'r'HD (15) _
3013
Reg. No.
(REVTSION,- 20ls)
Signature
DIPLOMA EXAMINATION IN
ENGINEERING/TECHNOI,OGY/
MANAGEMENT/COMMERCIAL PRACTICE OC'|OBER. 2OI7
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THEORY OF STRUCTURES. I
lTime : 3 hours
(rVlaximum marls : 100)
PAKT A
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E
(Marimum marks : 10)
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Marks
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I Answer c// questions in one or two sentences. Each question carries 2 marks.
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1. List the characteristics of a force.
2. Define radius of glnation. C
3. State Poisson's ratio.
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4. Define the term torque.
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5. State moment of resistance. (5x2=10)
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PAR'| __ B
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(Maximum marks : 30)
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Answer any five of the following questions. Each question carries 6 marks.
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l. Calculate the support reactions of a simply supported beam of 4m span with
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a Point Load of 10kN at its Centre of span and a u.d.l of 2kN/m thought
its span.
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2. Determine the Centre of Gravity of the solid body consists of right circular
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cone placed on a solid hemisphere as shown in figrre from C.
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3. An alloy bar lm long and 200mm2 in cross section area is subjected to
a compressive force of 20lrli. If the modulus of elasticity for the alloy is
100GPa, find the decrease in length of the bar.
4. Define the terms:
(i) volumetic strain (ii) Bulk modulus (iii) Modulus of rigidity.
5. Determine the maximum shear stress developed, if the average rorque
transmitted by a shaft is 2255Nm. The maximum torque is 4U/o rnor. th*t
the average torque and the diameter of the shaft is g0mm.
6. Dfferentiate longitudinal stress and hoop sftess in thin cylinden.
7. List the assumptions in the theory of simple bending. (5 x 6 = 30)
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PART C
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. (N4aximum marks : 60)
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(Answer one full question from each Unit. Each fi.rll question
carries 15 marks.)
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III (a) calculate the moment of inertia of the 'L' section shown in figwe
about a
vertical axis passing through its cente of gravity. C
mm
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10
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10 mrn
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r- 60 mm
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(b) Determine the centroiir of the lamina shown
in figrne fiom AR
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120 mm
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B]
' lOmm 'l
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[V (a) calculate the supporr reactiohs of a slmply supported beam Al] of span
4m with a uniformly varymg load of 2k\-/m ui .igirt support
I] to gk\rm
at the lefl support A.
(b) Determine thc polar moment of inertia of a reclangular section pf 200mm
width and i00mm denth.
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Marks
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(a) Define the terms :
(i) Elasticlty (ii) Hardness (iir) Ductility (rg Stiffiress.
(b) A brass rod 2m long is fixed at its two ends. If the thermal stress
is not to
exceed 76.5MPa, calculate the temperature through which the rod
can be
heated. Take a = 17 x l0-6/oc and E = 90Gpa.
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VI (a) A metal bm 50mm x 50mm section is subjected to an axial compressive
load of 500kN. The contraction for a 200mm gauge length is found to be
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0.5mm and increase in thickness is 0.04mm. Find the values of young's
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modulus and Poisson's ratio.
(b) A metallic bar of 500mm x 200mm and 2m long is subjected to a load of
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150kI{ applied gradually on it. If the stess at elastic limit of the bar material
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is 200N/mm2, determine
(i) Stain enerry
(ii) Proof resilience
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(iii) Modulus of resilience E : 200 l$tr/mm2.
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(a)
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VII Sketch SFD and BMD for an overhanging beam shown in figure and calculate
the maximr.nn bendine moment.
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(b) Calculate the maximum torque that can be safely applied to a shaft of 80mm
diameter. The permissible angle of twist is 1.5 degree for a length of 5m and
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shear stress not to exceed 42MPa. Take N = 84GPa.
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VIII (a) Sketch SFD and BMD of a cantilever beam shown in flgure.
(b) A spherical shell diameter is made up o{'10mm thick plates. Calculate
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the change in dizrneter and volume of the shcll, when it is subjected to an
internal pressurc of'1.6MPa..lake E = 200GPa and lim = 0.3'
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supported at the two
x (a) Abeam of 200mm x 400mm in cross section is simply
Find the marimum
ends. It carries a u.d.l of 10kN/m over the entire span
permitted span, if the maximum bending stress Frmitted is 50N/mm2'
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fb) Derive a formula for shear stress at the section of a loaded beam' l
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X (a) Derive the equation for simple bencling.
(b) Calculate the marimum shear strcss at the section of a simply supported
beam of rectangular Section of size 200mm x 300mm, if the shear force
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at the section is l00klli. Also calculate the Shear stress at a point 50mm
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above Neutral axis- 7
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