SUB: STRUCTURAL ANALYSIS
MODULE-28C
MODULE-28C
Analysis of statically indeterminate structures by force methods.
.__________________________________________________________________________
_
1.
Identify the FALSE statement from the following, pertaining to the
effects due to a temperature rise ΔT in the bar BD alone in the
plane truss shown below:
(A) No reactions develop at supports A and D
(B) The bar BD will be subject to a tensile force
(C) The bar AC will be subject to a compressive force
(D) The bar BC will be subject to a tensile force
Ans: (b)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
2.
The degree of static indeterminacy, , and the degree of kinematic
indeterminacy,
, for the plane frame shown below, assuming
axial deformations to be negligible, given by
(A)
(B)
(C)
(D)
Ans:
3.
In the propped cantilever beam carrying a uniformly distributed
load of w N/m, shown in the following figure, the reaction at the
support B is
(A)
(B)
(C)
(D)
Ans:
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
4.
For the linear elastic beam shown in the figure, the flexural rigidity.
EI, is 781250 kN-m2. When w = 10 kN/m, the vertical reaction
RA at A is 50 kN. The value of RA for w = 100 kN/m is
(a) 500 kN
(c) 250 kN
(b) 425 kN
(d) 75 kN
Ans:
5.
For the plane frame with an overhang as shown below, assuming
negligible axial deformation, the degree of static indeterminacy, d,
and the degree of kinematic indeterminacy, k, are
(a) d = 3 and k = 10 (b) d = 3 and k = 13
(c) d = 9 and k = 10 (d) d= 9 and k = 13
Ans:
6.
The unit load method used in structural analysis is
(a) Applicable only to statistically indeterminate structures
(b) Another name for stiffness method
(c) An extension of Maxwell's reciprocal theorem
(d) Derived from Castigliano's theorem
Ans: (d)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
7.
A three-span continuous beam has a internal hinge at B Section B
is at the mind-span of AC. Section R is at the mid-span of CG. The
20 kN load is applied at section B whereas 10 kN loads are applied
at sections D and F as shown in the figure. Span GH is subjected to
uniformly distributed load of magnitude 5 kN/m. For the loading
shown, shear force immediate to the right of section E is 9.84 kN
upwards and the sagging moment at section E is 10.31 kN-m.
The magnitude of the shear force immediate to the left and
immediate to the right of section B are, respectively
(a) 0 and 20 kN (b) 10 kN and 10 kN
9.84 kN and 10.16 kN
(c) 20 kN and 0 (d)
Ans:
8.
A three-span continuous beam has a internal hinge at B Section B
is at the mind-span of AC. Section R is at the mid-span of CG. The
20 kN load is applied at section B whereas 10 kN loads are applied
at sections D and F as shown in the figure. Span GH is subjected to
uniformly distributed load of magnitude 5 kN/m. For the loading
shown, shear force immediate to the right of section E is 9.84 kN
upwards and the sagging moment at section E is 10.31 kN-m.
The vertical reaction at support H is
(a) 15kN upward
(b) 9.84kN upward
(c) 15 kN downward
(d) 9.84 kN downward
Ans:
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
9.
Considering beam as axially rigid, the degree of freedom of a plane
frame shown below is
(a) 9 (b) 8 (c)
7
(d)
6
Ans:
10. Vertical reaction developed at B in the frame be-low due to the
applied load of 100 KN (with 150, 000mm2 cross-sectional
areaand3.125 x 109 mm4 moment of inertia for both members) is
(a) 5.9 kN
(c) 66.3 kN
(b) 302 kN
(d) 94.1 kN
Ans:
KN
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
11. Consider a propped cantilever beam ABC under two loads of
magnitude P each as shown in the figure below. Flexural rigidity of
the beam is EI.
The reaction at C is
(a)
(upwards)
(b)
(downwards)
(c)
(upwards)
(d)
(downwards)
Ans:
(
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)
(
)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
12. Consider a propped cantilever beam ABC under two loads of
magnitude P each as shown in the figure below. Flexural rigidity of
the beam is EI.
The rotation at B is
(a)
(clockwise)
(b)
(anticlockwise)
(c)
(clockwise)
(d)
(anticlockwise)
Ans:
(
(
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)
)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
13. The right triangular truss is made of members having equal cross
sectional area of 1550 mm2 and Young’s modulus of 2 × 105 MPa.
The horizontal deflection of the joint Q is
(a) 2.47 mm (b) 10.25 mm
(c) 14.31 mm (d) 15.68 mm
Ans:
Taking moments about ‘P’
135
So the reaction at ‘P’ =
Horizontal reaction at R = 135KN
( )
( )
√(
)
( )
Applying unit load at ‘Q’ horizontally
( )
We get
( )
( )
]
= 15.68 mm
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
14. A two span continuous beam having equal spans each of length L
is subjected to a uniformly distributed load w per unit length. The
beam has constant flexural rigidly.
