Download A composite bar of length 200 mm shown below

DEFORMABLES SAMPLE PROBLEM 1
A composite bar of length 200 mm shown below consists of an aluminum shell (Ea = 70 GPa,
αa = 23.6 × 10-6 / oC, Aa = 1.5 10-3 m2) fully bonded to a steel core (Es = 200 GPa, αs = 11.7 ×
10-6 / oC, As = 0.5 10-3 m2) and is unstressed at a temperature of 20 oC. The bar is placed between
two rigid walls and the temperature is increased while monitoring the force, P, exerted on the wall
due to the thermal expansion of the composite bar. Determine the temperature at which the total
force exerted by the bar is 50 kN.
Aluminum shell
Steel core
200 mm
DEFORMABLES SAMPLE PROBLEM 2:
For the beam and loading shown below, determine the reaction at point A and the deflection at
point B.
y
w
C
B
A
L/2
x
DEFORMABLES SAMPLE PROBLEM 3:
The cylindrical portion of the 0.6 m diameter pressure vessel shown in the figure is fabricated
of 5-mm thick plate welded along a helix forming a 25o angle with a transverse plane. For a gage
pressure of 4 MPa, determine the normal stress perpendicular to the weld line and shearing stress
parallel to the weld line. Also compute the maximum value of the shearing stress in the shell wall
by constructing a three-dimensional Mohr’s circle.
25o
0.6 m
2.5 m
DEFORMABLES SAMPLE PROBLEM 4:
Cross-sectional area of the beam shown below is composed of two triangular areas joined at
their base. Determine the equation for the shearing stress τxy = τxy(y) for a vertical shear V.
y
z
3w
w