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ME 45 – STRENGTH OF MATERIALS
1. Strength of materials
Strength of materials is the science which deals with the relations between externally
applied loads and their internal effects on bodies. The bodies are no longer assumed to be rigid
and deformations are of major interest. During deformation the external forces acting upon the
body do work. This work is transferred completely or partially into potential energy of strain. If
the forces which produce the deformation of the body are gradually removed, the body returns
or try to return to its original shape. During this return the stored potential energy can be
recovered in form of external work. The main concern of the subject is regarding three S’s,
namely strength, stiffness and stability of various load carrying members
2. Simple stresses
When an external force is applied on a body, internal resistance is developed within thebody to balance the effect of externally applied forces. The resistive force per unit area is called
as stress. These internal forces are vectorial in nature and maintain an equilibrium withexternally applied forces. It is particularly significant to determine the intensity of these forces,called stress on any arbitrarily selected section (oriented in a particular direction to fit thespecial requirement), as resistance to deformation and capacity of material to resist forcesdepend on these intensities.
In general these stresses acting on infinitesimal areas of any section vary from point topoint. In general, they are inclined with respect to the sectional plane. But, in engineeringpractice it is customary to resolve the force perpendicular and parallel to the sectioninvestigated.
3. Types Of Stress
The stress can be classified in two categories.
a. Normal stressb. Shear stress
The intensity of force perpendicular or normal to the section is called normal stress,denoted by a. As a particular stress holds true only at a point, we can define it mathematicallyas;
Ó = limΔA →o (ΔFn/ΔA) Where,
Fn is force acting normal to the section and A is its corresponding area.
These normal stresses generally causes tension or compression on the surface of section. The stresses which case tension are termed ‘tensile stresses’ and those which create
compression are termed ‘compressive stresses’.
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COMPILED BY BIBIN.C, AP/AERO, THE RAJAAS ENGINEERING COLLEGE Page 1
compression are termed ‘compressive stresses’.
ME 45 – STRENGTH OF MATERIALS
COMPILED BY BIBIN.C, AP/AERO, THE RAJAAS ENGINEERING COLLEGE Page 2
On the other hand, component of intensity of force acting parallel to the plane of thesectional area is called shear stress. It is denoted by (tau). Mathematically we can define as;
r = limΔA →o (ΔFp/ΔA) or limΔA →o (ΔFt/ΔA)
Where
Fp represents the force parallel to section cut and A represents the area of sectionalplane. The shear stress causes the shearing at the sectional plane.
Note:
When stresses are multiplied by respective areas on which they act, it gives forces. It isthe sum of these forces at any imaginary section that keeps the body in equilibrium. The SI unitof stress is N/m2 or Pa.
4. Normal Stress
Such stress normally occurs in a straight axially loaded rod in tension or compression, atany plane perpendicular to the axis of the rod. The tensile or compressive stress acting on such aplane is maximum stress, as any other section which is not perpendicular to the axis of the rodprovides a larger surface area for resisting the applied load or force.
The maximum stress is of most significance as it tends to cause the failure of thematerial.
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ME 45 – STRENGTH OF MATERIALS
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If the rod is assumed weightless, two equal and opposite forces P are necessary. One ateach end to maintain equilibrium. Since, the body as a whole is in equilibrium any part of it willalso be in equilibrium.
Thus, from the definition of stress, the normal stress is
This normal stress is uniformly distributed over the cross-sectional area A. In general, force P is aresultant of a number of forces to one side of cut or another. Such a state of stress on anelement or section is referred to as uniaxial stress.
Note:
If the normal stresses try to create an extension in length of rod it is called tensile stressand in case it try to reduce the length of rod it is termed compressive stress.
5. Shear Stress
Such stresses are created when the forces are transmitted from one part of the body tothe other by causing stresses in the plane parallel to the applied force. Assuming that thestresses that act in the sectional plane are uniformly distributed;
r = P/A 9 N / m2)
Where x is shearing stress, P is the total force acting across and parallel to the cutand A is cross-sectional area of the sheared member. Since shear stresses actually aredistributed in a non-uniform fashion across the area of the section the quantity given by aboveequation represents an average shearing stress.
When a body is subjected to load P consisting of two equal and opposite parallel forcesnot in same line, it tends to shear off across the resisting section. The stress induced in the bodyis called shear stress and the corresponding strain is called shear strain.
The most common occurrences of pure shear are in riveted and cotter joints.
In the resisting cross-section area parallel to load P is A, then the average shear stress is
r = P/A
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