Mechanics of Materials Engr 350 - Lecture 1 Stress - Normal/Direct shear Mechanics of Materials Study of internal effects caused by external loads Considers real bodies that deform (statics assumes no deformation) 3 main concerns Strength - Will it _____________________?
Stiffness - Will it _____________________? Stability - Will it ______________________? 2 Stress Defined as the intensity of an internal force In equation form: stress forc = e Note: scalar - just a number area vector - quantity with magnitude and direction tensor - has magnitude & direction as well as a plane
Stress is a tensor First subscript is the direction of area normal Second subscript is direction of the stress component 3 Normal Stress Use method of sections to consider a rectangular
bar with an axial load We cut a section through the bar Now the whole cut surface is resisting the load 4 Normal stress
The stress is acting normal to the cut surface therefore it is called a normal stress We use the symbol for normal stress for normal stress Sign convention for normal stress Positive (tension): Negative (compression): 5 Stress Example Determine the stress in the concrete pilar
6 Two-bar loading How to find load carried by each bar? Sum x and y forces at
joint Two equations, three unknowns Why not sum moments? Calculate F1,allowable based on max stress and area Solve for F2 and P based on F1,allowable Check if F2 is higher or lower than F2,allowable If necessary, repeat using F2,allowable to solve for F1 and P 7 Demo TK Solver?
Use the following: A1 = 2.0 in2 A2 = 1.5 in2 for normal stress1,max = 12,000 psi for normal stress2,max = 18,000 psi At the joint, what are these equations? FFx = 0 FFy = 0 What are the max allowable forces for F1 and F2?
8 Stress on inclined plane (TB Section 1.5) What if we cut the bar at an angle? What stresses are acting on that surface? 9
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