Seat No.: ________ Enrolment No.
___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER–IV (NEW) EXAMINATION – WINTER 2023
Subject Code:3140603 Date:17-01-2024
Subject Name: Structural Analysis-I
Time: 10:30 AM TO 01:00 PM Total Marks:70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.
MARKS
Q.1 (a) Explain the Maxwell reciprocal deflection theorem with neat sketch. 03
(b) Calculate the static and kinematic indeterminacies of the structure in Fig 1 and 2 04
Fig. 1 Fig. 2
(c) A three hinged parabolic arch of 20 m span and 4 m central rise carries a point load 07
of 160 kN at 4 m from left side support. Calculate Normal thrust and shear force at
sectionunder load. Draw BMD.
Q.2 (a) A thin cylindrical shell of internal diameter d, wall thickness t and length l, is 03
subjected to internal pressure p. Derive the expression for circumferential stress
produced if the efficiencyof the longitudinal joint is η.
(b) A thin cylindrical shell has 100 mm internal diameter and wall thickness is 12 04
mm. It carries a steam pressure of 11 N/mm2, Find hoop stress and longitudinal
stress in the shell material.
(c) A thin cylindrical shell is 3000 mm long 1000 mm in diameter and thickness of 07
metal 10 mm after being filled with water at atmosphere pressure, more water is
pumped in until the pressure is 2.4 N/mm2 on relieving the pressure, what should
be amount of additional water let out if the water is assumed to incompressible.
Take E for steel = 200 kN/m2, Poisson’s ratio = 0.3
OR
(c) Find a slope at A and deflection at C for the beam shown in Figure 3 using a 07
Macaulay method. Take EI 3000 kN.m2.
20 kN 10 kN/m
A B
3m C 3m
Fig. 3
Q.3 (a) Explain following Terms, i) Resilience; ii) Proof Resilience; iii) Modulus of 03
Resilience.
(b) Derive the formula for strain due to sudden loading. 04
1
(c) A 1500 mm long wire of 30 mm2 cross sectional area is hanged vertically. It 07
receives a sliding collarof 100 N weight and stopper at bottom end. The collar is
allowed to full on stopper through 200 mmheight. Determine the instantaneous
stress included in the wire and corresponding elongation. Also determine the
strain energy stored in the wire. Take modulus of elasticity of wire as 200GPa
OR
Q.3 (a) What are the fundamental principles to consider when analyzing a fixed beam in 03
structural engineering?"
(b) Determine slope and deflection at free end of cantilever as shown in Figure 4. 04
Take E= 200GPa, and I = 150 x 106mm.
30 kN 20 kN
A C
1m 1m B
Fig. 4
(c) Using a moment area method, determine the slope at B and c and deflection at B 07
of the cantilever beam as shown in Figure 5.
W kN/ m P
A
L/2 L/2 B
C
Fig. 5
Q.4 (a)
Define conjugate beam. What are the different kinds of a support condition in 03
conjugate beam?
(b) A propped cantilever beam of span ‘l’ is subjected to a point load ‘w’ at the 04
center of the span. Determine all and draw shear force and bending moment
diagram.
(c) A 20 m height masonry chimney is 2 m square at base and trapper to 1 m square 07
at top the tapped central flue is circular in cross- section and 1 m diameter at the
base. If the total weight of the brick work, about the base is 1300 kN. Find for
what uniform intensity of wind pressure and one face of chimney the stress
distribution the base just ceases to be wholly compressive.
OR
Q.4 (a) Define “core” or “Kernel” of section. Obtained the “core” or “Kernel” of solid 03
square section.
(b) A cast iron column having a 150 mm diameter carries an eccentricity load of 50 04
kN. If maximum tensile stress is not exceed 7.5 N/mm2, find permissible
eccentricity of load column.
(c) A rectangular retaining wall section is 2 m wide. It retains water up to full height. 07
Fin the maximum height required for following: (a) when it is just at the point of
overturning; (b) when it is just on the point of sliding; (c) there is a no tensile
stress is produced at the base of section. The density of wall material and water
is 22 kN/m3 respectively and take efficiently of friction as 0.5.
Q.5 (a) Discuss Euler's formula for column buckling. What are its key assumptions, and 03
how is it used in column design?
(b) Describe the behavior of columns with initial curvature. How does this initial 04
curvature affect their stability, and what considerations are needed in their
design?
(c) A hollow cast iron column 6 m. long is fixed at both ends, and has an external 07
diameter of 400 mm. find the internal diameter of column if it supports an axial
load of 1000 kN. Factor of safety = 5; α = 1/1600, fc= 550 N/mm2.
OR
2
Q.5 (a) Differentiate between long and short column. 03
(b) Distinguish between direct stresses and bending stresses. 04
(c) A rectangular column section ABCD having AB = CD = 400 mm and BC = AD 07
= 300 mm carries a compressive load 300 kN at corner B. Find the stress at each
corner A, B, C and D and draw stress –distribution diagram for each side.
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