Q.1 The figure shows a simply supported beam PQ of uniform flexural rigidity El carrying two moments M and 2M
The slope at P will be [2018 : 2 Marks, SetI]
(a) 0
(b) ML/(9EI)
(c) ML/(6EI)
(d) ML/(3EI)
Ans. (C)
Solution:
Methodl
Methodll
Moment area method:
δ_{Q/P} = Defleciton of point Q wrt to tangent at point P
Q.2 Two prismatic beams having the same flexural rigidity of 1000 kNm^{2} are shown in the figures.
If the midspan deflections of these beams are denoted by δ_{1} and δ_{2} (as indicated in the figures), the correct option is [2017 : 2 Marks, SetII]
(a) δ_{1} = δ_{2}
(b) δ_{1} < δ_{2}
(c) δ_{1 }> δ_{2}
(d) δ_{1} >> δ_{2}
Ans. (A)
Solution:
∴ δ_{1 }= δ_{2}
Q.3 Two beams PQ (fixed at P with a roller support at Q, as shown in Figure I, which allows vertical movement) and XZ(with a hinge at Y) are shown in the Figures I and II respectively. The spans of PQ and XZ are L and 2L respectively. Both the beams are under the action of uniformly distributed load (w) and have the same flexural stiffness, EI (where, E and I respectively denote modulus of elasticity and moment of inertia about axis of bending). Let the maximum deflection and maximum rotation be δ_{max1} and δ_{max1}, respectively, in the case of beam PQ and the corresponding quantities for the beam XZ be δ_{max2} and δ_{max2}, respectively.
Which one of the following relationship is true? [2016 : 2 Marks, SetI]
(a)
(b)
(c)
(d)
Ans. (D)
Solution:
Deflection in beam xy at y = Deflection in beam yz at y
⇒
∴ R = 0
In beam PQ also at support Q, vertical reaction in zero because of roller support.
So, beam PQ, xyand yz are same.
∴
Q.4 A 3 m long simply supported beam of uniform cross section is subjected to a uniformly distributed load of w= 20 kN/m in the central 1 m as shown in the figure
If the flexural rigidity (El) of the beam is 30 x 10^{6} Nm^{2}, the maximum slope (expressed in radians) of the deformed beam is [2016 : 2 Marks, SetI]
(a) 0.681 x 10^{7}
(b) 0.361 x 10^{3}
(c) 4.310 x 10^{7}
(d) 5.910 x 10^{7}
Ans. (B)
Solution:
Method1
Due to symmetrical loading,
According to Macaulay method,
After integrating once
Due to symmetrical loading slope will be zero at mid section (x = 1.5 m),
∴
∴ Equation of slope,
The slope will be maximum at the support,
Methodll
Moment Area Method,
Area of M/El diagram between points P and B.
Q.5 Two beams are connected by a linear spring as shown in the following figure. For a load P as shown in the figure, the percentage of the applied load P carried by the spring is_____. [2015 : 2 Marks, SetI]
Solution:
Compression of spring
% force carried by spring = 25%
Q.6 A steel strip of length, L = 200 mm is fixed at end A and rests at 6 on a vertical spring of stiffness, k = 2 N/mm. The steel strip is 5 mm wide and 10 mm thick. A vertical load, P= 50 N is applied at 6, as shown in the figure. Considering E = 200 GPa, the force (in N) developed in the spring is ________ . [2015 : 2 Marks, SetII]
Solution:
Deflection of point B = Deflection of spring
Where, R= Force in the spring,
0.064(50  R) = R
3.2= R+ 0.064 R
R = 3.0075 N
Q.7 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of contraflexure from end A (in m) is _______ . [2015 : 1 Mark, SetII]
Solution:
Reaction at B,
Δ_{B} = 0 (Compatibility condition)
∴ R_{B} = 15 kN
BM at a distance x from free end,
BM_{x} = 10 * x  15 x (x  0,25)= 0
⇒ 10x = 15x3.75
⇒ 5x = 3.75
∴ x = 0.75m
∴ From end A, distance is 0.25 m.
Q.8 The beam of an overall depth 250 mm (shown below) is used in a building subjected to two different thermal environments. The temperatures at the top and bottom surfaces of the beam are 36^{0}C and 72^{0}C respectively. Considering coefficient of thermal expansion (α) as 1.50 x 10^{5} per ^{0}C, the vertical deflection of the beam (in mm) at its midspan due to temperature gradient is _______ . [2014 : 2 Marks, SetII]
Solution: MethodI
From properties of circle,
(Considering ‘δ’ very small so neglect δ^{2})
⇒
= 2.43
Methodll
Q.9 The tension (in kN) in a 10m long cable, shown in the figure, neglecting its selfweight is [2014 : 2 Marks, SetII]
(a) 120
(b) 75
(c) 60
(d) 45
Ans. (B)
Solution:
⇒ 2T cosθ = 120 ...(i)
Here,
⇒
Q.10 The axial load (in kN) in the member PQ for the arrangement/assembly shown in the figure given below is _________. [2014 : 2 Marks, SetII]
Solution:
Free body diagram,
For principle of superposition,
Deflections due to axial forces will be very less as compared to bending forces.
So we can neglect the axial deformation.
∴ From equation (i),
⇒ V_{Q} = 50 kN
Q.11 For the cantilever beam of span 3 m (shown below), a concentrated load of 20 kN applied at the free end causes a vertical displacement of 2 mm at a section located at a distance of 1 m from the fixed end. If a concentrated vertically downward load of 10 kN is applied at the section located at a distance of 1 m from the fixed end (with no other load on the beam), the maximum vertical displacement in the same beam (in mm) is ____. [2014 : 2 Marks, SetI]
Solution:
Q.12 A uniform beam (EI= constant) PQ in the form of a quarter circle of radius R is fixed at end P and free at the end Q, where a load H/is applied as shown. The vertical downward displacement δ_{Q} at the loaded point Q is given by Find the value of β correct to 4decimal place. [2013 : 2 Marks]
Solution:
Q.13 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 I and EI respectively. The deflection at midspan of the beam is [2012 : 2 Marks]
Ans. (B)
Solution:
MethodI
Methodll
Total deflection
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