Engineering Questions with Answers - Multiple Choice Questions

# Strength of Materials MCQs Bending Equation

1 - Question

In simple bending, ______ is constant.
a) Shear force
c) Deformation
d) Bending moment

Explanation: If a beam is undergone with simple bending, the beam deforms under the action of bending moment. If this bending moment is constant and does not affect by any shear force, then the beam is in state of simple bending.

2 - Question

If a beam is subjected to pure bending, then the deformation of the beam is_____
a) Arc of circle
b) Triangular
c) Trapezoidal
d) Rectangular

Explanation: The beam being subjected to pure bending, there will be only bending moment and no shear force it results in the formation of an arc of circle with some radius known as radius of curvature.

3 - Question

When a beam is subjected to simple bending, ____________ is the same in both tension and compression for the material.
a) Modulus of rigidity
b) Modulus of elasticity
c) Poisson’s ratio
d) Modulus of section

Explanation: It is one of the most important assumptions made in the theory of simple bending that is the modulus of elasticity that is Young’s modulus [E] is same in both tension and compression for the material and the stress in a beam do not exceed the elastic limit.

4 - Question

E/R = M/I = f/y is a bending equation.
a) True
b) False

Explanation: The above-mentioned equation is absolutely correct.
E/R = M/I = f/y is a bending equation. It is also known as flexure equation (or) equation for theory of simple bending.
Where,
E stands for Young’s modulus or modulus of elasticity.
R stands for radius of curvature.
M stands for bending moment
I stand for moment of inertia
f stands for bending stress
y stands for neutral axis.

5 - Question

Maximum Shearing stress in a beam is at _____
a) Neutral axis
b) Extreme fibres
c) Mid span

Explanation: Shearing stress is defined as the resistance offered by the internal stress to the shear force. Shearing stress in a beam is maximum at a neutral axis.

6 - Question

At the neutral axis, bending stress is _____
a) Minimum
b) Maximum
c) Zero
d) Constant

Explanation: Neutral axis is defined as a line of intersection of neutral plane or neutral layer on a cross section at the neutral axis of that section. At the NA, bending stress or bending strain is zero. The first moment of area of a beam section about neutral axis is also zero. The layer of neutral axis neither contracts nor extends.

7 - Question

Curvature of the beam is __________ to bending moment.
a) Equal
b) Directly proportion
c) Inversely proportion
d) Coincides

nswer: b
Explanation: From the flexural equation, we have 1/R is called as the “curvature of the beam”.
1 / R = M / EI
Hence the curvature of the beam is directly proportional to bending moment and inversely proportional to flexural rigidity (EI).

8 - Question

What are the units of flexural rigidity?
a) Nm2
b) Nm
c) N/m
d) m/N3

Explanation: The product of young’s modulus (E) of the material and moment of inertia (I) of the beam section about its neutral axis is called flexural rigidity.
Units for E are N/m2
Units for I are m4
Their product is Nm2.

9 - Question

What are the units for section modulus?
a) m2
b) m4
c) m3
d) m

Explanation: The ratio of moment of inertia to the distance to the extreme fibre is called modulus of section or section modulus. It is generally denoted by the letter Z. Section modulus is expressed in m3
Z = I/y
= m4/ m
= m3.

10 - Question

What are the units of axial stiffness?
a) m3
b) m2
c) N/ m
d) -m

Explanation: Axial rigidity is a product of young’s modulus (E) and the cross-sectional area (A) of that section. Axial rigidity per unit length is known as axial stiffness the si units of axial stiffness are Newton per metre (N/m).

11 - Question

Calculate the modulus of section of rectangle beam of size 240 mm × 400 mm.
a) 5.4 × 106 mm3
b) 6.2 × 106 mm3
c) 5.5 × 106 mm3
d) 6.4 × 106 mm3

Explanation: b = 240 mm & d = 400 mm
Moment of inertia (I) = bd3/12; y = d/2
Section modulus (Z) = I/y = bd2/ 6
= 1/6 × 240 × 400 ×400
= 6.4 × 106 mm3.

12 - Question

What is the product of force and radius?
a) Twisting shear
b) Turning shear
c) Turning moment
d) Tilting moment

Explanation: Twisting moment will be equal to the product of the perpendicular force and existing radius. Denoted by letter T and SI units are Nm.

