/THE INSTITUTION OF ENGINEERS SRI LANKA

IESL ENGINEERING COURSE - PART IIDECEMBER 2013

214- STRENGTH OF MATERIALS

TIME ALLOWED: THREE HOURS

BEFORE ANSWERING QUESTION PAPER, READ THE INSTRUCTIONS GIVENBELOW

o Answer only five (05) questions.

o All questions carry equal marks. No marks will be assignedto any answers which exceed five.

o In the cage provided on the cover page of the answer book,write the relevant number of the question to which youanswer. Marks will not be given if the question numbers arenot written on the cover page appropriately.

o Start each answer from a new page and write the relevantquestion number on this new page.

o Do not use red ink or pencil to write your answer.

o Write your Index Number clearly on the answer book

o Delete by drawing a line on the page / s in the answer book,where you have material which do not require the attentionof the examiner.

Question 01:

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A horizontal beam 4.2 m long resting on two simple supports 3 m apart carries auniformly distributed load of 25 kN/m spreads over the span between the supportstogether with concentrated loads of 15 kN and 20 kN at the ends of the beam as shown inFig.Ol. Assuming that the weight of the beam is negligible and the reactions at thesupports are RJ and R2, sketch the shear force (S.F) and the bending moment (80M)diagrams for the beam and find the positions of any point of contra flexure.

15 25 kN/m 20kN

4.2m

Fig.Ol

Question 02:

a) Define briefly the terms principal stress and principal plane in a 2-dimensionalstress system.

b) The stresses acting on three mutually perpendicular planes at a point in an elasticmaterial are 72 N/mm2 tensile and 28 N/mm2 shear on plane 1, 14 N/mm2compressive and 28 N/mm2 complementary shear on plane 2, and no stresses onplane 3.

Sketch Mohr's circle to show the stress components on different planes, and thuscalculate the following

1. principle stresses11. maximum shear stress

111. position of the planes on which there is no normal stressIV. principle strain

Take v = 0.3 and E =200xl06 Nrmnr'

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(a) State bending formula and write down the assumptions used to derive thisformula.

QUESTION 03:

(b) A concrete column of cross-sectional area 400 mm x 400 mm is reinforced byfour longitudinal 50 mm diameter round steel bars placed at each comer. If thecolumn carries a compressive load of 300 kN, determine:(i) Loads carried(ii) The compressive stress produced in the concrete and steel bars.

Young's modulus of elasticity of steel is 15 times that of concrete.

QUESTION 04:

A steel shaft ABCD having a total length of 3 m consists three sections as shown inFig.Q4. The section AB is hollow having outside and inside diameter of 120 mm and 75mm respectively. BC and CD are solid, BC having a diameter of 120 mm and CD adiameter of85 mm. The shaft is subjected to a torque 'T'. If the angle of twist is the samefor each section, determine the length of each section. Find the value of applied torque(T) and the total angle of twist if the maximum shear stress in the hollow portion is 45MPa and G = 82.5 GPa.

A B C

1--1I!Fig.Q4

QUESTION 05:

(a) Prove that the second moment of area of a triangle having a base 'b' and height'h', about an axis along the base is bh 3 /12 . Hence show that a square section hasthe same second moment of area about a centroidal axis parallel to a side of thesquare.

(b) Fig.Q5 shows an unsymmetrical I-section. Determine the second moment of areaabout the axis XvX passing through its center of gravity (C.G).

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~~~=----

100mmI •• I .I~

50mm

T200mm50mm_

xCjG

r-------I I ~--~~

x50mm

I .•• 2006m ---+.1 --r--Fig.Q5

Question 06:

(a) For a strut of length L and uniform section modulus EI, fixed at one end and

27[2E1L2pinned at the other, show that the critical load is approximately

(b) Find the Euler's buckling load and maximum deflection for a steel tube of 10mminternal diameter, 30mm external diameter and 2.5m length having both endspinned. Take E as 2xl05 N/mm2 and yield stress for steel as 330 N/mm2

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(c) Find the safe load if the factor of safety is 3.

Question 07:

A cast iron cylinder has outside and inside diameter of240 mm and 150 mm respectivell'with an internal pressure applied on it. If the ultimate strength of cast iron is 150 MN/mand Poisson's ratio is 0.25, find the internal pressure, according to each of the followingtheories, which would cause rupture.

(i) Maximum principal stress theory(ii) Maximum strain theory(iii) Maximum strain energy theory

Assume no longitudinal stress in the cylinder

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QUESTION 08:

Explain the followings.

(i) Fatigue failure(ii) Castigliano Theorem(iii) Stress concentration factor(iv) Reciprocal Theorem(v) Tresca Theory

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