Q.1 A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of 50 kN is acting at joint R in the horizontal direction. The flexural rigidity. El, of each member is 10^{6} kNm^{2}. Under the applied load, the horizontal displacement (in mm, round off to 1 decimal place) of joint R would be______. [2019 : 2 Marks, SetI]
Solution:
Q.2 The rigidjointed plane frame QRS shown in figure is subjected to load P at the joint R. Let the axial deformations in the frame be neglected. If the support S undergoes a settlement of the vertical reaction at the support S will be become zero when β is equal to [2019 : 2 Marks, SetI]
(a) 7.5
(b) 3.0
(c) 48.0
(d) 0.1
Ans. (A)
Solution:
Assume 'R sinks by Δ.
Sway analysis:
End moment distribution,
Sway force
Alternate method:
Q.3 A prismatic beam PQR of flexural rigidity El = 1 x 10^{4} kNm^{2} is subjected to a moment of 180 kNm at Q as shown in the figure.
The rotation at Q (in rad, up to two decimal places) is ________ . [2018 : 2 Marks, SetII]
Solution:
Method1
Methodll
Q.4 A vertical load of 10 kN acts on a hinge located at a distance of LI4 from the roller support Q of a beam of length L (see figure). [2018 :1 Mark, SetII]
The vertical reaction at support Q is
(a) 0.0 kN
(b) 2.5 kN
(c) 7.5 kN
(d) 10.0 kN
Ans. (A)
Solution:
Bending moment about hinge point A = 0
(consider the right hand side of A)
Q.5 Consider the portal frame shown in the figure and assume the modulus of elasticity, E = 2.5 x 10^{4} MPa and the moment of inertia, I = 8 x 10^{8} mm^{4} for all the members of the frame.
The rotation (in degrees, up to one decimal place) at the rigid joint Q would b e _________ . [2017 : 2 Marks, SetII)
Solution:
MethodI
= 700 kNm (ACW)
EI = 2.5 x 10^{4} x 8 x 10^{8}
= 20 x 10^{12} Nmm^{2}
= 20000 kNm^{2}
As the two members QR and QS are identical, moment will be equally divided i.e., 350 kNm each.
Methodll
Fixed end moment:
Slope deflection equation:
Joint equilibrium equation at joint Q,
Q.6 The value of M in the beam ABC shown in the figure is such that the joint B does not rotate.
The value of support reaction (in kN) at B should be equal to ________. [2017 : 2 Marks, SetI]
Solution:
MethodI
Fixed end moment:
By super position,
Note : The value of 'M' shown in the figure,
Q.7 The portal frame shown in the figure is subjected to a uniformly distributed vertical load w(per unit length).
The bending moment in the beam at the join ‘Q ’ is [2016 : 2 Marks, SetII]
(a) zero
(b)
(c)
(d)
Ans. (A)
Solution:
As there is no horizontal force,
Hence,
H_{P} = H_{S} = 0
∴ BM at Q = 0
Q.8 For the beam shown below, the value of the support moment M is ____ kNm. [2015 : 1 Mark, SetI]
Solution:
By symmetry we can consider two parts of beam separately with half the load.
Moment at joint B = 10 kNm
Carry over moment at joint A due to 10 kNm moment at propped end = 10/2= 5kNm
Q.9 Considering the symmetry of a rigid frame as shown below, the magnitude of the bending moment (in kNm) at P (preferably using the moment distribution method) is [2014 : 2 Marks, SetII]
(a) 170
(b) 172
(c) 176
(d) 178
Ans. (C)
Solution:
As the frame and loading is symmetrical, θ_{P}= 0. So, joint Pcan be replaced by a fixed support as shown.
Fixed end moment:
Distribution factor:
Q.10 All members in the rigidjointed frame shown are prismatic and have the same flexural stiffness EI. Find the magnitude of BM at Q (in kNm) due to given loading. [2013 : 2 Marks]
Solution:

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