Combined Stress: 1. The rear axle on a truck has tubular elements as shown.
1000 lb
1000 lb
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
stress
Solution
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
CE
4m
FCE
25
10, 000kPa (tension)
A CE 25*1/1002
3m
B
o
similarly, FDE=-FCE Cos(53.13 )=-15.00kN, and
Beam Deflections 15. 200 lb
180 lb
12
2
E = 900,000 lb/in
I = 1/12*bh3 = 1/12*12*23 = 8 in4
2
8
4
4
Given the situation depicted above, find the deflection, y(x), across the beam.
Solution:
The governing equation relates the deflection of the beam to the
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.
L1=600 mm
L2=800 mm
200 kN
200 kN
A1=1500 mm2
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.
4 mm
2000 N
2000 N
12 mm
Solu
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 ).
A
B
C
1m
D
1.5 m
1m
E
0.5 m
Fixed end
d=50 mm
150 N*m (cw)
75 N*m (cw)
50 N*m (ccw)
200 N*m (ccw)
25 N*m (cw)
Solutio
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
the followin
Beams: 2. A simply supported beam of square tube cross-section is subjected to load F at midspan. Find
max
the maximum load F such that x 10 ksi .
Cross
section
3
y
4i
n
z
0.20i
n
F
ft
3ft
A
B
x
4in
6ft
Solution:
Consider that the reactions at A and B are
Beams: 1.
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)
A
I 394
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
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.
y
1000 lb
1000 lb
15
A=4 in2
Find the shear and normal stresses at the glue seam. The modulus of elasticity (E) a
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.
4 mm
2000 N
2000 N
12 mm
Solu
Beam Deflections 7. For a cantilever beam of length L and stiffness EI loaded at its end by load
Px 2
P, the deflection is given by u(x)
(3L x)
6EI
P
x
B
A
L
Based on that, find the deflection at the end C of a cantilever beam of length 2L and stiffness
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.
Solution:
pDm
4t
4t
p
Dm
95 10 6
t 0.0