h^3}$

Q. A mild flat of width 120 mm and thickness 10 mm is bent into an arc of a circle of radius 10 m by applying a pure moment M. If E is $2\times {10}^{5}N/m{m}^2$, then the magnitude of the pure moment M will be

1. $2\times {10}^{6}Nmm$
2. $2\times {10}^{5}Nmm$
3. $0.2\times {10}^{5}Nmm$
4. $0.2\times {10}^{4}Nmm$

Q. Consider the following statements for a beam of rectangular cross-section and uniform flexural rigidity EI subjected to pure bending:
1. The bending stresses have the maximum magnitude at the top and bottom of the cross-section.
2. The bending stresses vary linearly through the depth of the cross-section.
3. The bending stresses vary parabolically through the depth of the cross-section.

Which of these statements is/are correct?

1. 1, 2 and 3
2. 1 only
3. 2 only
4. 1 and 2 only

Q. Match List-I with List-II and select answer using the the codes given below the lists :
List-I
A. Assumption in the theory of simple bending
B. The point at which the bending stress is maximum for any cross-section
C. The point at which the bending stress is zero for any cross-section
D. The point in the cross section through which the neutral axis passes

List - II
1. Neutral axis
2. Centroid
3. The plane sections remain plane
4. Extreme fibre
5. The cross-section is circular

Code:
A B C D

1. 5 4 1 2
2. 3 1 2 4
3. 5 1 2 4
4. 3 4 1 2

Q. Which of the following points are considered while deriving the formula

$\frac{M}{I}=\frac{f}{y}=\frac{E}{R}$?

1. Type of material.
2. Transverse shear force.
3. The stresses in the remaining principle direction.
4. ${\sigma }_y={\sigma }_z={\tau }_{xz}={\tau }_{zx}=0$
5. Linear variation of strain

Select the correct answer using the codes given below :

1. 1, 2 and 4
2. 2, 3 and 5
3. 4 and 5
4. 1 and 3

Q. Shear span is defined as the zone where

1. bending moment is zero
2. shear force is zero
3. shear force is constant
4. bending moment is constant