Report

SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures MODULE 2 LOAD AND STRESS ANALYSIS LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures LOAD AND STRESS ANALYSIS Load Equilibrium equations Complex stresses Stress transformation Mohr’s circle Stress-strain relations Stress concentration LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Mechanics of Materials A branch of mechanics that studies the relationships between external loads applied to a deformable body and the intensity of internal forces acting within the body. LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Typical Engineering Structures Applications involving combined loading LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Types of Loading on Structures LOAD SYMBOL UNITS (Metrics) UNITS (Engineering) Direct Force F, P N lbf Shear Force V, Q N lbf Torsion T Nm lbf-ft Bending Moment M Nm lbf-ft Fluid Pressure p Nm-2 psi T oC oF Temperature Difference LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Types of Loading on Structures LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Equilibrium of a Deformable Body A body is said to be in equilibrium when the resultant of all forces and moments acting on the body is zero. F 0 Mo 0 LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Under General Loading Conditions Stress – intensity of a force acting at a material point LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Simple Stresses Tr J LOAD AND STRESS ANALYSIS P A M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Complex Stresses T A• P Shear stress A Normal stress LOAD AND STRESS ANALYSIS What is the magnitude of stress and strain on specific plane at A? Does the stress and strain represent critical / maximum values at A? If not… what is the maximum & minimum (principal) stresses and maximum shear stresses? What is the corresponding strain values? On which planes do these stresses act? M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Transformation Equations x x y xy 2 x y LOAD AND STRESS ANALYSIS 2 x y 2 cos 2 xy sin 2 sin 2 xy cos2 M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Mohr’s Circle LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Fracture Planes LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Engineering Stress and Strain P Lo L Engineering stress, s P Ao Engineering strain, e L Lo L - Lo Lo P – applied force Ao – original cross-sectional area Lo – original gage length L – instantaneous length P LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Engineering Stress-strain Curve s Fractured Tensile failure in ductile material is associated with large plastic deformation. Necking So Fractured eTotal eel + epl Elastic LOAD AND STRESS ANALYSIS Plastic e M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Engineering Stress-strain Curve 800 SS316 steel STRESS, (MPa) 600 Non-linear /Power-law = K(p)n 400 200 200 = E 0 0.0 0.1 0.2 0.3 STRAIN, 0.4 STRESS, (MPa) 150 Linear 100 0.5 0.6 = E 50 0 0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 STRAIN, LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Mechanical Properties of Some Materials MATERIALS E GPa (!06 psi) So MPa(ksi) SU MPa(ksi) AISI 1040 steel 207 (30) 413 (60) 620 (90) Stainless Steel 314 193 (28) 205 (30) 515 (75) 7075 Al alloy 72 (10.5) 105 (15) 230 (33) Gray cast iron - - 152 (22) LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Concentration LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Concentration Stress concentration factor Kt LOAD AND STRESS ANALYSIS max avg M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Concentration LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures SKMM 4133 Failure of Engineering Components and Structures Stress Concentration Factors LOAD AND STRESS ANALYSIS M.N. Tamin, UTM