A cantilever beam AB of span ‘L’ is subjected to a moment ‘M’ at the free end as shown in figure. What is the slope and deflection at free end B?

\(\frac{M}{{LEI}}\frac{{M{L^2}}}{{EI}}\)

\(\frac{{ML}}{{EI}},\;\frac{{M{L^2}}}{{2EI}}\)

\(\frac{M}{{LEI}}\frac{{M{L^2}}}{{EI}}\)

\(\frac{{2ML}}{{EI}},\frac{{2M{L^2}}}{{EI}}\)

\(\frac{{ML}}{{EI}},\frac{{2M{L^2}}}{{EI}}\)

Choose the INCORRECT option for the equation of elongation of a uniform rod having length L due to the self-weight W.

\(\delta = \frac{{WL}}{{2AE}}\)

\(\delta = \frac{{2WL}}{{AE}}\)

\(\delta = \frac{{2WL}}{{AE}}and\;\delta = \frac{{WL}}{{AE}}both\)

A cantilever beam of span I and flexural rigidity EI is subjected to a concentrated load W at mid-span. The slope at the free end is

\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{3{\rm{EI}}}}\)

\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{2{\rm{EI}}}}\)

\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{4{\rm{EI}}}}\)

\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{8{\rm{EI}}}}\)

\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{3{\rm{EI}}}}\)

Assertion (A): The principle of superposition for deflection of beams subjected to a number of loads can be applied in the case of large deformations.Reason (R): In the principle of superposition, the resultant deflection due to all the loads will be the algebraic sum of the deflections due to each load acting separately.

Both A and R are true and R is the correct explanation of A

Both A and R are true but R is not the correct explanation of A

If the hinged end of a propped cantilever of span L and flexural rigidity EI undergoes a rotation, then the shear force in the beam will be

\(\frac{{{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)

\(\frac{{2{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)

\(\frac{{3{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)

\(\frac{{6{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)

A short column of external diameter D and internal diameter d is subjected to a compressive load P acting with an eccentricity ‘e’. If the stresses at one of the extreme fibre is zero then the eccentricity has to be

\(\frac{{{{\rm{D}}^2} - {{\rm{d}}^2}}}{{8{\rm{D}}}}\)

\(\frac{{{{\rm{D}}^2} + {{\rm{d}}^2}}}{{8{\rm{\pi D}}}}\)

\(\frac{{{{\rm{D}}^2} + {{\rm{d}}^2}}}{{8{\rm{D}}}}\)

\(\frac{{{{\rm{D}}^2} - {{\rm{d}}^2}}}{{8{\rm{D}}}}\)

\(\frac{{{{\rm{D}}^3} - {{\rm{d}}^3}}}{{8{{\rm{D}}^2}}}\)

A cantilever beam ACB has end A fixed and subjected to a point load P at free end B. The point C is mid-point of AB and the moment of inertia of AC is twice that of CB. The deflection at the free end will be

\(\frac{{5\;P{l^3}}}{{96\;EI}}\)

\(\frac{{9\;P{l^3}}}{{48\;EI}}\)

A simply-supported beam of length l carries two equal unlike couples M at two ends. If the flexural rigidity EI = constant, then the central deflection of the beam is given by

\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{4{\rm{EI}}}}\)

\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{64{\rm{EI}}}}\)

\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{16{\rm{EI}}}}\)

\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{8{\rm{EI}}}}\)

For a simply supported beam of span L and carrying a uniformly distributed load of W kN/m over the entire span, the maximum deflection is

\(\frac{7~W{{L}^{4}}}{384~EI}\)

\(\frac{9~W{{L}^{4}}}{384~EI}\)

\(\frac{5~W{{L}^{4}}}{384~EI}\)

For both ends of the fixed beam shown in the figure carrying a concentrated load eccentrically placed on the beam, deflection under load is

\(- \frac{{W{a^3}{b^2}}}{{3EI{L^{2\;}}}}\)

\( - \frac{{W{a^2}{b^2}}}{{3\;EI{L^2}}}\)

\( - \frac{{Wa{b^2}}}{{3EIL}}\)

\( - \frac{{W{a^3}{b^3}}}{{3EI{L^3}}}\)

\(- \frac{{W{a^3}{b^2}}}{{3EI{L^{2\;}}}}\)

If a prismatic bar of uniform c / s ‘A’ and length ‘L’ is suspended from top, then the elongation of bar due to its self-weight only is ______. Where E is modulus of elasticity of bar material and γ is the density of bar.

