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SAFE 605: Application of Safety Engineering Principles Strength of Materials

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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

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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.

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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.”

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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

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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

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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

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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.

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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.

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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.

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

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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.

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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.

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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

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Stress-Strain Diagram

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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.

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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.

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

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