AA

Rt

0lim

(1.1)

dA

dV

A

V

dA

dP

A

PAA

00

limlim

(1.2)

A

V

A

P

(1.3)

FIG. 1.4 Deformations produced by the components of internal forces and couples

FIG. 1.6 A bar loaded axially by (a) uniformly distributed load of intensity p; and (b) a statically equivalent centroidal force P = pA

A

P

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

2cos

cos/

cos

A

P

A

P

2sin

2cossin

cos/

sin

A

P

A

P

A

P

(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 two-member 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 maxi- mum 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.