STRESS
SIMPLE STRESSES
Simple stresses are expressed as the ratio of the applied force divided by the resisting area or
𝑭
𝝈=
𝑨
It is the expression of force per unit area to structural members that are subjected to external forces and/or
induced forces. Stress is the lead to accurately describe and predict the elastic deformation of a body.
There are three types of simple stress:
• normal stress;
• shearing stress;
• bearing stress.
I. NORMAL STRESS
The resisting area is perpendicular to the applied force, thus normal. There are two types of normal stresses;
tensile stress and compressive stress. Tensile stress applied to bar tends the bar to elongate while compressive stress
tends to shorten the bar.
𝑷
𝝈=
𝑨
where P is the applied normal load in Newton and A is the area in mm 2. The maximum stress in tension or compression
occurs over a section normal to the load.
ILLUSTRATIVE PROBLEM
1. 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
2. A homogeneous 800 kg bar AB is supported at either end by a cable as shown in Fig. 1.1. Calculate
the smallest area of each cable if the stress is not to exceed 90 MPa in bronze and 120 MPa in steel.
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3. The homogeneous bar shown in Fig. 1.2 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.
4. A rod is composed of an aluminum section rigidly attached between steel and bronze sections, as shown
in Fig. 1.3. 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.
5. Determine the largest weight W that can be supported by two wires shown in Fig. 1.4. 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.
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II. SHEARING STRESS
Forces parallel to the area resisting the force cause shearing stress. It differs to tensile and compressive
stresses, which are caused by forces perpendicular to the area on which they act. Shearing stress is also known
as tangential stress.
𝑽
𝝉=
𝑨
where V is the resultant shearing force which passes which passes through the centroid of the area A being sheared.
ILLUSTRATIVE PROBLEM
1. What force is required to punch a 20-mm-diameter hole in a plate that is 25 mm thick? The shear
strength is 350 MN/m2.
2. Find the smallest diameter bolt that can be used in the clevis shown in Fig. 2.1 if P = 400 kN. The
shearing strength of the bolt is 300 MPa.
3. As in Fig. 2.2, a hole is to be punched out of a plate having a shearing strength of 40 ksi. The
compressive stress in the punch is limited to 50 ksi. (a) Compute the maximum thickness of plate in which a hole 2.5
inches in diameter can be punched. (b) If the plate is 0.25 inch thick, determine the diameter of the smallest hole
that can be punched.
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III. BEARING STRESS
Bearing stress is the contact pressure between the separate bodies. It differs from compressive stress, as it
is an internal stress caused by compressive forces.
𝑷𝒃
𝝈𝒃 =
𝑨𝒃
ILLUSTRATIVE PROBLEM
1. In Fig. 3.1, assume that a 20-mm-diameter rivet joins the plates that are each 110 mm wide. The
allowable stresses are 120 MPa for bearing in the plate material and 60 MPa for shearing of rivet. Determine (a) the
minimum thickness of each plate; and (b) the largest average tensile stress in the plates.
2. The lap joint shown in Fig. 3.2 is fastened by four 3⁄4-in.-diameter rivets. Calculate the maximum safe
load P that can be applied if the shearing stress in the rivets is limited to 14 ksi and the bearing stress in the plates
is limited to 18 ksi. Assume the applied load is uniformly distributed among the four rivets.
3. In the clevis shown in Fig. 3.3, find the minimum bolt diameter and the minimum
thickness of each yoke that will support a load P = 14 kips without exceeding a shearing stress of
12 ksi and a bearing stress of 20 ksi.
Reference Book:
Pytel, A. & Singer, F.L. STRENGTH OF MATERIALS 4th Edition
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