# beam bending,deflection,buckling,mechanics of solid, Formulas and forms for Mechanics. Indian Institute of Technology (IIT)

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ESO204: Mechanics of Soilds

Stress strain curve

ESO202A: Mechanics of Solids

studied the cases of three rods made of the same material.

loaded by forces applied at the ends and we were interested in the relative motion between the points of application of forces

Uni-axial loading & Deformation We define : Stress = Load/ Initial Area Strain = Change in length per unit length

With this definition, we get identical stress versus strain curves for bars 1,2 and 3.

For small strains, we observed that the stress and strain are linearly related. We defined:

Modulus of elasticity = Stress/Strain

(We use E to denote the modulus of elasticity).

Typical E for steel = 200 X 109 N/m2

Typical values of modulus of elasticity

Material E (GPa) 1 Pa = 1 N/m2

1 GPa = 109 N/m2

Steel & Iron 194-205

Aluminum 69

Brass 103

Cast Iron 69-138

Wood 10

Soft Rubber .0014-.005

Tensile test The most

important test of a material’s mechanical response is the tensile test.

Tensile test In a tensile

test, one end of a rod or flat specimen is clamped in a loading frame and the other subjected to a controlled displacement or load.

Tensile test A displacement transducer connected in series with the specimen gives an indication of the change in length between two gage marks

Tensile test

Specimen grips Attaching displacement transducer

Tensile test Figure shows the two gage marks and the change in length between the two gage marks

Tensile test In general, axial

extension is accompanied by a decrease in cross sectional dimensions.

Engineering stress and strain The Engineering stress and strain are defined on the basis of the initial specimen cross-sectional area A0 and gage length L0 .

Engineering stress and strain Engineering Stress σe = Load / A0 Engineering Strain εe = Change in length / L0

True stress and strain The specimen cross-sectional area A and

gage length L keep changing as the load is applied. These changes have a negligible effect except during the final stages of the test.

True Stress σtrue = Load / A True Strain εtrue = Change in length / L

Tensile testing machine

Tensile testing machine- grips

Tensile testing machine- Attaching displacement transducer

Tensile testing machine- Chart recorder

Tensile testing of Aluminum specimen

Specimen after failure

Specimen after failure

Necking