STRESS-STRAIN PROBLEMS

A composite bar is made up of two or more bars of equal lengths but of different materials rigidly fixed with each other and behaving as one unit for extension or compression.

1.In case of a composite bar having two or more bars of different cross sections, the extensions or compression in each bar will be equal. The strain in the both materials will be same.

Strain in bar 1, ε1 = σ1/E1 = (P/AE)1

Strain in bar 2, ε2 = σ2/E2 = (P/AE)2

Strain ε1 = Strain ε2  = dl/L    ----(1)

2.The total load will be equal to the sum of the loads carried by each member. 

P = P1 +P2

The Stress in bars are σ1 and  σ2

P= σ1 x A1 + σ2 x A2   -----(2)

Solve the equation (1) and (2) for unknowns

Assignment:

1.Find the stresses in the rods for the figure shown below. (Answer: 4.67, 1.39 N/mm2 )

2. A 2m long bar of uniform section 50 mm2 extends 2mm under a limiting axial stress of 200N/mm2.What is the modulus of resilience for the bar.. 

3. A material has modulus of rigidity equal to 0.4 x 105 N/mm2 and bulk modulus equal to 0.75 x 105 N/mm2. Find the Young’s Modulus and Poisson’s Ratio. 

4. A steel rod 30 mm diameter and 300mm long is subjected to tensile force P acting axially.The temperature of the rod is then raised through 600C and total extension measured as 0.30mm. Calculate the value of tensile force P. Take ES for of steel =200 GN/m2 and thermal coefficient of steel =12 x 10-6 /oC 

5. A hollow cast-iron cylinder 4 m long, 300 mm outer diameter, and thickness of metal 50 mm is subjected to a central load on the top when standing straight. The stress produced is 75000 kN/m2. Assume Young's modulus of cast iron as 1.5 x 108 KN/m2, find 

i) Magnitude of the load,ii) Longitudinal strain produced and iii) Total decrease in length 

6. Define Resilience and derive the equation of stresses for a body subjected to sudden and Impact loading 

7. A vertical circular bar 20mm diameter, 3m long carries a tensile load of 150 kN. Calculate 

a) Elongation b) Decrease in diameter and 

c) Volumetric strain. 

8.As shown in Fig., a rigid bar with negligible mass is pinned at O and attached to two vertical rods. Assuming that the rods were initially stress-free, what maximum load P can be applied without exceeding stresses of 150 MPa in the steel rod and 70 MPa in the bronze rod.