13 - Question

Determine section modulus for beam of 100mm diameter.<br/>

a) 785 × 103 mm3<br/>
b) 456 × 103 mm3<br/>
c) 87 × 103 mm3<br/>
d) 98 × 103 mm3

Explanation: d = 300mm
For circular sections; I = π / 64 × d4
y= d/2
Z = π/32 × d3 (d = 100 mm)
Z = 98.17 × 103mm3.

14 - Question

### Strength of Materials MCQs Pure Bending Stress

In simply supported beams, the _____ stress distribution is not uniform.
a) Bending
b) Shearing
c) Tensile
d) Compressive

Explanation: In a simply supported beam, there is compressive stress above the neutral axis and tensile stress below it. It bends with concavity upwards. Hence the bending stress distribution is not uniform over the section.

15 - Question

The maximum _________ stresses occur at top most fibre of a simply supported beam.
a) Tensile
b) Compressive
c) Shear
d) Bending

Explanation: As bending stress distribution is not uniform over the section in simply supported beams, the maximum compressive stress lies above the neutral axis. Obviously, top most fibre of beam. The maximum tensile stress occurs at bottom most fibre.

16 - Question

The stress is directly proportional to _______
a) E
b) u
c) y
d) R

Explanation: By two equations; we have e = y/R & e = f/E
Equating both equations; we get e = f/E = y/R
Hence stress (f) is directly proportional to the distance from neutral axis(y).

17 - Question

At the extreme fibre, bending stress is______
a) Minimum
b) Zero
c) Constant
d) Maximum

Explanation: Bending stress is defined as the resistance offered by internal stress to bending. In beams, stresses occurs above or below the neutral axis i.e at the extreme fibres. Hence bending stress is maximum at the extreme fibres.

18 - Question

The curvature of a beam is equal to _____
a) EI/M
b) M/E
c) M/EI
d) E/MI

Explanation: From the bending equation, E/R = M/I = f/y.
Where R is called “radius of curvature “
1/R is called “curvature of the beam “.
So, 1/R = M/EI.
So curvature of the beam is directly proportional to bending moment.

19 - Question

Skin stress is also called as ______
a) Shear stress
b) Bending stress
c) Lateral stress
d) Temperature stress

Explanation: The bending moment leads to deform or deflect the beam and internal stress resists bending. The resistance offered by internal stress to bending is called bending stress or “fibre stress” or “skin stress” or “longitudinal stress”.

20 - Question

________ is the total Strain energy stored in a body.
a) modulus of resilience
b) impact energy
c) resilience
d) proof resilience

Explanation: When a load acts on a body, there is deformation of the body which causes movement of the applied load. Thus work is done is stored in the body as energy and the load is removed this stored energy which is by virtue of strain is called resilience.

21 - Question

In cantilever beams, there is _______ stress above neutral axis.
a) Compressive
b) Tensile
c) Temperature
d) Shear

Explanation: In a cantilever beam maximum compressive stress occurs at bottom most fibre and maximum tensile stress occurs at the top most fibre and zero at neutral axis hence the tensile stresses lies above the neutral axis.

22 - Question

The product of modulus of elasticity (E) and polar moment of inertia (J) is called torsional rigidity.
a) True
b) False

Explanation: The product of the modulus of rigidity (C) and polar moment of inertia (J) is called torsional rigidity and it produces a twist of one radian in a shaft of unit length.

23 - Question

Calculate the maximum stress due to Bending in a steel strip of 30 mm thick and 60 mm wide is bent around a circular drum of 3.6 m diameter [Take Young’s modulus = 200kN/m2].<br/>

a) 2341.76 N/mm2<br/>
b) 1666.67 N/mm2<br/>
c) 5411.76 N/mm2<br/>
d) 4666.67 N/mm2

Explanation: Thickness of steel strip = 30 mm; b = 60 mm; d = 3.6m
R = 3.6/2 = 1.8 m
E = 200 kN/m2
y = 30/2 = 15 mm
E/R = f/y ; f = 200000×15/1800
= 1666.67 N/mm2.

