R
t  lim
 A 0  A
 P dP
  lim

 A 0  A
dA
P
 
A
 V dV
  lim

 A 0  A
dA
V

A
(1.1)
(1.2)
(1.3)
FIG. 1.4 Deformations produced by the components of
internal forces and couples
P

A
FIG. 1.6 A bar loaded axially by (a) uniformly distributed load of
intensity p; and (b) a statically equivalent centroidal force P = pA
FIG. 1.7 Normal stress distribution in a strip caused by a concentrated load
ILLUSTRATING ST. VENANT’S PRINCIPLE
FIG. 1.9 Determining the stresses acting on an inclined section of a bar


P cos 
P
 cos2 
A / cos  A
P sin 
P
P
 sin  cos  
sin 2
A / cos  A
2A
(1.5a)
(1.5b)
FIG. 1.10
Stresses
acting on two
mutually
perpendicular
inclined
sections of a
bar
PROCEDURE FOR STRESS ANALYSIS
In general, finding the normal stress in an axially
loaded member of a structure involves the
following steps:
•Equilibrium Analysis
•Computation of Stresses
Sample Problem 1.1
The bar ABCD in Figure (a) consists of three cylindrical
steel segments, each with a different cross-sectional area.
Axial loads are applied as shown. Calculate the normal
stress in each segment.
Sample Problem 1.2
For the truss shown in Fig. (a), calculate the normal
stresses in (1) member AC; and (2) member BD. The
cross-sectional area of each member is 900 mm2.
Sample Problem 1.3
Figure (a) shows a twomember truss supporting
a block of weight W. The
cross-sectional areas of
the members are 800 mm2
for AB and 400 mm2 for
AC. Determine the maximum safe value of W if
the working stresses are
110 MPa for AB and 120
MPa for AC.
(a)
GUIDED PROBLEMS
Problem 1.1
The compound bar ABCD consists of three segments,
each of a different material with different dimensions.
Compute the stress in each segment when the axial
loads are applied.
Problem 1.2
Neglecting the
weights of bars
OAB and AC,
determine the
stress in the
bar AC.
Problem 1.3
The cross-sectional
area of each member
of the truss is 4.2 in2.
Calculate the stresses
in members CD and
CF.