LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures MODULE 2 LOAD AND STRESS ANALYSIS SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 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 SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures  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. Mechanics of Materials SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Applications involving combined loading Typical Engineering Structures SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Types of Loading on Structures LOADSYMBOLUNITS (Metrics) UNITS (Engineering) Direct ForceF, PNlb f Shear ForceV, QNlb f TorsionTNmlb f -ft Bending MomentMNmlb f -ft Fluid PressurepNm -2 psi Temperature Difference TT oCoC oFoF SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Types of Loading on Structures SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 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. SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Under General Loading Conditions Stress – intensity of a force acting at a material point SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Simple Stresses SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Complex Stresses T P A  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?   A Shear stress Normal stress SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Transformation Equations SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Mohr’s Circle SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Fracture Planes SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Engineering Stress and Strain P – applied force A o – original cross-sectional area L o – original gage length L – instantaneous length s  P AoAo e  LL LoLo  L - L o LoLo Engineering stress, Engineering strain, P P L LoLo SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Engineering Stress-strain Curve e SoSo PlasticElastic s Necking Fractured Tensile failure in ductile material is associated with large plastic deformation. e Total  e el + e pl SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures  = E  Linear Non-linear /Power-law  = E   = K(  p ) n SS316 steel Engineering Stress-strain Curve SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Mechanical Properties of Some Materials MATERIALSE GPa (!0 6 psi) S o MPa(ksi) S U MPa(ksi) AISI 1040 steel 207 (30) 413 (60) 620 (90) Stainless Steel (28) 205 (30) 515 (75) 7075 Al alloy 72 (10.5) 105 (15) 230 (33) Gray cast iron (22) SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Concentration SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Concentration Stress concentration factor SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Concentration SKMM 4133 Failure of Engineering Components and Structures

LOAD AND STRESS ANALYSIS M.N. Tamin, UTM SME 4133 Failure of Engineering Components and Structures Stress Concentration Factors SKMM 4133 Failure of Engineering Components and Structures