GROUP 1

A specimen is originally 350 mm long, has a diameter of 12 mm and is subjected to a force of 2000 N. When the force is increased from 2000 N to 7200 N, the specimen elongates 0.25 mm. Determine the modulus of elasticity for the material if it remains linear elastic

GROUP 2

The elastic portion of the stress-strain diagram for a steel alloy is shown in the figure. The specimen from which it was obtained had an original diameter of 13 mm and a gauge length of 50 mm. When the applied load on the specimen is 50 kN, the diameter is 12.99265 mm. Determine Poisson’s ratio for the material. Est= 200 GPa.

GROUP 3

An A-36 steel bar has a length of 1250mm and cross-sectional area of 450 mm2. Determine the length of the bar if it is subjected to an axial tension of 20 kN. The material has linear-elastic behavior. (EA-36 = 210 GPa)

GROUP4

Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum absolute value (a) of the shear, (b) of the bending moment.

GROUP 5Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum absolute value (a) of the shear, (b) of the bending moment

GROUP 6

Draw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum absolute value (a) of the shear, (b) of the bending moment

GROUP 7

A cooper strip (Ec=105 GPa) and an aluminium strip (Ea=75 GPa) are bonded together to form the composite bar shown. Knowing that the bar is bent about a horizontal axis by a couple moment 35 Nm, determine the maximum stress in (a) the aluminium strip, (b) the copper strip.

GROUP 8

The composite beam is made of steel (A) bonded to brass (B) and has the cross section shown. If it is subjected to a moment of M=6.5 kNm, determine the maximum bending stress in the brass and steel. Ebr = 100 GPa, Est= 200 GPa.

GROUP 9

The steel shaft is made from two segments: AC has a diameter of 10 mm, and CB has a diameter of 20 mm. If it is fixed at its ends A and B and subjected to a torque of 500 Nm, determine the maximum shear stress in the shaft.

Group 10

Determine the absolute maximum shear stress in the shaft.

Group 11

A spherical gas tank has an inner radius r=1.5 m. If it is subjected to an internal pressure of P= 300 kPa, determine its required thickness if the maximum normal stress is not exceed 12 MPa.

The open-ended polyvinyl chloride pipe has an inner diameter of 4 cm and thickness of 0.2 cm. If it carries flowing water at 0.6 MPa pressure, determine the state of stress in the walls of the pipe.

If the flow of water within the pipe in the previous problem is stopped due to the closing of a valve, determine the state of stress in the walls of the pipe. Neglect the weight of the water. Assume the supports only exert vertical forces on the pipe.

Group 12

The cross section of a composite beam made of aluminium and steel is shown in the figure. The modulus of elasticity are EA = 75 GPa and ES = 200 GPa. Under the action of bending moment that produces a maximum stress of 50 MPa in the aluminium, what is the maximum stress s in the steel?

Group 13

A prismatic bar of circular cross section is loaded by forces P = 140 kN. The bar has length L=4.0m and diameter d = 30 mm. It is made of aluminum alloy (2014-T6) with modulus of elasticity E = 73 GPa and Poisson’s ratio = 1/3. Calculate the elongation l, the decrease in diameter d and the increase in volume V of the bar.

Given;P = 120 kN ; L = 3.0 m ; d= 30 mm ; E = 73 GPa ; v = 1/3

Group 14

A high strength steel wire, 1/8 cm in diameter, stretches 1.41 cm when a 50 cm length of it is stretched by a force of 850 N. What is the modulus of elasticity E of the steel? If

the diameter of the wire decreases by 0.000085 cm, what is Poisson’s ratio? What is the unit volume change for the steel?

Given,

; L = 1.41 cm ; L = 50 cm ; F = 850

N

Modulus of elasticy E;

;

d = 0.000085 cm, Poisson’s ratio:

and

Volume change;e = ( 1 – 2 ) = 0.00099

Group 15

Draw complete shear force and bending moment diagrams for the beam.