MEC2403/MAE2401
Problem Set 3
Q1
PROBLEM 2.61
A 2.75 kN tensile load is applied to a test coupon made from 1.6-mm flat steel plate (E=200 GPa, v=0.30). Determine the resulting change (a) in the 50-mm gage length, (b) in the width of portion AB of the test coupon, (c) in the thickness of portion AB, (d) in the cross-sectional area of portion AB.
Q2
PROBLEM 2.63
A 20-mm-diameter rod made of an experimental plastic is subjected to a tensile force of magnitude P=6 kN. Knowing that an elongation of 14 mm and a decrease in diameter of 0.85 mm are observed in a 150-mm length,l determine the modulus of elasticity, the modulus of rigidity, and Poisson's ratio for the material.
Q3.
PROBLEM 2.64
The change in diameter of a large steel bolt is carefully measured as the nut is tightened. Knowing that E=200 GPa and v=0.30, determine the internal force in the bolt, if the diameter is observed to decrease by 13 μm.
Q4.
PROBLEM 2.65
A 2.5-m length of a steel pipe of 300-mm outer diameter and 15-mm wall thickness is used as a column to carry a 700-kN centric axial load. Knowing that E=200 GPa and v=0.30, determine (a) the change in length of the pipe, (b) the change in its outer diameter, (c) the change in its wall thickness.
Q5.
PROBLEM 2.67
The block shown is made of a magnesium alloy, for which E=45 GPa and v=0.35. Knowing that σ,=-180 MPa, determine (a) the magnitude of σ, for which the change in the height of the block will be zero, (b) the corresponding change in the area of the face ABCD, (c) the corresponding change in the volume of the block.
Q6.
PROBLEM 2.66
A 30-mm square was scribed on the side of a large steel pressure vessel. After pressurization, the biaxial stress condition at the square is as shown. For E=200 GPa and v=0.30, determine the change in length of (a) side AB, (b) side BC, (c) diagnonal AC.
Q7.
PROBLEM 2.68
An aluminum plate (E=74GPa and v=0.33) is subjected to a centric axial load that causes a normal stress σ. Knowing that, before loading. a line of slope 2:1 is scribed on the plate, determine the slope of the line when σ=125 MPa.
Q8.
PROBLEM 2.74
The homogeneous plate ABCD is subjected to a biaxial loading as shown. It is known that σz=σ0 and that the change in length of the plate in the x direction must be zero, that is, εx=0. Denoting by E the modulus of elasticity and by v Poisson's ratio, determine (a) the required magnitude of σx, (b) the ratio σo/εz.
Q9.
PROBLEM 2.75
An elastomeric bearing (G=0.9 MPa) is used to support a bridge girder as shown to provide flexibility during earthquakes. The beam must not displace more than 10 mm when a 22-kN lateral load is applied as shown. Knowing that the maximum allowable shearing stress is 420 kPa, determine (a) the smallest allowable dimension b, (b) the smallest required thickness a.
Q10.
PROBLEM 2.82
Two blocks of rubber with a modulus of rigidity G=10 MPa are bonded to rigid supports and to a plate AB. Knowing that b=200 mm and c=125 mm, determine the largest allowable load P and the smallest allowable thickness a of the blocks if the shearing stress in the rubber is not to exceed 1.5 MPa and the deflection of the plate is to be at least 6 mm.