\(\frac{{\gamma {L^2}}}{{3E}}\)

\(\frac{{\gamma {L^2}}}{{2E}}\)

\(\frac{{\gamma {L^2}}}{{3E}}\)

\(\frac{{\gamma {L^2}}}{{5E}}\)

\(\frac{{\gamma {L^2}}}{{6E}}\)

For a beam as shown below, the maximum deflection is

\(\frac{5}{{384}}\frac{{W{L^4}}}{{EI}}\)

If the strain energy of a deformed elastic body is represented as a function of the displacements d1, d2, ...., a partial derivative of that function with respect to any chosen displacement gives the corresponding force. This statement/ principle is called as

Maxwell's law of reciprocal delfections

Conjugate beam/ truss principle

A simply supported beam of a span, L is subjected to a point load, P at its mid-span. The maximum deflection induced will be:Where EI is flexural rigidity

\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{8{\rm{EI}}}}\)

\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{96{\rm{EI}}}}\)

\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{24{\rm{EI}}}}\)

\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{48{\rm{EI}}}}\)

\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{8{\rm{EI}}}}\)

A cantilever of length l, and flexural rigidity El, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown.The transverse deflection under the load is

\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI}}{{3EI\;+\;2k{l^3}}}} \right]\)

\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{6EI\;-\;k{l^3}}}{{6EI}}} \right]\)

\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI\;-\;k{l^3}}}{{3EI}}} \right]\)

\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI}}{{3EI\;+\;k{l^3}}}} \right]\)

87 + Mcqs in Deflection Of Beam in Civil Engineering Page 1 McqOptions

1.	Clockwise moments M at one end and anti-clockwise moments M at another end is acting on a uniform simply supported beam. The ratio of slope at the centre to the slope at end will be
A.	0
B.	1
C.	2
D.	3
Answer» B. 1

Discussion

2.	A 6.4 m long simply wrought iron beam carries a point load of 48 kN at its mid-point. The moment of inertia is 80 × 106 mm4. If the elastic modulus is 192 Gpa, then the deflection at the mid-point of the beam is
A.	15.06
B.	16.26
C.	17.3
D.	17.8
E.	17.06
Answer» F.

Discussion

3.	A cantilever beam AB of span ‘L’ is subjected to a moment ‘M’ at the free end as shown in figure. What is the slope and deflection at free end B?
A.	\(\frac{{ML}}{{EI}},\;\frac{{M{L^2}}}{{2EI}}\)
B.	\(\frac{M}{{LEI}}\frac{{M{L^2}}}{{EI}}\)
C.	\(\frac{{2ML}}{{EI}},\frac{{2M{L^2}}}{{EI}}\)
D.	\(\frac{{ML}}{{EI}},\frac{{2M{L^2}}}{{EI}}\)
Answer» B. \(\frac{M}{{LEI}}\frac{{M{L^2}}}{{EI}}\)

Discussion

4.	Choose the INCORRECT option for the equation of elongation of a uniform rod having length L due to the self-weight W.
A.	\(\delta = \frac{{WL}}{{2AE}}\)
B.	\(\delta = \frac{{2WL}}{{AE}}\)
C.	\(\delta = \frac{{WL}}{{AE}}\)
D.	\(\delta = \frac{{2WL}}{{AE}}and\;\delta = \frac{{WL}}{{AE}}both\)
Answer» E.

Discussion

5.	A fletched beam composed of two different pieces, each having breath b and depth d, supports an external load. This statement implies that1. the two different materials are rigidly connected2. there will be relative movement between the two materials3. for transforming into an equivalent single-material section under ‘strength’ consideration, the depth is kept constant and only the breadth is variedWhich of the above statement are correct?
A.	1 and 2 only
B.	1 and 3 only
C.	2 and 3 only
D.	1, 2 and 3
Answer» C. 2 and 3 only

Discussion

6.	A beam-column is alternately bent either (1) in single curvature, or (2) in double curvature. The secondary moments induced are to be compared. These are indicated SM1 and SM2 as per the conditions (1) and (2) respectively
A.	SM1 > SM2
B.	SM1 < SM2
C.	SM1 = SM2
D.	Cannot be ascertained
Answer» B. SM1 < SM2

Discussion

7.	A cantilever beam is deflected by δ due to load P. If length of beam is doubled, the deflection compared to earlier case will be changed by a factor of:
A.	2
B.	1/2
C.	1/8
D.	8
Answer» E.

