MOS Lecture of unit no 3 of strength og materials for civle ngine

mos unit 3

1. SRES’s Sanjivani K.B.P. Polytechnic Kopargaon-423603 (Continue 9 years NBA Accredited Institute) Department of Civil Engineering Academic Year: 202 3 -2 4 Sem: Third (ODD) Program: Civil Engineering Course & Code: MOS (22303) Date: 27 / 08 /202 3 UNIT NO.3: ELASTIC CONSTANTS Topics: Important Definitions, Volumetric Strain, Concept of Single Shear and Double Shear Presented By: Mr.Avhad N.V. LCE, SKBP, Kopargaon-423603

2. Important Definitions: Lateral Strain: “ The ratio of change in lateral dimension to original lateral dimension is called as lateral strain.” Unit- It has no unit. Linear Strain: “ The ratio of change in linear dimension to original dimension is called as linear strain.” Unit- It has no unit. Poisson’s Ratio: “ The ratio of lateral strain to the linear strain is called as poisson’s ratio.” Unit- It has no unit. Modulus of Rigidity: “ The ratio of shear stress to shear strain is called as modulus of rigidity.” Unit- N/   = or or   =   or = -   G =  

3. Volumetric Strain: “ The ratio of change in volume of body to original volume of body is called as volumetric strain.” Unit- It has no unit. Bulk Modulus: “It is ratio of Direct stress to the volumetric strain” Unit- N/   K =   =  

4. Volumetric Strain: Uni-axial Stress System: Consider a rectangular bar of width ‘b’, thickness ‘t’ and length ‘L’. It is subjected to axial pull (tensile) force ‘P’. In this system, force is applied in one direction only. Hence it is called as uni -axial stress system. As force is applied in only one direction, stress is developed in only one direction. = , = 0, = 0 = -------- (1) We know, = - and also = - = = - x = - from equation (1) = - Volumetric Strain, = = + + = - -       Strain = stress /E = (1- 2 )  

5. Volumetric Strain: Bi-axial Stress System: Consider a rectangular bar of width ‘b’, thickness ‘t’ and length ‘L’. It is subjected to axial pull (tensile) force ‘ P x ’ in longitudinal direction and ‘ P y ’ in lateral upward direction. In this system, force is applied in ‘x’ and ‘y’ directions. Hence it is called as bi-axial stress system. As force is applied in two directions, stress is developed in two directions. = , = , = 0 = Linear strain due to + lateral strain due to But Linear strain due to , = and lateral strain due to , = - ------ (1) = Linear strain due to + lateral strain due to = - -------- (2)          

6. Volumetric Strain: Bi-axial Stress System: Similarly, = - -------- (3) From (1), (2) and (3), = = + + = - + = + - = (1- 2 ) + (1-2 )   = (1- 2 )  

7. Volumetric Strain: Tri-axial Stress System: Consider a rectangular bar of width ‘b’, thickness ‘t’ and length ‘L’. It is subjected to axial pull (tensile) force ‘ P x ’ in longitudinal direction and ‘ P y ’ and ‘ P z ’in lateral directions. In this system, force is applied in ‘ x’,‘y ’ and ‘z’ directions. Hence it is called as tri-axial stress system. As force is applied in three directions, stress is developed in all three directions. = , = , = = Linear strain due to + lateral strain due to + lateral strain due to But Linear strain due to , = , lateral strain due to , = - lateral strain due to , = - = - - -------- (1) Similarly, =Linear strain due to +lateral strain due to + lateral strain due to              

8. Volumetric Strain: Tri-axial Stress System: = - - -------- (2) Similarly, = - - -------- (3) From (1), (2) and (3), = = + + = - - + = (1- 2 ) + (1-2 ) + (1-2 )   = (1- 2 )  

9. Concept of Single Shear and Double Shear: Single Shear: When two metal plates joined by riveted connections as shown in above figure subjected to axial force in either directions, single shear occurs. In single shear there is only one plane of shear failure. Shear stress q = = , where d = diameter of rivet at failure plane. Double Shear: When three metal plates joined by riveted connections as shown in above figure subjected to axial force in either directions, double shear occurs. In double shear there are two planes of shear failure. Shear stress = = , where d = diameter of rivet at failure plane.   P P P P P