Strength of Materials - MADE EASY Study Material for GATE, ESE and SES Exams

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Nature of Bending Stress

Bending Stress (i) Simply supported beam: When a simply supported beam is subjected to a sagging bending moment, the cross-section

The equation of bending is applicable when the beam is free from shear force, i.e., the equation of bending is

In figure shown, fibres are in compression above neutral surface or layer in longitudinal direction, so in transverse direction, fibres

Normal Stresses in beams As per Hooke’s law, εx = σ/E Here, σ is the bending stress in longitudinal direction

Normal strain in beams Consider a simply supported beam of length L subjected to moments at ends A and B

Theory of Pure Bending The material of the beam is homogeneous, isotropic, and linear elastic, in which Hooke’s law is

Consider a simply supported beam AB of length L subjected to moment M0 at its ends as shown in figures.

For design purpose, a beam should be so designed that it has adequate stiffness so that the deflections are within

Bending moment at section of a beam is defined as the algebraic sum of the moments about the section as

Elastic constants are those factors which determine the deformation produced by a given stress system acting on material. Modulus of

When a material behaves elastically and exhibits a linear relationship between stress and strain, it is called linearly elastic. In

All the grades of steel have the same Young’s modulus but different yield stresses. where, σ= Stress, Ductile material :

Stress and Strain Stress It is the resistance offered by a body to deformation. Nominal stress (Engineering stress) = Load/

The maximum angle of inclination of an inclined plane with horizontal for which a body lying on the inclined plane

Consider a body A which is just about to move on plane under external applied force F. The W is

The limiting friction force fL is directly proportional to the normal reaction between two bodies in contact. fL ∝ N

Static Friction The force of friction always acts in a direction opposite to the impending motion. The limiting force of

The friction is of the following types : Static friction: It is the friction experienced by two bodies in contact

When a body moves or tends to move on another body, the property of two bodies by virtue of which