Discussion

8.	A cantilever beam of length ‘L’ is subjected to an end load ‘P’. What is the deflection under the load?
A.	PL3/24EI
B.	PL3/EI
C.	PL3/3EI
D.	PL3/48EI
Answer» D. PL3/48EI

Discussion

9.	A cantilever beam of span I and flexural rigidity EI is subjected to a concentrated load W at mid-span. The slope at the free end is
A.	\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{2{\rm{EI}}}}\)
B.	\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{4{\rm{EI}}}}\)
C.	\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{8{\rm{EI}}}}\)
D.	\(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{3{\rm{EI}}}}\)
Answer» D. \(\frac{{{\rm{W}}{{\rm{l}}^2}}}{{3{\rm{EI}}}}\)

Discussion

10.	Assertion (A): The principle of superposition for deflection of beams subjected to a number of loads can be applied in the case of large deformations.Reason (R): In the principle of superposition, the resultant deflection due to all the loads will be the algebraic sum of the deflections due to each load acting separately.
A.	Both A and R are true and R is the correct explanation of A
B.	Both A and R are true but R is not the correct explanation of A
C.	A is true but R is false
D.	A is false but R is true
Answer» E.

Discussion

11.	If the hinged end of a propped cantilever of span L and flexural rigidity EI undergoes a rotation, then the shear force in the beam will be
A.	\(\frac{{{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)
B.	\(\frac{{2{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)
C.	\(\frac{{3{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)
D.	\(\frac{{6{\rm{EI}}}}{{{{\rm{L}}^2}}}{\rm{\theta }}\)
Answer» E.

Discussion

12.	A short column of external diameter D and internal diameter d is subjected to a compressive load P acting with an eccentricity ‘e’. If the stresses at one of the extreme fibre is zero then the eccentricity has to be
A.	\(\frac{{{{\rm{D}}^2} + {{\rm{d}}^2}}}{{8{\rm{\pi D}}}}\)
B.	\(\frac{{{{\rm{D}}^2} + {{\rm{d}}^2}}}{{8{\rm{D}}}}\)
C.	\(\frac{{{{\rm{D}}^2} - {{\rm{d}}^2}}}{{8{\rm{D}}}}\)
D.	\(\frac{{{{\rm{D}}^3} - {{\rm{d}}^3}}}{{8{{\rm{D}}^2}}}\)
Answer» C. \(\frac{{{{\rm{D}}^2} - {{\rm{d}}^2}}}{{8{\rm{D}}}}\)

Discussion

13.	Determine the equivalent stiffness in (N/m) of the system shown below:
A.	2.1 × 109
B.	4.2 × 109
C.	21 × 109
D.	42 × 109
Answer» C. 21 × 109

Discussion

14.	If the depth of a simply supported beam carrying an isolated load at its centre, is doubled then the deflection of the beam at the centre will be changed by a factor of
A.	2
B.	½
C.	8
D.	1/8
Answer» E.

Discussion

15.	In the case of a beam simply supported at both ends, if the same load instead of being concentrated at centre is distributed uniformly throughout the length, then deflection at centre will get reduced by
A.	1/2 times
B.	1/4 times
C.	5/8 times
D.	3/8 times
Answer» E.

Discussion

16.	A cantilever beam ACB has end A fixed and subjected to a point load P at free end B. The point C is mid-point of AB and the moment of inertia of AC is twice that of CB. The deflection at the free end will be
A.	\(\frac{{P{l^3}}}{{3\;EI}}\)
B.	\(\frac{{P{l^3}}}{{48\;EI}}\)
C.	\(\frac{{5\;P{l^3}}}{{96\;EI}}\)
D.	\(\frac{{9\;P{l^3}}}{{48\;EI}}\)
Answer» E.

Discussion

17.	A simply supported beam with a rectangular cross-section is subjected to a central concentrated load. If the width and depth of the beam are doubled, while retaining the same elastic properties, then the deflection at the center of the beam w.r.t. the original deflection will be reduced to
A.	50%
B.	25%
C.	75%
D.	12.50%
E.	6.25%
Answer» F.

