SAFE 605: Application of Safety Engineering Principles

1. SAFE 605: Application of Safety Engineering Principles Strength of Materials

2. Load • A load is a force applied to a body. • In engineering, a load can be due to any one of the following forces: • Stationary load (dead load) • Change in velocity (inertia force) • Rotation • Friction • Bending • Twisting (Torsion) • Change in temperature • Load Units are in force per unit length

3. Force • Represents the action of one body on another which may or may not change the motion of the body. • External forces: Reactions and loads placed on a structure. • Internal forces: Forces present in a structure, which are developed within the body of the structure necessary to balance the external forces.

4. Resultant Forces • The reduction of several forces in a force system is referred to as “resolving the force system.” • The resulting single force is called the “resultant force.”

5. Moment • A measure of the tendency of a force to cause rotation about an axis. • The graphical representation of a moment acting on an object is called a curl. • A curl is an arc shaped arrow drawn near and about the axis of rotation. • Typical units are in-lbs, ft-lbs and ft-kips, N-m • Moment(M) = Force(F) times the perpendicular distance to the axis(d). • M = F x d

6. Stress • The application of force to a body causes deformation which results in an equal and opposite resisting force in the material • Stress is the ratio of applied load to the cross-sectional area of an element in  tension and is expressed in pounds per square inch (psi) or kg/mm2.   • Stress = Load/Area

7. Strain • Strain is the measure of deformation produced in a component due to the load imposed. • The measure of the deformation of the material is dimensionless. • Strain = New length/original length   

8. Elasticity • Metal deformation is proportional to the imposed loads over a range of loads. • A material is elastic as long as the strain disappears with the removal of the load. • The load point which this does not happen and the corresponding stress is referred to as the elastic limit.

9. Modulus of elasticity (Young’s Modulus) • Since stress is proportional to load and strain is proportional to deformation, this implies that stress is proportional to strain. • Hooke's Law is the statement of that proportionality.   • Stress     =  E  X Strain • The constant, E, is the modulus of elasticity, (Young's modulus) or the tensile modulus and is the material's stiffness. • Young's Modulus is in terms of 106 psi or 103 kg/mm2.  • If a material obeys Hooke's Law, it is elastic.

10. Ultimate strength • The maximum stress a material withstands when subjected to an applied load.  • Dividing the load at failure by the original cross sectional area determines the value. 

11. Elastic limit • The point on the stress-strain curve beyond which the material permanently deforms after removing the load .

12. Bending stress • When bending a piece of metal, one surface of the material stretches in tension while the opposite surface compresses.  • It follows that there is a line or region of zero stress between the two surfaces, called the neutral axis.

13. Yield Strength • Point at which material exceeds the elastic limit and will not return to its origin shape or length if the stress is removed (permanent deformation occurs). • This means, in effect, the maximum load that will allow the material to return to its original shape when the load is removed. • The value is determined by evaluating a stress-strain diagram produced during a tensile test.

14. Yielding • Yielding occurs when the design stress exceeds the material yield strength. • Safety factor is a function of design stress and yield strength. • The following equation denotes a safety factor: • Safety Factor = YS / DS • Where YS  is the Yield Strength and DS  is the Design Stress

15. Stress-Strain Diagram

16. Coplanar Force Systems • Coplanar force systems are analyzed on an X – Y coordinate system. • The assumption is that forces may exist upon the structure in two dimensions. • To solve a coplanar force system, all forces acting upon the structure are resolved into their respective X – Y components.

17. Moment of Inertia TheMoment of Inertia (I) is a term used to describe the capacity of a cross-section to resist bending. It is a mathematical property of a section concerned with a surface area and how that area is distributed about the reference axis.

18. Deflection When a load is placed on a beam, the formerly-straight horizontal (centroidal) axis of the beam is deformed into a curve