Combined Stress: 1. The rear axle on a truck has tubular elements as shown.
The axle tubes are made of 4 in outside diameter steel
tube with 0.1 in wall thickness. If the brakes can
apply a torque of 150 ft-lb to each tube, find the
Using the method of joints, and the fact that angle DEC=53.13o, we have
FCE Sin(53.13o)=20kN, then FCE=25.00kN. Then, the stress in bar CE is
10, 000kPa (tension)
A CE 25*1/1002
similarly, FDE=-FCE Cos(53.13 )=-15.00kN, and
Beam Deflections 15. 200 lb
E = 900,000 lb/in
I = 1/12*bh3 = 1/12*12*23 = 8 in4
Given the situation depicted above, find the deflection, y(x), across the beam.
The governing equation relates the deflection of the beam to the
Fall 2006 Exam 3, closed book/notes, calculator allowed
N i Li
N ( x ) dx
= r max = r =
max = 3
GI p ( x )
= d =
= d =
Shear: 1. Two 12 mm thick steel plates are joined by two bolts 4 mm in diameter. The tensile
force applied is 2,000 N. (a) Evaluate the (average) shear stress in the bolts; (b) Evaluate the
bearing stress on the steel plates.
Normal Stress: 2 Given the following structure, find and draw: (a) the distribution of normal
stress along the length of the structure; (b) the distribution of normal strain along the length
of the structure.
Shafts: 2. A shaft with four externally applied torques is shown. Find the relative of twist for the shaft
between points B and D ( BD ).
150 N*m (cw)
75 N*m (cw)
50 N*m (ccw)
200 N*m (ccw)
25 N*m (cw)
Shafts: 1. A hollow steel shaft, depicted in the following
diagram, must transmit a torque of 300,000 in-lb. The
ultimate shear stress (max) is 21,000 psi. If the safety factor is
3.0 and the inner diameter is half of the outer diameter, find
Stress Transformation 7 An element is made from two shorter pieces of material with the
glue joint at 15 from the loading axis. A 1,000 lb tensile load is applied as shown, and in
the vicinity of the glue joint, a compressive stress of 87.5 psi is applied
Find the percentage of the moment carried by the flanges of a W12 x 50 wide-flange
beam. (Hint: find the stress distribution for the entire cross-section of the beam and for a hypothetical
beam consisting only of the flanges or the web)
Stress Transformation 1 A simple tension element is made from two shorter pieces of
material with the glue joint at 15 from the loading axis.
Find the shear and normal stresses at the glue seam. The modulus of elasticity (E) a
Pressure Tanks: 1. The diameter of a ping pong ball is 40 mm and the wall thickness is 0.5
mm. The ball is made of Nylon with an ultimate compressive strength of 95 MPa. Find the
pressure required to crush the ball.
95 10 6
H11. Oil (Specific Gravity 0.97, dynamic viscosity 1.0E-2 lb-s/ft2) is pumped through a
horizontal pipe of diameter 2 inches at a flowrate of 0.20 cfs. What is the pres
Shear: 1. Two 12 mm thick steel plates are joined by two bolts 4 mm in diameter. The tensile force
applied is 2,000 N. (a) Evaluate the (average) shear stress in the bolts; (b) Evaluate the bearing stress on
the steel plates.
Beam Deflections 7. For a cantilever beam of length L and stiffness EI loaded at its end by load
P, the deflection is given by u(x)
Based on that, find the deflection at the end C of a cantilever beam of length 2L and stiffness
Shear: 3. A truss joint connecting bars OA, OB, and OC is shown. The connecting plate is 20mm thick,
and the diameter of the connection bolts is D=10mm. Find: (a) the shear stress for each of the six bolts