Discussion

18.	A free end of a cantilever beam rotates by 0.001 radians under a point load 10 kN. Then deflection at the free end due to a moment of 100 KN - m is:
A.	10 mm
B.	20 mm
C.	25 mm
D.	40 mm
Answer» B. 20 mm

Discussion

19.	Deflection of a Cantilever beam, measured at its free end, subjected to uniform load intensity ‘w’ over a span ‘l’ is given as: (E = Young’s Modulus; I = Moment of Inertia about Neutral axis)
A.	wl4/6EI
B.	wl4/8EI
C.	wl4/ 4EI
D.	wl4/16EI
Answer» C. wl4/ 4EI

Discussion

20.	A simply-supported beam of length l carries two equal unlike couples M at two ends. If the flexural rigidity EI = constant, then the central deflection of the beam is given by
A.	\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{4{\rm{EI}}}}\)
B.	\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{64{\rm{EI}}}}\)
C.	\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{16{\rm{EI}}}}\)
D.	\(\frac{{{\rm{M}}{{\rm{l}}^2}}}{{8{\rm{EI}}}}\)
Answer» E.

Discussion

21.	A simply supported beam of constant flexural rigidity and length 2L carries a concentrated load P at its mid-span and the deflection under the load is δ. If a cantilever beam of the same flexural rigidity and length L is subjected to a load P at its free end, then the deflection at the free end will be
A.	δ/2
B.	δ
C.	2δ
D.	4δ
Answer» D. 4δ

Discussion

22.	In slope deflection equations, the deformations are considered to be caused by
A.	Axial force
B.	Shear force
C.	Bending moment
D.	All the above
Answer» D. All the above

Discussion

23.	An overhanging beam, having same overhangs of length L/2 on both the sides, is subjected to clockwise moment M on the left side free end and anticlockwise moment M on the right side free end. What is the deflection of midpoint of the beam, if distance between the supports is L? (Take Flexural Rigidity of beam = EI)
A.	Zero
B.	ML2/2EI
C.	ML2/8EI
D.	ML2/9√3EI
Answer» B. ML2/2EI

Discussion

24.	For a simply supported beam of span L and carrying a uniformly distributed load of W kN/m over the entire span, the maximum deflection is
A.	\(\frac{7~W{{L}^{4}}}{384~EI}\)
B.	\(\frac{9~W{{L}^{4}}}{384~EI}\)
C.	\(\frac{5~W{{L}^{4}}}{384~EI}\)
D.	\(\frac{W{{L}^{4}}}{384~EL}\)
Answer» D. \(\frac{W{{L}^{4}}}{384~EL}\)

Discussion

25.	Maximum deflection of cantilever is equal to ______ (where W is load, I is length, E is Young’s modulus and I is moment of inertia)
A.	\(\frac{Wl^4}{2EI}\)
B.	\(\frac{Wl^4}{4EI}\)
C.	\(\frac{Wl^4}{8EI}\)
D.	\(\frac{Wl^4}{16EI}\)
Answer» D. \(\frac{Wl^4}{16EI}\)

Discussion

26.	A simply supported beam AB of span 10 m carries a point load W = 10 kN at C such that AC = 3 m and BC = 7 m, maximum deflection occur ______.
A.	at C
B.	at centre of span
C.	between A and C
D.	between B and C
Answer» E.

Discussion

27.	For both ends of the fixed beam shown in the figure carrying a concentrated load eccentrically placed on the beam, deflection under load is
A.	\( - \frac{{W{a^2}{b^2}}}{{3\;EI{L^2}}}\)
B.	\( - \frac{{Wa{b^2}}}{{3EIL}}\)
C.	\( - \frac{{W{a^3}{b^3}}}{{3EI{L^3}}}\)
D.	\(- \frac{{W{a^3}{b^2}}}{{3EI{L^{2\;}}}}\)
Answer» D. \(- \frac{{W{a^3}{b^2}}}{{3EI{L^{2\;}}}}\)

Discussion

28.	If a prismatic bar of uniform c / s ‘A’ and length ‘L’ is suspended from top, then the elongation of bar due to its self-weight only is ______. Where E is modulus of elasticity of bar material and γ is the density of bar.
A.	\(\frac{{\gamma {L^2}}}{{2E}}\)
B.	\(\frac{{\gamma {L^2}}}{{3E}}\)
C.	\(\frac{{\gamma {L^2}}}{{5E}}\)
D.	\(\frac{{\gamma {L^2}}}{{6E}}\)
Answer» B. \(\frac{{\gamma {L^2}}}{{3E}}\)

