(a) 1N/mm2 (b) 1.

125 N/mm2
Q.1 simply supported beam of span Lcarries
A (c) 1.33 N/mm2 (d) 1.5 N/mm2
aconcentrated load W at mid-span. If the
width bof the beam is constant and its Q.5 The ratio of the flexural strengths of two
depth is varying throughout the span, then Square beams one placed with two sides
what should be its mid-span depth, when horizontal and the other placed with one
design stress is f? diagonal vertical and other horizontal is
l6WL 6WL (a) /2 (b) /3
(a) (b) bf 1
bf
(c) 5 (a)
3WL 3WL
(c) V 2bf (d) 2bf Q.6 The modular ratioof the materials used in
the flitched beam is 10and the ratio of the
Q.2 A beam of T-section hasI= 1200 cm and allowable stresses is also 10. FOur different
depth = 12 cm. Flange of the section is in sections of the beam are shown in the
compression. If the maximum tensile stress given figures. The material shown hatched
is two times the maximum compressive has larger modulus of elasticity and
stress, what is section modulus in allowable stress than the rest.
Compression? d

(a) 300 cm3 (b) 200 cm3

(c) 100 cm3 (d) None of these

Q.3 The width of a beam of uniform strength

having a constantdepth d, length L, Simply
(0) (I1)
Supportedat the ends with a central load
W is
2WL 3WL
(a) 3fd² (b) 2fd? d+2t d+2t

2fL 3fL2
(c) 3Wd4 (d) 3Wd
() (IV)
Q.4 A beam of rectangular cross-section is Which one of the following statements is
100 mm wide and 200 mm deep. If the true for the beam under consideration?
section is subjected to a shear force of (a) Allthe given sections would support
20 kN, the maximum shear stress is the same magnitude of load.
 (b) Sections I|, Illand V would support Q.10 A
beam with the cross-section given below
equal loads which is more than what is subjected to a positive bending
section Iwould support. moment (causing compression at top)of
(c) Sections I andIl would support equal 16 kNm acting around the horizontal axis.
loads which is more than what section The tensile force acting on the hatched
Illand IV would support. area of cross-section is
(d) Section lwould support greatest load.
200mm
Q.7 mm
5
600 X A +X B -X 60
mm
800 mm
25
mm

Cross-sections of two beams A (600 mm

50
mm
x 200mm) and B (800 mm x 60mm) are
shown in the figure given above. Both the
beams have the same material. By how
many times is the beam A stronger than -50 mm50 mm
the beam B in resisting bending
(a) 80 (b) 60
(a) Zero (b) 5.9 kN
(c) 50 (d) 25
(c) 8.9 kN (d) 17.8 kN
Q.8 Abeam of uniform strength refers to which
one of the following? Q.11 Shear stress in a beam having triangular
(a) Abeam in which extreme fibre cross-section is maximum at
stresses are same at all cross (a) extreme top fibre
sections along the length of the (b) mid-depth
beam (c) neutral axis
(b) A beam in which the mnoment of (d) extreme bottom fibre
inertia about the axis of bending is Q.12 The cross-section of a beam in bending is
Constant at all cross-section of the
as shown in the figure. It is subjected to
beam
shear force acting in the plane of cross
(c) A beam in which the distribution of
section.Which among the following figure
bending stress across the depth of showsthe correct shear stress distribution
cross-section is uniform at the all across the depth of the cross-section of
cross-sections of the beam
the beam?
(d) Abeam inwhich the bending stress
is uniform at the maximum bending
moment cross-section.
D/2
Q.9 Maximum shear stress in a circular cross
section is
4
(a av (b) av DI2

3
(c) av (d)
 Q.16 A beam is of I-section with flanges
mn and web 180 nrm
200 mm x 10
to the bending mornent
10 mm. Due
beam section, rmaxirurn
(a) (b) - applied on the
the beam Section ie
stress developed in
stress developedat
100 MPa, what is the
inner edge of
the flange?
(b) 100MPa
(a) 110 MPa
(d) 120 MPa
(c) 90 MPa

beam is subjected to abendina

(d) Q. 16 A MS stress of 100 MPa js
moment,such that a
distance of
developed in a layer at a
neutral layer. If
100 mm from the of
200 GPa, what is the radius
G.13 beam of square cross-section (B x B)iS
A E =
beam?
Curvature of the
used as a beam with one diagonal (b) 200 m
(a) 400 m
horizontal. The location of the maximum (d) 50 m
will be (c) 100 m
shear stress from the neutral axis
uniform strength o, having
at distance of
B
Q.17 Acantilever of constant breadth b
(b) rectangular section of
(a) zero 4 subjected to a UDL
but variable depthdis depth of the
(c)
B
(d) throughout its length. If the then
4N2 8 fixed end,
section is 150mm at the
the middle of the
Q.14 Which one of the following
diagrams what is the depth of
distribution for length of cantilever
indicates the shear stress
(b) 100 mm
the beam as shown in the figure below? (a) 150 mm
(c) 75 mm (d) 125 mm

