Simple Stress

Stress is defined as the strength of a material per unit area i.e. resisting force per unit area. The stress develop due to the load which act on the perpendicular of the surface of the material is called normal stress. Formally it is expressed in psi, N/mm2 or MPa. And mathematically we can express

Where,

P = applied normal load in Newton.

A= Area in mm.

Normal stress is either tensile stress or compressive stress. Members subject to tensile force are under tensile stress, while members subject to compressive force are under compressive stress.

Compressive force will tend to shorten the member. Tension force on the other hand will tend to lengthen the member.

SOLVED PROBLEM AND SOLUTION
PROBLEM: 101

A composite bar consists of an aluminum section rigidly fastened between a bronze section and a steel section as shown in figure 1-8a. Axial loads are applied at the positions indicated. Determine the stress in each section.

SOLUTION:

PROBLEM-102

For the truss shown in figure 1-9a, determine the stress in members AC and BD. The cross-sectional area of each member is 900 mm2

SOLUTION:

PROBLEM-103

The block of weight in figure hangs from the pin at A. The bars AB and AC are pined to the support at B and C. The areas are 800 mm^2 for AB and 400 mm^2 for AC. Neglecting the weight of the bars. Determine the maximum safe value of W if the stress in AB is limited to 110 MPa and that in AC to 120 MPa.

SOLUTION:

PROBLEM-104

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.

SOLUTION:

where,

PROBLEM-105

A homogeneous 800 kg bar AB is supported at either end by a cable as shown in Fig. P-105. Calculate the smallest area of each cable if the stress is not to exceed 90 MPa in bronze and 120 MPa in steel.

SOLUTION:

PROBLEM-106
The homogeneous bar shown in Fig. P-106 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.

SOLUTION:

PROBLEM-107

A rod is composed of an aluminum section rigidly attached between steel and bronze sections, as shown in Fig. P-107. Axial loads are applied at the positions indicated. If P = 3000lb and the cross sectional area of the rod is 0.5 in2, determine the stress in each section.

SOLUTION:

PROBLEM-108

An aluminum rod is rigidly attached between a steel rod and a bronze rod as shown in Fig. P-108. Axial loads are applied at the positions indicated. Find the maximum value of P that will not exceed a stress in steel of 140 MPa, in aluminum of 90 MPa, or in bronze of 100 MPa.

SOLUTION:

PROBLEM-109

Determine the largest weight W that can be supported by two wires shown in Fig. P-109. 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.