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MECHANICS OF MATERIALS: ENGR 2070 – SPRING 2014

ASSIGNMENT 4 DUE: Monday 10 February

1. A wire is used to hang a lantern over a pool. Neglect

the weight of the wire, and assume it is straight, but strain-

free, before the lantern is hung. When the lantern is hung,

it causes a 9 inch sag in the wire. Determine the normal

strain in the wire with the lantern hanging as shown.

2. The rotation of the "rigid" beam AF is resisted

by the stretching of rod AB until the beam comes

into contact with the top column DE. Assume that

the angle θ through which beam AF rotates is small

enough that only vertical motion of the beam is

significant. a) A load P is applied at end F that is

just sufficient to close the 4 mm gap between the

beam and the top of the column at D. What is the

normal strain in rod AB for this value of load P? b) If

load P is increased further until the strain in AB

reaches 0.005 mm/mm, what is the corresponding

strain in column DE?

3. Two identical symmetrically placed rubber pads

transmit load from a rectangular bar to a C-shaped

bracket, as shown. a) Determine the average shear

stress in the rubber pads on planes parallel to the

top and bottom surfaces of the pads if P = 300 N

and the dimensions of the rubber pads are: b = 30

mm, w = 80 mm, and h = 25 mm. b) If the relative

displacement between the rectangular bar and the

C-shaped bracket, = 2 mm due to the 300 N load,

what is the average shear strain in the rubber pad?

9 in.

4 mm

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4. The data in the table was obtained in a tensile test of a flat-bar steel specimen having the dimensions shown. a)

Using Excel, plot engineering stress versus engineering strain. b) Determine the stress and strain at the proportional

limit, the modulus of elasticity of this material, the ultimate stress, and the fracture stress for the material. c) Use the

0.2% offset method to determine the yield stress of the material.

5. A tensile test is performed on an aluminum

specimen that is 0.45 inch in diameter using a gage

length of 2 inch, as shown in the figure. a) When the

load is increased by an amount P = 2 kips, the distance

between gage marks increases by an amount ΔL =

0.002 inch. a) Calculate the modulus of elasticity for this specimen. b) If the proportional limit stress for this

specimen is 60 ksi, what is the distance between gage marks at this value of stress?

6. Two wires are connected to a rigid bar, as shown. The wire on the

left is made of A36 steel, having a cross-sectional area of 0.15 in2. The

6061-T6 aluminum-alloy wire on the right has a cross-sectional area of

0.20 in2. a) If a weight W = 1900 lb is applied as shown, how much

vertical deflection will it experience due to the stretch in the wires

(calculate the deflection at the bar/weight center, 10 inch from the left

end)? b) Where should the weight be located so that the bar would

remain horizontal?

Tension Test Data for Flat Steel Bar

P (kips) ΔL (in.)

1.2 0.0008

2.4 0.0016

3.6 0.0024

4.8 0.0032

5.7 0.0040

5.95 0.0050

6.25 0.0060

6.50 0.0075

6.65 0.0100

6.85 0.0125

6.90 0.0150

Thickness t = 0.30 in.

0.45 in.