section of 80 mm x
Q. 18 Abeam with a square
supported at its ends. A
80 mm is simply
centre of the
load W is applied at the
stress
beam. If the maximum shear
is
developed in the beam section
of W?
6 N/mm. What is the magnitude
(a) 2.56 kN (b) 25.6 kN
(b) (c) 51.2 kN (d) 5.12 kN
(a)
Q.19 A I-section is subjected to transverse
3 3 shear force. At which layer maximum
1 shear stress is developed?
2
1
2 (a) Neutral axis
(d) (b) Attop edge of flange
(c) (c) At bottom edge of flange
(d) None of these
3

**
 Q.1 A Simply supported beam with width 'b'
and depth 'd' carries a central load Wand
Undergoes deflection 8at the centre. If the
width and depth are interchanged, the M

deflection at the centre of the beam would (a) PL2/2EI + ML?I3EI

attain the value (b) PLY3EI + ML2/2EI
(C) PLI2EI + ML 73EI
(d) PL3/48EI + ML2/48EI
1/2 Q.4 Anoverhang bearm of uniform El is loaded
(d) as shown
P
Q.2 Two identical cantilevers are loaded as
B
shown in figure. If slope at the free end of A

the cantilever in figure (a) is 0, the slope

at the free end of the cantilever in figure (b) bL/3
will be
The deflection at the free end will be
PL PL3
PL (a) 81El (b) 27EI
M=
2
(a) 4PL3 2PL3
IP (c) 81EI (d) 27 EI

Q.5 A horizontal beam of length lof uniform

(b) cross-section is pinned at ends Aand B.
At end Athere isa anticlockwise
moment
(a) (b) Mand at end Bthere is clockwise moment
3 2
20
2M. The slope at end A and end B are
(c) 3 (d) 0 respectively
2ML
Q.3 The given figure shows a cantilever of span (a) and 5ML ML
(b) 3EI
L subjected to a 3EI 7EI 6E|
Concentrated load P and
moment M at the free end. Deflection at ML ang ML
the free end is given by (c) 2ML 5ML
El 7EI (d) and
3EI 6EI
 Q6 A cantlever beam of length 'T carries a Q.11 For cantilever bearn shown in the figure.
UDL Wfrom fixed end till mid
span. The the deflection at C due to a cOuple M
detlecton at the free end is given by applied at B is equal to
5w/ 7w4
(a)
384EI (b)
384EI
(C)
7 w/ w/
M

128EI (d) 384E)

ML? ML?
Q.7 A (a) 2EI (b)
cantilever beam of length 'L' is
subjectedto aconcentrated loadP at free 3ML? 2ML
end what is the deflection at the centre of (c) 2EI (d) EI
beam?
5PL'
Q.12 Consider the following statements.
PL
(a) 48EI (b) 24E| 1. Conjugate beam can be used to
determine slopes and deflection in a
5PL PL non-prismatic beam.
(c) 6EI (d) 3EI 2. Conjugate beam may be statically
Q.8 A 4-metre long beam, simply indeterminate.
supported 3. Conjugate beam method gives
at its ends; carries a point load Wat its
centre. Ifthe slope at the ends of beam is absolute slope and deflection.
The correct answer is
1°, then deflection at the centre of beam is
(a) 10.56 mm (b) 18.32 mm (a) 1and 3 (b) 1and 2
(c) 23.27 mm (d) 39.37 mm (c) 2and 3 (d) 1,2 and 3
Q.9 A simply supported beam AB of span 'T Q.13 Which of the following statements are
has a uniform cross-section throughout. It correct. Macaulay's method for calculation
carries a central concentrated load Wand of slope .and deflection in a beam is
another load which is uniformly distritbuted suitable for
Over the entire span, its total magnitude 1. Prismatic beams only.
being W. The maximum deflection in the 2. Several concentrated loads and can
beam iS be extended to uniformly distributed
9 WI loads.
13 W/
(a) (b) 3. Both prismatic and
384 EI 384 El Non-prismatic
10 WI 15 W3 beams.
384 El (3) Onl1
384 EI
(c) Only 3 (d) 2 and 3
Q.10 Acantilever beam of span 'T and uniform
flexural rigidity 'EI' is loaded with an Q.14 Asimply supported beam of span L and
upward force 'W at the mid point and depth d carries a central load W. The ratio
downward force 'P' at the free end. The of maximum deflection to maximum
deflection at the free end will be zero if bending stress is
3P L
(a) W= (b) W = 2P
2 (a) 6Ed (b) 8Ed
16P
(c) W= (d) W
= 5P L2
5 (c) (d)
12Ed 48Ed
 Q.15 Calculate the reacton at he rollet support (a) bending mornent location
(b) shear force location
for the cantilever beam shown in the figure?
(c) slope location
w/unit length
(d) shear force location and also z9ro
bending moment location

