Applied Mechanics- Stress and Strain

INTRODUCTION TO MECHANIC OF MATERIALS (GATE PI PAPER RECHNICAL SECTION PART 2)

Introduction External Loads Internal Loads Support Reactions

MECHANICS OF MATERIALS Mechanics of materials is a branch of mechanics that studies the relationships between the external loads applied to a deformable body and the intensity of internal force acting within the body The subject also involves computing the deformations of the body, and it provides a study of the body's stability when the body is subjected to external forces

WHY MECHANICS OF MATERIALS? (WHY IS STATICS NOT ENOUGH3) Real world structures are typically designed for strength, stiffness, and stability considerations. None of these can be accomplished with what we have learned in Statics . Strength: The ability of the structures to carry or transmit loads. Stiffness: The ability of the structures to resist changes in shape. . Stability: The ability of the structure to resist buckling under compressive loads.

EXTERNAL LOADS Surface Forces are caused by the direct contact of one body with the surface of another. Concentrated Force idealization this area is small in comparison with the total surface force can be idealized as a single concentrated force, which is applied to a point on the body. Linear Distributed load idealization If the surface loading is applied along a narrow area. Body Force contact between the bodies. Gravitation, this force called the weight of the body *ls developed when one boy exerts a force on another body without direct physical

EXTERNAL LOADS Concentrated force idealization Surface force WYS) Body torcc Linear distributed load idcalization

EQUILIBRIUM OF A DEFORMABLE BODY Equations of Equilibrium For equilibrium balance of forces balance of moments Draw a free-body diagram to account for all forces acting on the body Apply the two equations to achieve equilibrium state

For an X, y, Z coordinat system is established with the origin at point O F, -0 The forces in the x-y plane Mo 0

INTERNAL FORCES Normal force, N the force acts perpendicular to the area. It is developed whenever the external loads tend to push or pull on the two segments of the body. Shear force, V the shear force lies in the plane of the area and is developed when external loads tend to cause the two segments of the body to slide over one another.

Torsional moment or torque, T this effect is developed when the external loads tend to twist one segment of the body within respect to the other. >Bending moment, M the bending moment is caused by the external loads that tend to bend the body about an axis lying within the plane of the area.

SUPPORT REACTIONS FOR 2D PROBLEMS Type of connection Reaction Type of connection Reaction Cable One unknown:F External pin Two unknowns: FF Roller One uaknown: F Internal pin MF Smooth support One unknown: F Fixed support Three unknowns:FFM 5