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2–1. An air-filled rubber ball has a diameter of 6 in. If the air pressure within it is increased until the ball’s diameter becomes 7 in., determine the average normal strain in the rubber. d0 = 6 in. d = 7 in. e = pd - pd0 7 - 6 = = 0.167 in./in. pd0 6 Ans.

2–2. A thin strip of rubber has an unstretched length of 15 in. If it is stretched around a pipe having an outer diameter of 5 in., determine the average normal strain in the strip. L0 = 15 in. L = p(5 in.) e = L - L0 5p - 15 = = 0.0472 in.>in. L0 15 Ans.

2–3. The rigid beam is supported by a pin at A and wires BD and CE. If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain developed in wires CE and BD.

D

E

4m

P

¢LBD ¢LCE = 3 7 ¢LBD = eCE 3 (10) = 4.286 mm 7 ¢LCE 10 = = = 0.00250 mm>mm L 4000 ¢LBD 4.286 = = 0.00107 mm>mm L 4000

A

B

C

3m

2m

2m

Ans. Ans.

eBD =

1

02 Solutions 46060

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*2–4. The two wires are connected together at A. If the force P causes point A to be displaced horizontally 2 mm, determine the normal strain developed in each wire. œ LAC = 23002 + 22 - 2(300)(2) cos 150° = 301.734 mm

C

300

mm

eAC = eAB

œ LAC - LAC 301.734 - 300 = = = 0.00578 mm>mm

...SCHOOL OF ENGINEERING &TECHNOLOGY MECHANICAL & AUTOMOBILE ENGINEERING DEPARTMENT III TERM SECOND YEAR 1 Course number MEC211 2 Course Title STRENGTH OF MATERIALS 3 Credits 5 4 Contact Hours (LT- P) 3-1-2 5 Course Objective To understand the relationship between stress and strain in solids. 6 Course Outcomes On successful completion of this module students will be able to 1. Understand the concept of strain and stress, stress- strain diagram, Elastic constants and constitutive relations.. 2. Determine principal stresses and strain and locate principal planes. 3. Apply the theory of simple bending to compute stresses in beams of homogenous and composite sections of different shapes. 4. Calculate slope and deflection in beams.Use Double integration method, Macaulay’s method, moment area method methods to calculate slope and deflection for the following : a) Cantilevers b) Simply supported beams with or without overhang Under concentrated loads, uniformly distributed loads or combination of concentrated and uniformly distributed loads. 5. Apply different formulae to analyze stresses in struts and columns subjected to axial loads. 7 Outline syllabus 7.01 MEC211.A Unit A Simple stresses and strains 7.02 MEC211.A1 Unit A Topic 1 Concept of stress and strain, St. Venant’s principle, Stress and strain diagram, Hooke’s law, Young’s modulus (E), Modulus of Rigidity(G), Bulk modulus(K), Poisson ratio. 7.03 MEC211.A2 Unit A Topic 2 Stress and elongation...

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