Introduction to
Strength of Materials
Strength of Materials
Engineering Mechanics - The study of forces that act on
bodies and the resultant motion that those bodies experience.
1.
2.
3.
Statics
Dynamics
Strength of Materials
A
*Statics –
P
B
assumes that the material (bar and cable) supporting the load is rigid.
Hence, the only concern here is the magnitude of the reaction (P) that shall maintain
the system in equilibrium.
*Strength of Materials – assumes that the supporting materials are deformable
bodies. Hence, the concern is on the maximum load that the whole assembly can
carry without allowing the supporting materials break or bend.
Strength of Materials
Simple Stresses
Stress -
The measure of strength of a material per unit
area usually expressed in N/mm2 or MPa.
1. Normal Stress
2. Shear Stress
3. Bearing Stress
Normal Stress
AXIAL STRESS
Normal stress develops when a force is applied
perpendicular to the resisting area.
P
__
δ=A
δ
P
A
where P┴ A
Normal stress
TENSION
Internal Axial Force
Cross – Sectional Area
COMPRESSION
EXAMPLE no. 01
Which bar is stronger A or B?
Assume that the given loads are the maximum loads each
can carry.
BAR 1
BAR 2
A1=50 mm2
A2=20 mm2
1000 N
500 N
answer :
Bar 2 with max. Normal
Stress of 25 N/mm2
EXAMPLE no. 02
A hollow steel tube with an inside diameter of 100 mm must
carry a tensile load of 400 kN. Determine the outside
diameter of the tube if the stress is limited to 120 MN/m2.
answer :
D= 119.325 mm
EXAMPLE no. 03
A homogeneous 800 kg bar AB is supported at either end
by a cable as shown in Figure. Calculate the smallest
area of each cable if the stress is not to exceed 90 Mpa
in bronze and 120 MPa in steel.
answer :
Abr = 43.6 mm2
Asteel = 32.70 mm2
EXAMPLE no. 04
The homogeneous bar shown in Figure is supported by a
smooth pin at C and a cable that runs from A to B around
the smooth peg at D. Find the stress in the cable if its
diameter is 0.6 inch and the bar weighs 6000 lb.
answer :
δcable = 10,458.71 psi
EXAMPLE no. 05
A rod is composed of an aluminum section rigidly
attached between steel and bronze sections, as shown in
Figure. Axial loads are applied at the positions indicated.
If P = 3000 lb and the cross sectional area of the rod is
0.5 in2, determine the stress in each section.
answer :
δ s = δal = 24 ksi
δ br = 18 ksi
EXAMPLE no. 06
An bronze rod is rigidly attached between a aluminum
rod and a steel rod as shown. Axial loads are applied at
the positions indicated. Find the maximum allowable
value of P that will not exceed a stress in steel of
140MPa, in aluminum of 90MPa or in bronze of 100MPa.
Aluminum
A = 500mm2
3P
Bronze
A = 200mm2
Steel
A = 150mm2
P
L br = 2m
2P
L st = 1.2m
L al = 3.5m
answer :
P = 10,500 N
EXAMPLE no. 07
Determine the weight of the heaviest traffic lighting
system that can be carried by the two bars shown if the
allowable stress on bar AB is 90MPa and on bar AC is
110MPa given that the cross sectional areas of bar AB is
50mm2 and that of AC is 80 mm2
B
C
70
answer :
A
35
5,305.50 N
EXAMPLE no. 08
Determine the required cross sectional areas of members BE,
CD and CE of the given truss shown, if the allowable stress in
tension is 120MPa while in compression is 105MPa.
D
C
G
4m
3m
3m
B
A
3m
E
3m
50KN
F
3m
3m
75KN
answer :
H
50KN
ACD = 941.52 mm2
ACE = 73.66 mm2
ABE = 729.17 mm2
EXAMPLE no. 09
Determine the weight of the heaviest cylinder that can be
supported by the structure shown if the cross sectional area of
the cable is 120mm2 and its allowable stress is 80MPa.
C
B
8m
9m
A
3m
answer :
W = 19,081.11 N
EXAMPLE no. 10
Determine the largest weight W that can be supported by two
wires shown in Figure. The stress in either wire is not to exceed
30 ksi. The cross-sectional areas of wires AB and AC are 0.4
in2 and 0.5 in2, respectively.
answer :
W = 17.10 kips