Hall Ticket No Question Paper Code: AAE002
INSTITUTE OF AERONAUTICAL ENGINEERING
(Autonomous)
Four Year B.Tech III Semester End Examinations (Regular) November, 2018
Regulation: IARE R16
THEORY OF STRUCTURES
Time: 3 Hours Max Marks: 70
Answer ONE Question from each Unit
All Questions Carry Equal Marks
All parts of the question must be answered in one place only
UNIT I
1. Derive an expression for the total elongation of a bar of uniform sectional area due to its own
weight, when the bar is fixed at its upper end and hanging freely at the lower end.
Draw SFD and BMD for a simply supported beam of length 8 m carries point loads of 4 kN and
6 kN at a distance of 2 m and 4 m from the left end.
2. Determine the diameter of a solid circular shaft which will transmit 337.5 kW at 300 rpm. The
maximum shear stress should not exceed 35 MPa and twist should not be more than 100 in a
shaft length of 2.5 m. Take the modulus of rigidity as 90 GPa.
A cantilever of length 5 m carries a uniformly distributed load of 2 kN/m length over the whole
length and a point load of 4 kN at the free end. Draw the shear force and bending moment
diagrams for the beam.
UNIT II
3. Explicate the terms Neutral axis, section modulus and moment of resistance.
An I-section has flanges of width 100 mm and the overall depth is 200 mm. The flanges and web
are of uniform thickness 20 mm. Find the ratio of the maximum shear stress to the average shear
stress.
4. Show that the ration of maximum shear stress to mean shear stress in a rectangular cross-section
is equal to 1.5 when it is subjected to a transverse shear force F.
A Castiron beam 20 mm x 20 mm in section and 1000 mm long is simply supported at the ends.
It carries a point load W at the center. The maximum stress induced is 120 N/mm2. What
uniformly distributed load will break a cantilever of the same material 50 mm wide, 100 mm
deep and 2 m long.
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UNIT III
5. A beam with a span of 4.5 metres carries a point load of 30kN at 3 metres from the left support.
If for the section I 54.97x10􀀀6m4 and E 200GN/m2, find
The deflection under the load.
The position and amount of maximum deflection.
A bar of length 4m when used as a simply supported beam and subjected to a u.d.l. of 30 kN/m
over the whole span, deflects 15mm at the centre. Determine the crippling load when it is used
as a column with following end conditions:
Both end pin-jointed
One end fixed and other end hinged
Both ends fixed.
6. Define 'equivalent length of a column'? Enumerate the ratios of equivalent length and actual
length of columns with various end conditions.
Determine slope at the left support, deflection under the load and maximum deflection of a simply
supported beam of length 10 which is carrying a point load of 10 kN at a distance 6 m from
the left end. Take E 2 x 105 N/mm2 and I 1.1 x 108 mm4.
UNIT IV
7. Analyze the axial forces in all the members of the plane truss as shown in Figure 1
Figure 1
State and explain the Clapeyron's theorem of three moments.
8. Five members OA, OB, OC, OD and OE meeting at are hinged at A and C and fixed at D
and E. The lengths of OA, OB, OC, OD and OE are 3m, 4m, 2m, 3m and 5m and their moments
of inertia are 400mm4, 300mm4, 200mm4, 300mm4 and 250mm4 respectively. Determine the
distribution factors for the members and the distributed moments, when a moment of 4000 kN-m
is applied O.

Explain what you understand by perfect frame, deficient frame and redundant frame.
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UNIT V
9. Define stress. Define stress at a point. How many stress components completely define state of
stress at a point.
The tensile stresses at a point across two mutually perpendicular planes are 120 N/mm2 and
60N/mm2. Determine the normal, tangential and resultant stresses on a plane inclined at 300 to
the axis of the minor stress.
10. Draw a typical three dimensional element and indicate state of stress in their positive sense on
it. Also express the equations of equilibrium in case of a three dimensional stress system.
An elemental cube is subjected to tensile stresses of 30 N/mm2 and 10 N/mm2 acting on two
mutually perpendicular planes and a shear stress of 10 N/mm2 on these planes. Draw the Mohr's
circle of stresses and hence or otherwise determine the magnitudes and directions of principal
stresses and also the greatest shear stress.