Discussion

29.	A simply supported beam of span l is carrying a point load W at mid span. The deflection at the centre of the beam is equal to
A.	WL2/48EI
B.	WL3/48EI
C.	5WL3/348EI
D.	WL2/348EI
Answer» C. 5WL3/348EI

Discussion

30.	A simply supported beam of span 'L' is carrying uniformly distributed load 'w' on the entire span. If uniformly distributed load is replaced by a concentrated load 'W' at centre such that it produces same deflection at centre. Keeping all other parameters same, ratio of 'W' to 'w' will be:
A.	\(\dfrac{5L}{8}\)
B.	\(\dfrac{5L}{48EI}\)
C.	\(\dfrac{L}{8}\)
D.	\(\dfrac{8L}{5}\)
Answer» B. \(\dfrac{5L}{48EI}\)

Discussion

31.	Deflections in a truss depends upon
A.	axial rigidity
B.	flexural rigidity
C.	axial and flexural rigidity
D.	None of these
Answer» B. flexural rigidity

Discussion

32.	For a beam as shown below, the maximum deflection is
A.	\(\frac{{W{L^3}}}{{3\;EI}}\)
B.	\(\frac{{W{L^3}}}{{48\;EI}}\)
C.	\(\frac{{W{L^2}}}{{2\;EI}}\)
D.	\(\frac{5}{{384}}\frac{{W{L^4}}}{{EI}}\)
Answer» C. \(\frac{{W{L^2}}}{{2\;EI}}\)

Discussion

33.	A cantilever beam of length ‘L’ carries a concentrated load ‘P’ at its midpoint, what is the deflection of the free end of the beam?
A.	\(\frac{{P{L^3}}}{{24EI}}\)
B.	\(\frac{{P{L^3}}}{{48EI}}\)
C.	\(\frac{{P{L^3}}}{{16EI}}\)
D.	\(\frac{{5P{L^3}}}{{48EI}}\)
Answer» E.

Discussion

34.	A cantilever beam of length L (EI being constant throughout the section) is subjected to a couple M at the free end. The slope and deflection at the free end will be given by
A.	ML/EI & ML2/2EI
B.	2ML/EI & ML2/2EI
C.	ML/EI & ML2/4EI
D.	ML/EI & ML2/8EI
E.	ML3/EI & ML2/2EI
Answer» B. 2ML/EI & ML2/2EI

Discussion

35.	A beam of length L simply supported at its ends carrying a total load W uniformly distributed over its entire length deflects at the center by δ and has a maximum bending stress σ. If the load is substituted by a concentrate load W1 at mid-span such that the deflection at the center remains unchanged, the magnitude of the load W1 and the maximum bearding stress will be
A.	0.3 W and 0.3σ
B.	0.6 W and 0.6σ
C.	0.3 W and 0.6σ
D.	0.6 W and 1.25σ
Answer» E.

Discussion

36.	A beam of span l is fixed at one end and simply supported at other end. It carries uniformly distributed load of w per unit run over the whole span. The reaction at the simply supported end is
A.	\(\frac{3}{8}wL\)
B.	\(\frac{{wL}}{2}\)
C.	\(\frac{5}{8}wL\)
D.	\(\frac{{3wL}}{4}\)
Answer» B. \(\frac{{wL}}{2}\)

Discussion

37.	A beam of length L and flexural rigidity El is simply supported at the ends and carries a concentrated load W at the middle of the span. Another beam of identical length L and flexural rigidity El is fixed horizontally at both ends and carries an identical concentrated load W at the mid-span. The ratio of central deflection of the first beam to that of the second beam is
A.	1
B.	2
C.	0.25
D.	4
Answer» E.

