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# Strength of Materials MCQs Maximum Shear Force

Which of these is the correct way of sign convention for shear force?

a) R U P

b) L U P

c) R U N

d) L D P

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Answer: c

Explanation: According to the theoretical approach, there are many sign conventions to follow but the standard one is “right upwards negative” the sign convention is thoroughly followed unanimously.

At hinge, the moments will be _________

a) Maximum

b) Minimum

c) Uniform

d) Zero

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Answer: d

Explanation: At the support of a member, there is no distance prevailing to take the upcoming load. As we know the moment is a product of force and perpendicular distance, but at hinge (end support) the distance is zero. Hence the moment developed is zero.

What is variation in SFD, if the type of loading in the simply supported beam is U.D.L is ____

a) Rectangle

b) Linear

c) Trapezoidal

d) Parabolic

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Answer: b

Explanation: The shear force is defined as the algebraic sum of all the forces taken from any one of the section. If you figure out the SFD for a simply supported beam carrying U.D.L throughout its entire length, in the SFD we can observe that shear force is same at supports. In the centre, the shear force is zero. Hence the diagram varies linearly.

The rate of change of shear force is equal to _____

a) Direction of load

b) Change in BMD

c) Intensity of loading

d) Maximum bending

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Answer: c<br/>

Explanation: Consider a simply supported beam subjected to udl for the entire span considered a free body diagram of small portion of elemental length dx.

Let the shear force at left of the section is = F

Let the increase in shear force in length of the dx = dF

Let the Indian city of load on this part of the beam = w

Total downward load in this elemental length = wdx

€V = 0

dF = -wdx

dF/dx = -w

This rate of change of shear force at any section is equal to the intensity of loading at that section.

The shear force in a beam subjected to pure positive bending is _____

a) Positive

b) Negative

c) Zero

d) Cannot determine

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Answer: c

Explanation: In the determination of shear force and bending moment diagrams it is clear that shear force changes its sign when the bending moment in a beam is maximum and the shear force in a beam subjected to pure positive bending will be zero as the neutralizing effect comes under.

In SFD, vertical lines are for ______

a) Point loads

b) UDL

c) UVL

d) LDP

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Answer: a

Explanation: Shear Force diagram started from left side of the m as per the load. For point loads draw vertical lines and under UDL draw slope lines.

A cantilever beam loaded with udl throughout, the maximum shear force occurs at____

a) Free end

b) Fixed end

c) At centre

d) At point of contraflexure

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Answer: b

Explanation: In a case of a cantilever beam subjected to udl, at the free end there will be zero shear force because, we need to convert udl to load by multiplying with distance. Hence at the fixed end the shear force is w×l i.e (maximum).

A simply supported beam of span 1 m carries a point load “w” in centre determine the shear force in the half left of the beam.

a) W/3

b) W/4

c) W/2

d) W

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Answer: c

Explanation: Let the two ends of the beam be A and B, the given load on a beam is symmetrical hence RA = RB= W/2. SFD at any section in the left of the beam is equal to the W/2. SFDat any section in the right half of the beam is equal to -W/2.

At the Point of contraflexure, what is the value of bending moment?

a) one

b) zero

c) three

d) infinity

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Answer: b

Explanation: Point of contraflexure in a beam is a point at which bending moment changes its sign from positive to negative and vice versa. At the point of contraflexure, the value of bending moment is zero.

When SF is zero, the bending moment is _____

a) Zero

b) Maximum

c) Very difficult to say

d) Minimum

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Answer: b

Explanation: When is shear force changes its sign, the bending moment in a beam will be either maximum positive or maximum negative. This is because of the sign convention adopted.

Strength of Materials MCQs Maximum Bending Moment

A cantilever beam subjected to point load at its free end, the maximum bending moment develops at the ________ of the beam.

a) Free end

b) Fixed end

c) Centre

d) Point of inflection

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Answer: b

Explanation: As the moment is the product of perpendicular distance and force. In cantilever beam, at its free end the moment will be zero as there is no distance, but at the fixed end the moment is maximum that is W×l.

Bending moment in a beam is maximum when the _________

a) Shear force is minimum

b) Shear force is maximum

c) Shear force is zero

d) Shear force is constant

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Answer: c

Explanation: The maximum bending moment occurs in a beam, when the shear force at that section is zero or changes the sign because at point of contra flexure the bending moment is zero.

Positive bending moment is known as _______

a) Hogging

b) Sagging

c) Ragging

d) Inflection

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Answer: a

Explanation: The positive bending moment in a section is considered because it causes convexity downwards. Such bending moment is called a sagging bending moment or positive bending moment.

A simply supported beam of span “x” meters carries a udl of “w” per unit length over the entire span, the maximum bending moment occurs at _____

a) At point of contra flexure

b) Centre

c) End supports

d) Anywhere on the beam

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Answer: b<br/>

Explanation: As we know that BM occurs at center. Because at supports the moment is obviously zero.

At the centre, maximum bending moment is wl2/8.

The maximum BM is ______

a) 40 kNm

b) 50 kNm

c) 90 kNm

d) 75 kNm

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Answer: c

Explanation: Above diagram depicts cantilever beam subjected to point load at the free end. The maximum bending moment at A is W × I

= 30 × 3

= 90 kNm.

