STUPIDSID
1 (a)
Explain term 'Plastic hinge'. State (i) Upper bound theorem and (ii) Lower bound theorems for collapse load in plastic analysis.
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1 (b)
Discuss the characteristics of stiffness matrix. Formulate Stiffness matrix [S] for a prismatic cantilever beam, of length 'L', also considering axial deformation with
usual notations. Take EI = Constant.
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2 (a)
Derive formula for meridional and hoop force in conical dome subjected to
concentrated load 'W' at the vertex, with usual notations.
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2 (b)
Derive formulae of shear force, bending moment and torsional moment at any
section, for the quarter circular cantilever beam curved in plan, subjected to
uniformly distributed load w per unit run throughout its length, with usual notations.
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2 (c)
Find Shape factor for the section shown in fig. (i)
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3 (a)
Formulate the flexibility matrix [F] and vector {DQL} for the beam shown in fig.
(ii). Assume fixed end moment at A and internal moment at support B as redundant Q1 and Q2 respectively.
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3 (b)
For the beam (given in Q.3(a) above), calculate values of all unknown reactions using flexibility method. Also draw SF and BM diagram.
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3 (c)
A circular beam curved in plan is symmetrically supported on six columns. The radius of beam is 6 m and is subjected to UDL of 5 kN/m throughout its length. Determine the value of shear force, bending moment and torsional moment at φ =0°, φ = 30° and φ =60°. (Mid span and Supports)
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3 (d)
Determine collapse load in terms of Mp for the portal frame loaded as shown in fig. (iii)
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4 (a)
Formulate the stiffness matrix [S] and load vector {AD ? ADL}for the beam shown
in fig. (ii).
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4 (b)
For the beam (given in Q.4(a) above), calculate joint displacement and final end
moments using stiffness method.
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4 (c)
A conical dome of 6 m diameter and central rise of 4 m supports total UDL including self weight of 10 kN/m2 over the entire surface. The thickness of dome is 100 mm. Calculate meridional stress and hoop stress at the base of the dome.
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4 (d)
Define term 'collapse load'. Determine collapse load in terms of Mp, using static method for the beam fixed at both ends and subjected to UDL 'w' kN/m throughout its length 'L' m as shown in fig. (iv).
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5 (a)
A spherical dome having 8 m span and 2 m rise, subjected to UDL of 10 kN/m2 including self weight. The thickness of the dome is 100 mm. Calculate meridional and hoop stresses at each θ = 10° interval from crown to base of the dome.
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5 (b)
A beam curved in plan is fixed at both the ends. The radius of the beam is 5 m and
subtended angle is 75°. It is subjected to UDL of 10 kN/m throughout its length. If the
section of the beam is 230 mm × 600 mm, determine shear force, bending moment
and torsional moment at mid span and end supports. Take EI = 5.608GJt.
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5 (c)
Discuss various types of stresses in spherical domes with sketch. Using formula of
hoop force prove that in a spherical dome, subjected to UDL over entire surface, the
hoop force changes its nature at an angle 51.83° from crown.
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5 (d)
A semi-circular beam curved in plan is supported on three equally spaced supports,
carries UDL of w per unit run throughout its length. The radius of the beam is 'r'.
Determine maximum value of bending and torsional moment.
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