SAFE 605: Application of Safety Engineering Principles Strength of Materials

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

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.

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.”

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

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/mm 2 . 

Stress = Load/Area

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

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.

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 10 6 psi or 10 3 kg/mm 2 .

If a material obeys Hooke's Law, it is elastic.

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.

Elastic limit

 The point on the stress-strain curve beyond which the material permanently deforms after removing the load .

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.

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.

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

Design Stress is the

Stress-Strain Diagram

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.

Moment of Inertia

 The Moment 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.

Deflection

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