O.19 The stepped cantilever is subjected to

moments, Mas shown in the figure below
The vertical deflection at the free end
(neglecting self weight) is
3w/ 3ElA 5w/ 3EIA
(a) (b)
M

W/ 6EIA 2 EI
3w/ 6EIA
(c) 3EI (d) 8
-L/2 -LI2
Q.16 A cantilever carries a load P as shown in ML? ML?
the given figure (a) 8EI (b) 4EI

ML?
(c) 2EI (d) Zero
A B

Q.20 A simply supported beam of length 'L'

El = Constant carries two equalunlike couples. Mat the
two ends. The central deflection of the
The deflection at B is beam is given by
Pa Pa, ML? ML?
(a) 2-a) (6) 3F(-a) (a) 4EI (b) 16EI

ML? ML?
(c) 64El (d) 8EI
(c) (d)
Q.21 A simply supported beam of span 'T is
Q.17 A simply Supported beam of uniform subjected to clockwise moments M at
flexural rigidity is loaded as shown in the both the ends A and B. The rotation of
given figure. end A will be
The rotation at the end A is ML ML

oP
(a) 2E1 (b) 3El
A ML ML
B (c) 4El (a) AEL
k-L/3L3--L/3
Q.22 A beam of length L, simply supported at
PL? PL'
(a) 9EI (b) 6EI its ends and carries a UDL w throughout
its length. The centre of the beam is
PL? PL? propped so that centre is brought to the
(c) 18EI (d) 12El levelof ends. The reaction at the prop is
(a) 0.33 wL (b) 0.5 wL
Q.18 The maximum deflection of simply (c) 0.675 wL (d) None of these
Supported beam occurs at zero
 o23 A simply supported beam of length 6 m
carries a concentrated load Wat its centre
frorn A
such that BM at centre of the beam is 3
6 kNm I El is the flexural rigidity of the
beam then deflection at the centre is
(b) from B
18 3
(a) (b) E
12-b?
36 54 (c) from A
(c) 3
F (d)
EI

O.24 Abeam AB of 10 m long is supported over (d)

L2 from B
3
a spanof 8 m with equaloverhang on both
the sides. Aload Wis applied at the centre Q.27 A simply supported beam of length
of the beam. What is the slope at free ends (a+ b)carries a concentrated load Wata
of the beam?
distance 'a' from one end. If Elis flexural
6.25W 5W rigidityof the bar, the deflection under the
(a) t (b) t load will be:
EI El m|
W a?
4W (a)
(c) t (d) None of these El 6(a +b)
El
W b?
Q.25 Slope and deflection of beams of varying (b)
El 6(a + b)
flexural rigidity may be easily computed
by the method of Wa?b²
(c)
(a) Macaulay El 4(a +b)
(b) Mohr W ab2
(c) Conjugate beam (d)
El 3(a +b)
(d) Momnent distribution
Q.28 For the application of moment area method
Q.26 Asimply supported beam of length Lcarries for finding deflection at a section in a beam
a point load P as shown. The maximum (a) the position of atleast one tangent to
deflection occurs at the elastic curve, at any section should
P
be known
a
(b) the M/EIdiagram must be triangle
A (c) the beam must be of uniform moment
of inertia
(d) the BM diagram if known is sufficient
 o12 A simplv sUppoted beam is loaded as Q.17 The bendinq noment in asirnple supported
shown in the figue The maximum shear beam can be calculated with the help of
forre in the beam will be influence line drawn for the folowing types
2W
of load
(a) asingle point load
(b) a uniformly distributed load
(c) anumber of point loads
(a) Zero (b) W (d) All of the above three
(c) 2 W (d) 4 W
Q.18 In asimply Supported beam of length 'L
o 13 The shape ot the bending moment diagram with a triangular load varying from zero at
tor a cantilever beam carrying a uniformly one end to the maximum value at the other
distrbuted load over its length is end, the maximum bendingmoment is
(a) astraight line (b) a hyperbola
(c) an ell1pse (d) a parabola wL' 2wL'
(a) (b) 9/3
Q.14 Asimply supported beam is subjected to
a distributed loading as shown in the
wL
diagram given (c) (d) 943
4

w N/m Q.19 For a simply supported beam of length L

the bending moment Mis described as
M=a(x- x°/L2), 0sx<L; where a is a
Constant. The shear force willbe zero at
(a) the supports (b) x = L2
(c) x = L//3 (d) x = L/3

What is the maximum shear force in the Q.20 Match List-l (Type of beam with type of
beam? loading) with List-ll(Maximum BM formula)
(a) wL/4 (b) wL/2 and select the correct answer using the
(c) wL/3 (d) wL/6 codes given below the lists:
List-I List-|
Q.15 The point of contraflexure is a point where W

(a) Shear force changes sign WL?

(b) Bending moment changes sign A. 1.
12
(c) Shear force is maximum
(d) Bending moment is maximum w/m

Q.16 The ratio of reactions R, and R of the 2.

6
simply supported bearn (as shown) is

51 2/n 3t
wL
C. 3.
2

2m 2m 2m w/m

(a) 1/2 (b)2/3

(d) 3/2
D.f 4.
8
(c) 1
 Codes: (a) unilormly varying
A B C D (b) uniform
(a) 3 1 4 (c) zerO
and B only
(b) 2 3 (d) concentrated at A
(c) 4 3 1 diagram for the
Q.24 The correct shear force
2
(d) 2
beam shown in the figure iS
4 3
+10|
Q.21 With reference to following figure, match
01 m
LUst-l with LJst-l and select the correct
ans,C iirn halau tha

lists: 10 m

0.1t
37 kg (a)
16 kg/m
A

m
-2 3m 4 m 0.1t
(b)
Ust-l LUst-ll
A. SF at A 1. 6 kg 0.5t
B. SF at B 2. 58 kg
C. SF atC 3. 43 kg U.5t
D. SF at D 4. 48 kg (d)
Codes: beam of span Iis
A B C D Q.25 A simply supported
intensity w,
2 3 4 loaded (as shown) with a udlof
(a) 1 per unit length
1 4 2 per unit length at A and w,
(b) 3 support B is
1 1 2 at B the shear force at the
(c) given by
2 4 1 3
(d)
Q.22 In figure the maximum bending moment at W
the fixed end of the cantilever caused by W

the UDL is M.

Wim
AK B

K-/5 (w, +W;)! (W, +W, )/

(a) (b) 6
3
(c) W W,!
The bending moment at a section l/5 from (d) 3 6
the free end is 6

(a) 4% of M
(b) 5% of M
(d) 20% of M Q.28 The beam shown in the given figure hasa
(c) 10% of M design value of bending moment of
O.23 The shear force along the beam shown in 4 kN
4 kN-m 2kN-m
the figure is

a
k0.5 m-+ 4 m

(a) 8 kN-m (b) 6 kN-m

(c) 4 KN-m (d) 2 kN-m
 O27 ACantilevet heam is O.30 A proppedcantilever beanshown in the
Subjected tO
onents as shoWn in he given figure The figure given is havinginternal hinge at its
RM diaUlamfor the beam will be mid-span Which one of the following is
50 Nm the shape of bending monernt diagrarn for
the given loading?
d

2m

(a)
20kNm
-parabolic
50 KNm
(a) A
50 kNm
Straight line
(b) 80 Nm
(b) A
B parabolic
(c) 20 KNm
50 kNm (c)

B parabolic
50 kNm (d) A
(a) 80 kNm
Q.31 In the case of |-section, the web resists

Q.28 The fixed end mainly

moment M, of the beam (a) axial force
shown in the given figure is (b) shear force
Hinge |20kN (c) bending moment
BA (d) both shear force and bending moment
Q.32 A 10 m long beam carries point loads.
4m4m 2m When SF diagram is drawn, there are two
Ro
(a) +40 kNm (b) -40 kNm rectangles of 10 kN x 2m side; one is
(c) +80 kNm starting from one end and above the base
(d) -80 kNm
and other starting from the other end and
Q.29 A simply Supported beam with equal below the base line. The BM at the centre
Overhang on both sides is loaded as of the beam is
shown in the figure. If the bending moment (a) 20 kNm (b) 30 kNm
at mid-span is zero, then the percentage (c) 40 kNm (d) 50 kNm
Overhang on each side will be Q.33 A beam of overall length I with equal
Overhangs on both sides carries a
uniformly distributed load over the entire
length. To have numerically equal bending
(a) 33.3 (b) 25 moments at centre of the beam and at
(c) 20 (d) 15 supports, the distance between the
supports should be:
(a) 0.2771 (b) 0.403 /
(c) 0.586/ (d) 0.7071