Bending moment can be denoted by ____

a) K

b) M

c) N

d) F

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Answer: b

Explanation: Bending moment is the product of force and perpendicular distance. Units are kNm

It is denoted by “M”. Whereas SF is denoted by “F”.

Number of points of contra flexure for a double over hanging beam.

a) 3

b) 2

c) 4

d) Infinite

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Answer: b

Explanation: Point of contraflexure in a beam is a point at which bending moment changes its sign from positive to negative and vice versa. In the case of overhanging beam, there will be two points of contraflexure.

Maximum bending moment in a cantilever beam subjected to udl (w)over the entire span (l).

a) wl

b) wl3

c) wl2

d) w

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Answer: c

Explanation: In a cantilever beam the maximum bending moment occurs at the fixed end. Moment at the free end is 0 and maximum at the fixed end. Maximum shear force is w×l.

Determine the maximum bending moment for the below figure.<br/>

a) wl/2<br/>

b) wl/3<br/>

c) wl/4<br/>

d) wl

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Answer: c

Explanation: First of all, let’s assume the length between end supports be ”l” the maximum bending moment in a simply supported beam with point load at its centre is wl/4. We know that in simply supported beam the maximum bending moment occurs at the centre only.

What is the variation in the BM, if the simply supported beam carries a point load at the centre.

a) Triangular

b) Rectangular

c) Trapezoidal

d) Other quadrilateral

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Answer: a<br/>

Explanation: For simply supported beam with point load at the centre, the maximum bending moment will be at the centre i.e. wl/4. The variation in bending moment is triangular.

### Strength of Materials MCQs Shear Force and Bending Moment diagram

What is the bending moment at end supports of a simply supported beam?

a) Maximum

b) Minimum

c) Zero

d) Uniform

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Answer: c

Explanation: At the end supports, the moment (couple) developed is zero, because there is no distance to take the perpendicular acting load. As the distance is zero, the moment is obviously zero.

What is the maximum shear force, when a cantilever beam is loaded with udl throughout?

a) w×l

b) w

c) w/l

d) w+l

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Answer: a

Explanation: In cantilever beams, the maximum shear force occurs at the fixed end. In the free end, there is zero shear force. As we need to convert the udl in to load, we multiply the length of the cantilever beam with udl acting upon. For maximum shear force to obtain we ought to multiply load and distance and it surely occurs at the fixed end (w×l).

Sagging, the bending moment occurs at the _____ of the beam.

a) At supports

b) Mid span

c) Point of contraflexure

d) Point of emergence

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Answer: b

Explanation: The positive bending moment is considered when it causes convexity downward or concavity at top. This is sagging. In simply supported beams, it occurs at mid span because the bending moment at the supports obviously will be zero hence the positive bending moment occurs in the mid span.

What will be the variation in BMD for the diagram? [Assume l = 2m].<br/>

a) Rectangular<br/>

b) Trapezoidal<br/>

c) Triangular<br/>

d) Square

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Answer: c<br/>

Explanation: At support B, the BM is zero. The beam undergoes maximum BM at fixed end.

By joining the base line, free end and maximum BM point. We obtain a right angled triangle.

What is the maximum bending moment for simply supported beam carrying a point load “W” kN at its centre?

a) W kNm

b) W/m kNm

c) W×l kNm

d) W×l/4 kNm

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Answer: d

Explanation: We know that in simply supported beams the maximum BM occurs at the central span.

Moment at A = Moment at B = 0

Moment at C = W/2 × l/2 = Wl/ 4 kNm (Sagging).

How do point loads and udl be represented in SFD?

a) Simple lines and curved lines

b) Curved lines and inclined lines

c) Simple lines and inclined lines

d) Cant represent any more

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Answer: c<br/>

Explanation: According to BIS, the standard symbols used for sketching SFD are

Point load = ———–

________ curve is formed due to bending of over hanging beams.

a) Elastic

b) Plastic

c) Flexural

d) Axial

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Answer: a

Explanation: The line to which the longitudinal axis of a beam bends or deflects or deviates under given load is known as elastic curve on deflection curve. Elastic curve can also be known as elastic line or elastic axis.

The relation between slope and maximum bending moment is _________

a) Directly proportion

b) Inversely proportion

c) Relative proportion

d) Mutual incidence

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Answer: b

Explanation: The relationship between slope and maximum bending moment is inversely proportional because, For example in simply supported beams slope is maximum at supports and zero at midspan of a symmetrically loaded beam where as bending moment is zero at supports and maximum at mid span. Hence we conclude that slope and maximum bending moment are inversely proportional to each other in a case of the simply supported beam.

What is the SF at support B?<br/>

a) -54 kNm<br/>

b) -92 kNm<br/>

c) -105 kNm<br/>

d) – 65 kNm

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Answer: d

Explanation: Total load = 2×2 = 4kN

Shear force at A = 4 kN ( same between A and C )

Shear force at C = 4 kN

Shear force at B = 0 kN

Maximum SF at A = 4 kN.

Where do the maximum BM occurs for the below diagram.<br/>

a) -54 kNm<br/>

b) -92 kNm<br/>

c) -105 kNm<br/>

d) – 65 kNm

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Answer: c

Explanation: Moment at B = 0

Moment at C = – (10 × 3) × (3/2)

= – 45 kNm

Moment at A = – (10 × 3) × (1.5 + 2 )

Maximum BM at A = – 105 kNm

= 105 Nm (hogging).