Stress and strain STRESS AND STRAIN EXPLAIN THE

Stress and strain STRESS AND STRAIN EXPLAIN THE EQUILIBRIUM OF A DEFORMABLE BODY AND THE CONCEPT OF STRESS AND STRAIN; THIS INCLUDED ON HOW TO COMPUTE THE AVERAGE NORMAL STRESS IN AN AXIALLY LOADED BAR, AVERAGE SHEAR STRESS, ALLOWABLE STRESS, DEFORMATION AND STRAIN. (2 HOURS)

Introduction �Stress is associated with the strength of material from which the body is made. �Strain is a measure of the deformation of the body.

Equlibrium of Deformable Body �External Loads �Support Reactions �Equations of Equilibrium �Internal Resultant Loadings

External Loads �Surface Forces Concentrated force Uniform Distributed Load etc �Body Forces weight

Support Reaction

Equilibrium Equation

Internal Resultant Loadings Normal force, N Shear force, V Torsional moment or torque, T Bending moment, M

Calculation Example 1. 1: Determine reactions at support.

Stress �Normal stress – acting normal to the surface �Shear stress – acting tangent to the surface �Unit: N/m 2 1 Pa = 1 N/m 2, 1 MPa = 1 N/mm 2

Normal Stress

Calculation Example 2 �Example 1. 9 : Determine the position of x of this force so that the average compressive stress at support C is equal to the average tensile stress in the tie rod. Arod = 400 mm 2, Ac =650 mm 2

Calculation Example 2

Shear Stress

Shear Stress

Calculation Example 3 �Example 1. 10: Determine the average shear stress in the 20 mm diameter pin at A and the 30 mm diameter pin at B that support the beam

Calculation Example 3

Allowable Stress

Design of Simple Connection

Calculation Example 4 Example 1. 16: Determine the first stress developed. Steel rod AC dia. : 20 mm A for Aluminium Block AB: 1800 mm 2 18 mm dia. pin subjected to single shear Failure stress: (σst)fail = 680 MPa (σal)fail = 70 MPa τfail = 900 MPa F. S. = 2

Calculation Example 4

Calculation Example 4

Calculation Example 4

Strain

Strain

03_CR 02

Strain

Calculation Example 5 � F 2 -3: The rigid beam is supported by a pin at A and wires BD and CE. If the load P on the beam causes the end C to be displaced 10 mm downward, determine the normal strain developed in wires CE and BD.

Assignment Refer Hibbler’s book for the question