The reaction at the middle support is
(A)
(B)
(C)
(D)
Ans:
The downward deflection due to load = Upward deflection due
(
)
(
)
R=
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
15. A two span continuous beam having equal spans each of length L
is subjected to a uniformly distributed load w per unit length. The
beam has constant flexural rigidly.
The bending moment at the middle support is
(a)
(b)
(c)
(d)
(
)
Ans:
2
2
(
)
Bending moment at middle support =
=
=(
= (- )
)
(Hogging)
16. The degree of static indeterminacy of the rigid frame having two
internal hinges as shown in the figure below, is
(A) 8 (B) 7 (C) 6 (D) 5
Ans: (D)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
17. The members EJ and IJ of a steel truss shown in the figure below
are subjected to a temperature rise of 30 C. The coefficient of
thermal expansion of steel is 0.000012 per C per unit length. The
displacement (mm) of joint E relative to joint H along the direction
HE of truss, is
(A)
(B)
(C)
(D)
0.255
0.589
0.764
1.026
Ans:
(
)
As there is no load first term will be zero.
3000
√
18. Beam GHI is supported by three pontoons as shown in the figure
below. The horizontal cross-sectional area of each pontoon is 8 m2,
the flexural rigidity of the beam is 10000 kN-m2 and the unit
weight of water is 10 kN/m3
When the middle pontoon is removed, the deflection at H will be
(A) 0.2m (B) 0.4m(C) 0.6m (D) 0.8m
Ans:
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
19. Beam GHI is supported by three pontoons as shown in the figure
below. The horizontal cross-sectional area of each pontoon is 8 m2,
the flexural rigidity of the beam is 10000 kN-m2 and the unit
weight of water is 10 kN/m3
When the middle pontoon is brought back to its position as shown
in the figure above, the reaction at H will be
(A) 8.6kN (B)15.7kN (C) 19.2kN (D)4.2kN
Ans:
(
)
( )
(
(
(
)
)
( )
)
(
)
20. The degree of static indeterminacy of a rigidly jointed frame in a
horizontal plane and subjected to vertical loads only, as shown in
figure below is
(A)
6
(B)
4
(C)
3
(D) 1
Ans: C
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
21. In the cantilever beam PQR shown in figure below, the segment
PQ has flexural rigidity EI and the segment QR has infinite flexural
rigidity.
The deflection and slope of the beam at 'Q' are respectively
(A)
(B)
(C)
(D)
Ans:
*
(
∫
+
)
(
)]
(
∫
)]
Second term become zero as EI is
∫
(
)
(
)]
(
)
Put p=0
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
∫
(
)(
)
∫ (
)
∫ (
)
[
]
[
∫
]
(
)
[
]
]
(
∫
)]
Second term becomes zero
(
∫
)
]
Put M=0
=
∫ (
)
*
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*
+
+
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
22. In the cantilever beam PQR shown in figure below, the segment
PQ has flexural rigidity EI and the segment QR has infinite flexural
rigidity.
The deflection of the beam at 'R' is
(A)
(B)
(C)
(D)
Ans:
(
∫
)]
(
∫
[
*
*
=
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(
)]
)
)
(
(
∫
]
)+
+
]
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
23. A simply supported beam is subjected to a uniformly distributed
load of intensity w per unit length, on half of the span from one
end. The length of the span and the flexural stiffness are denoted as
l and EI, respectively. The deflection at mid-span of the beam is
(A)
(B)
(C)
(D)
Ans:
24. Due to some point load anywhere on a fixed beam, the maximum
free bending moment is M. the sum of fixed end moments is
a) M
b) 1.5 M
c) 2.0 M
d) 3.0 M
Ans:
(
)
25. Match list-I (fixed beam and various types of loading) with list-II
(the moments at A) and select the correct answer using the codes
below the lists:
Codes:
a)
b)
c)
d)
A
4
3
4
3
B
3
4
3
4
C
1
1
2
2
D
2
2
1
1
Ans: (A)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
26. The moment at the indeterminate support of a two-span continuous
beam of 6 m each with simple support at the ends carrying a udl of
20 kN/m over only the left span is (flexural rigidity is the same for
both the spans)
a) 90kN – m hogging
b) 45kN – m hogging
c) 45kN – m sagging
d) Zero
Ans:
Taking moments about A
Bending moment at D = 7.5
(Hogging)
27. A propped cantilever of uniform flexural rigidity is loaded as
shown in the given figure. The bending moment at fixed end A is
a)
b)
c)
d)
150 kN-m hogging
300 kN-m sagging
