STRENGTH OF MATERIALS SIMPLE STRESSES STRAINS PART1 Stress

STRENGTH OF MATERIALS SIMPLE STRESSES & STRAINS (PART-1)

Stress : “Internal Resistance offered by material against deformation which is force per unit area. ”

Types of Stress 1. Normal Stress 2. Shear stress

Strain: Axial Strain Lateral Strain Shear Strain

STRENGTH OF MATERIALS SIMPLE STRESSES & STRAINS (PART-1)

Stress : “Internal Resistance offered by material against deformation which is force per unit area. ” Strain : “ Ratio of change in dimension to the original dimension of the member. ”

Hooke’s Law Assumptions : 1) Material is homogeneous. 2) Material is Isotropic. 3) Material is elastic. “ It states that under direct loading, within proportionality limit, stress is directly proportional to strain. ” Slope of stress strain curve is called Modulus of Elasticity

Modulus of Elasticity

Modulus Of Rigidity/ Shear Modulus

Bulk Modulus is Inversely proportional to compressibility.

Poisson’s Ratio

Physical Quantity Formula Stress Strain Modulus of Elasticity Modulus of Rigidity Unity Bulk Modulus Poisson’s Ratio No unit

E=2 G(1+μ) E=3 K(1 -2μ)

MATERIALS HOMOGENEOUS ISOTROPIC ORTHOTROPIC NON-ISOTROPIC Independent Elastic Constants 2 2 9 21

CONVERSIONS :

STRENGTH OF MATERIALS SIMPLE STRESSES & STRAINS (PART-2)

DEFORMATION OF A PRISMATIC BAR : A BAR OF UNIFORM CROSS SECTIONAL AREA

Members in series (Statically Determinate Members) 600 mm 1000 mm

Indeterminate Members

Members in Parallel

300 mm Q A reinforced concrete column is 300 mm × 300 mm in section. The column is provided with 8 bars of 20 mm diameter. The column carries a load of 360 KN. Find the stress in concrete and the steel bars E (steel)= 210 GPa and E(concrete)=14 GPa. 300 mm

SPECIAL REVISION 50/50 OF STRENGTH OF MATERIALS FOR ONLINE EXAMS PART- IV 10 QUESTIONS with EXPLANATIONS

500 mm 625 mm 750 mm 700 mm 25 KN 10 KN

Step 1 : Consider Rod BE Take Moment about Point D Step 2 : Algebraic Sum of Change in length of AB and BC. 500 mm 625 mm 750 mm 700 mm 25 KN 10 KN