Discussion

38.	For a symmetric continuous beam shown below, which is the correct distribution at B -
A.	δBA : δBC = 3 : 8
B.	δBA : δBC = 3 : 4
C.	δBA : δBC = 1 : 2
D.	δBA : δBC = 3 : 2
Answer» C. δBA : δBC = 1 : 2

Discussion

39.	In the propped cantilever as shown in figure, the value of propped reaction ‘R’ will be:
A.	9 kN
B.	6 kN
C.	3 kN
D.	2 kN
Answer» B. 6 kN

Discussion

40.	If the strain energy of a deformed elastic body is represented as a function of the displacements d1, d2, ...., a partial derivative of that function with respect to any chosen displacement gives the corresponding force. This statement/ principle is called as
A.	Principle of strain energy
B.	Maxwell's law of reciprocal delfections
C.	Conjugate beam/ truss principle
D.	First theorem of Castigliano
E.	Bette's law
Answer» E. Bette's law

Discussion

41.	A square bar of side 5 mm and 200 mm long, experience an extension of 0.01 mm upon a load of 100 N. Then young’s Modulus of the material is:
A.	200 GPa
B.	800 GPa
C.	80 GPa
D.	400 GPa
Answer» D. 400 GPa

Discussion

42.	A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is L, Young’s modulus E, and area moment of inertia I, the magnitude of the maximum deflection is
A.	\(\frac{{q{L^4}}}{{15EI}}\)
B.	\(\frac{{q{L^4}}}{{30EI}}\)
C.	\(\frac{{q{L^4}}}{{10EI}}\)
D.	\(\frac{{q{L^4}}}{{60EI}}\)
Answer» C. \(\frac{{q{L^4}}}{{10EI}}\)

Discussion

43.	If a simply supported beam with elastic modulus & MOI, E and I and of span length L carries a point load W at the mid-span, the downward deflection under the load will be
A.	WL3/3EI
B.	WL3/8EI
C.	WL3/48EI
D.	WL3/12EI
E.	WL3/9EI
Answer» D. WL3/12EI

Discussion

44.	A girder of uniform section and constant depth is freely supported over a span of 3 metres. The point load at the midpoint is 30 kN and Moment of inertia = 15 × 10-6 m4 and youngs modulus = 200 GN / m2. The deflection at centre will be
A.	6.6 mm
B.	8.6 mm
C.	5.6 mm
D.	6.6 m
Answer» D. 6.6 m

Discussion

45.	A simply supported beam of width 'b' and depth 'd' is subjected to a point load 'w' at its centre causing deflection 'δ' at that point. If the width and depth are interchanged the central deflection would be:
A.	\((\frac{d}{b})\delta\)
B.	\((\frac{d}{b})^2\delta\)
C.	\((\frac{d}{b})^3\delta\)
D.	\((\frac{d}{b})^{3/2}\delta\)
Answer» C. \((\frac{d}{b})^3\delta\)

Discussion

46.	Consider the beam shown in figure. The beam is simply supported at its left end A and fixed at its right end B. It carries a load that varies in intensity from zero at support A to ‘w’ at another support B according to the relation wx = (x/L)w. The reaction component at A is
A.	wL/10
B.	2wL/5
C.	5wL/2
D.	wL/5
Answer» B. 2wL/5

Discussion

47.	A simply supported beam of a span, L is subjected to a point load, P at its mid-span. The maximum deflection induced will be:Where EI is flexural rigidity
A.	\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{96{\rm{EI}}}}\)
B.	\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{24{\rm{EI}}}}\)
C.	\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{48{\rm{EI}}}}\)
D.	\(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{8{\rm{EI}}}}\)
Answer» D. \(\frac{{{\rm{P}}{{\rm{L}}^3}}}{{8{\rm{EI}}}}\)

Discussion

48.	A cantilever of length l, and flexural rigidity El, stiffened by a spring of stiffness k, is loaded by a transverse force P, as shown.The transverse deflection under the load is
A.	\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI}}{{3EI\;+\;2k{l^3}}}} \right]\)
B.	\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{6EI\;-\;k{l^3}}}{{6EI}}} \right]\)
C.	\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI\;-\;k{l^3}}}{{3EI}}} \right]\)
D.	\(\frac{{P{l^3}}}{{3EI}}\left[ {\frac{{3EI}}{{3EI\;+\;k{l^3}}}} \right]\)
Answer» E.

Discussion

49.	For the cantilever beam shown below, the moment to be applied at free end for zero vertical deflection at that point is -?
A.	9 kN.m anti clockwise
B.	9 kN.m clockwise
C.	12 kN.m clockwise
D.	12 kN.m anti clockwise
Answer» D. 12 kN.m anti clockwise

Discussion

50.	A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased by 19%, the tip deflection decreases approximately by
A.	19%
B.	29%
C.	41%
D.	50%
Answer» E.

Discussion

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