150 kN-m sgging
300 kN-m hogging
Ans:
The upward deflection at B = 300
The downward deflection at B due to R =
=
R = 150 KN
-M
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(Hogging)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
28. If a point load acting at the mid-span of a fixed beam of uniform
section produces fixed end moments of 60 kN-m, then the same
load spread uniformly over the entire span will produce fixed end
moments equal to
a) 20kN-m
b) 30kN-m
c)40kN-m
c) 45kN-m
Ans:
29. For the beam AB shown in the figure, the fixed end moments at
ends A and B will be respectively
a)
b)
c)
d)
-3.6 kN-m and + 1.1kN-m
-5.4 kN-m and + 4.6kN-m
-2.4 kN-m and + 3.6kN-m
-3.6 kN-m and + 6kN-m
Ans:
=
= -2.4, 3.6 KN-M
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
30. For the frame shown in the figure, the distribution factors for
members CB,CD and CG are respectively (Assume EL as constant)
a)
,
and
b)
,
and
c)
,
and
d)
,
and
Ans:
CB
CA
Sum =
+
CD
+
=
=
=
=
31. Clapeyron’s theorem is applied to
a) Simply supported beam
b) Propped cantilever beam
c) Fixed and continuous beam
d) Continuous beam only
Ans: (C)
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
32. Match list-I with List-II with respect to the diagram given below
and select the correct answer using the codes given below the lists:
a)
b)
c)
d)
List-I
moment at B
slope at A
reaction at A
stiffness of AB
1.
List-II
3/8wL
2.
3.
1.50 M where M =
4.
where M =
Codes:
A
a) 2
b) 3
c) 3
d) 2
B
1
1
4
4
C
4
4
1
1
D
3
2
2
3
Ans:
Moment at B =
Slope at A =
=
(
= (
)
)
Stiffness of AB =
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
33. A uniform beam of length 2L and flexural rigidity EI id fixed at
both the ends. What is the moment required for unit rotation at the
centre of span?
a)
b)
c)
d)
Ans:
34. A propped cantilever AB, with fixed edge A is propped at B and
carries uniformly distribution over the entire span, if the prop
heaves up (displaces upward), which one among the following is
true if prop reaction = , moment at A =
?
a) Both
will increase
b)
will increase,
will decrease
c)
will decrease,
will increase
d) Both
will decrease
Ans:
If
heaves up
Due to additional reaction at B
due to clockwise moment
increases and
decreases
35. A fixed beam AB of span L carries a uniformly distributed load w
per unit length. During loading, the support B sinks
Downwards by an amount . If =
, what is the fixing moment
at B?
a)
b)
)
d) Zero
Ans:
=
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
36. What are the bending moments at the ends A and B of a uniform
beam AB fixed in direction and position at A and B when acted
upon by two concentrated loads at 1/3rd span as shown in the figure
below?
a)
b)
c)
d)
2/9 WL
4/9 WL
6/9 WL
8/9 WL
Ans:
=)
=)
( )(
)
*
(
)( )
+
=)
37. What is the ratio of load carrying capacity of a fixed beam to that
of a cantilever beam of same span, having same maximum bending
moment and loaded with uniformly distributed throughout the
span?
a) 6
b) 4
c) 3
d) 2
Ans:
Maximum Bending moment =
Maximum bending moment =
=M
Ratio =
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
38. The propped cantilever AB carries a uniformly distributed load of
q/unit length. In this condition the moment reaction
=
What is the clockwise moment required at B to make the slope of
the deflection curve equal to zero
a)
b)
c)
d)
Ans:
R
(
)
39. The fixed beam AB has a hinge C at mid span. A concentrated load
P is applied at C. what is the fixed end moment
?
a)
PL
c) PL/4
b) Pl/2
d) PL/8
Ans:
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SUB: STRUCTURAL ANALYSIS
MODULE-28C
40. If the free end of a cantilever of span L and flexure rigidity EI
undergoes a unit displacement (without rotation), what is the
bending moment induced at the fixed end?
a)
b)
c)
d)
Ans: (D)
41. A fixed beam AB, of constant EI, shown in the figure below,
supports a concentrated load of 10 kN. What is the fixed endmoment
at support A?
a)
4.8 kN-m
c) 7.2kN-m
b)6.0kN-m
d) 9.5kN-m
Ans:
42. A fixed end beam of uniform cross-section is loaded uniformly
throughout the span. What is the proportion of the bending moment
at the centre to the end moment considering only elastic
conditions?
a) 1 : 1 b) 1 : 2 c) 1 : 4 d) 2 : 3
Ans: (B)
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