Chapter 1:
,
where P is an axial force and A the cross section area.
,
where P is an axial force and A is thickness times diameter (bearing stress)
,
where P is the shearing force and A is the cross sectional area
Keep in mind that there may be two areas (on a bolt) being sheared - double shear - it is best not to memorize a formula for this but consider each case separately. Sometimes it is better to double the area; sometimes it is more convenient to halve the force.
Factor of safety: 
Stresses on oblique sections if an axial force is applied:
The formulas are different if a shearing force is the initial force applied; see class notes.
Chapter 2:
If the diameter, force, or elastic modulus are variable, use
Statically indeterminate problems - use
the above formulas to obtain extra equations
Statically indeterminate problems with
temperature changes - use
Dilation & Bulk modulus - relationships between the moduli:
Also, 
Stress concentrations - see charts on page
108: 
.
Plastic deformations - these are best done using a load-deflection diagram or a stress-strain diagram.
Chapter 3:
