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MECHANICS OF MATERIALS

MECHANICS OF MATERIALS. STRAIN. ROSHAZITA CHE AMAT. CO 1: Ability to DETERMINE the stresses, strain and deformation of members in simple one-dimensional elastic system. Objective. Define and determine deformation using the concept of normal and shear strain in various types of problems.

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MECHANICS OF MATERIALS

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  1. MECHANICS OF MATERIALS STRAIN ROSHAZITA CHE AMAT CO 1: Ability to DETERMINE the stresses, strain and deformation of members in simple one-dimensional elastic system.

  2. Objective • Define and determine deformation using the concept of normal and shear strain in various types of problems.

  3. Deformation • When a force is applied to a body, it will change the body’s shape and size. • These changes are deformation. Note the before and after positions of 3 line segments where the material is subjected to tension.

  4. Strain Normal Strain • The elongation / contraction of a line segment per unit of length is referred to as normal strain. • Average normal strain is defined as • If the normal strain is known, then the approximate final length is +εline elongate -εline contracts

  5. Strain Units • Normal strain is a dimensionless quantitysince it is a ratio of two lengths. Shear Strain • Change in angle between 2 line segments that were perpendicular to one another refers to shear strain. θ<90 +shear strain θ>90 -shear strain

  6. Example 2.1 The slender rod creates a normal strain in the rod of where z is in meters. Determine (a) displacement of end B due to the temperature increase, and (b) the average normal strain in the rod.

  7. Solution: Part (a) Since the normal strain is reported at each point along the rod, it has a deformed length of The sum along the axis yields the deformed length of the rod is The displacement of the end of the rod is therefore

  8. Solution: Part (b) Assumes the rod has an original length of 200 mm and a change in length of 2.39 mm. Hence,

  9. Example 2.3 The plate is deformed into the dashed shape. If, in this deformed shape, horizontal lines on the plate remain horizontal and do not change their length, determine • the average normal strain along the side AB, and • (b) the average shear strain in the plate relative to the x and y axes.

  10. Solution: Part (a) Line AB, coincident with the y axis, becomes line after deformation, thus the length of this line is The average normal strain for AB is therefore The negative sign indicates the strain causes a contraction of AB.

  11. Solution: Part (b) As noted, the once 90° angle BAC between the sides of the plate, referenced from the x, y axes, changes to θ’ due to the displacement of B to B’. Since then is the angle shown in the figure. Thus,

  12. THANK YOU

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