24 - Question

The strength of beams depend merely on________
a) Modulus section
b) Moment of inertia
c) Flexural rigidity
d) Moment of resistance

Explanation: The ratio of moment of inertia to the distance to the extreme fibre is called modulus of section. The Beam is stronger when section modulus is more. The strength of beam depends on section modulus. The beams of same strength mean section modulus is same for the beams.

25 - Question

The steel plate is bent into a circular path of radius 10 metres. If the plate section be 120 mm wide and 20 mm thick, then calculate the maximum bending stress. [Consider Young’s modulus = 200000 N/mm2].
a) 350 N/mm2
b) 400 N/mm2
c) 200 N/mm2
d) 500 N/mm2

Explanation: R = 10000 mm; y = 20/2 = 10 mm; E = 200000 N/mm2
By bending equation we have E/R = f/y
f = 200000×10 / 10000
= 200 N/mm2.

26 - Question

### Strength of Materials MCQs Section Modulus

What is the section modulus (Z) for a rectangular section?
a) bd2/6
b) a3/6
c) BD3-bd3
d) D4-d4

Explanation: The modulus of section may be defined as the ratio of moment of inertia to the distance to the extreme fibre. It is denoted by Z.
Z= I/y ; For rectangular section, I = bd3/12 & y = d/2.
Z= bd2/6.

27 - Question

Find the modulus of section of square beam of size 300×300 mm.<br/>

a) 4.8 × 106 mm3<br/>
b) 4.5 × 106 mm3<br/>
c) 5.6 × 106 mm3<br/>
d) 4.2 × 106 mm3

Explanation: Here, a = side of square section = 300 mm.
I = a4/12. y= a/2.
Z = I/y = a3/6
= 3003/6
= 4.5 × 106 mm3.

28 - Question

_________ of a beam is a measure of its resistance against deflection.
a) Strength
b) Stiffness
c) Deflection
d) Slope

Explanation: A beam is said to be a strength when the maximum induced bending and shear stresses are within the safe permissible stresses stiffness of a beam is a measure of its resistance against deflection.

29 - Question

To what radius an Aluminium strip 300 mm wide and 40mm thick can be bent, if the maximum stress in a strip is not to exceed 40 N/mm2. Take young’s modulus for Aluminium is 7×105 N/mm2.
a) 45m
b) 52m
c) 35m
d) 65m

Explanation: Here, b = 300mm
d= 40mm. y= 20mm.
From the relation; E/R = f/y
R= E×y/f
=70×103 × 20 / 40
= 35m.

30 - Question

The bending stress in a beam is ______ to bending moment.
a) Less than
b) Directly proportionate
c) More than
d) Equal

Explanation: As we know, the bending stress is equal to bending moment per area. Hence, as the bending (flexure) moment increases/decreases the same is noticed in the bending stress too.

31 - Question

The Poisson’s ratio for concrete is __________
a) 0.4
b) 0.35
c) 0.12
d) 0.2

Explanation: The ratio of lateral strain to the corresponding longitudinal strain is called Poisson’s ratio. The value of poisons ratio for elastic materials usually lies between 0.25 and 0.33 and in no case exceeds 0.5. The Poisson’s ratio for concrete is 0.20.

32 - Question

The term “Tenacity” means __________
a) Working stress
b) Ultimate stress
c) Bulk modulus
d) Shear modulus

Explanation: The ultimate stress of a material is the greatest load required to fracture the material divided by the area of the original cross section in the point of fracture The ultimate stress is also known as tenacity.

33 - Question

A steel rod of 25 mm diameter and 600 mm long is subjected to an axial pull of 40000. The intensity of stress is?
a) 34.64 N/mm2
b) 46.22 N/mm2
c) 76.54 N/mm2
d) 81.49 N/mm2

Explanation: Cross sectional area of steel rod [Circular]be 490.87 mm2.
The intensity of stress = P/A = 40000/490.87
= 81.49 N/mm2.

34 - Question

The bending strain is zero at _______
a) Point of contraflexure
b) Neutral axis
c) Curvature

Explanation: The neutral axis is a line of intersection of neutral plane or neutral layer on a cross section. The neutral axis of a beam passes through the centroid of the section. At the neutral axis bending stress and bending strain is zero.

35 - Question

Strength of the beam depends only on the cross section.
a) True
b) False