02-Stress - Stress Civ E 270 Khattak N Stress Definition...

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Stress Civ E 270 Khattak, N 1 Stress Definition and Notation: The force per unit area, or intensity of the force distributed over a given section, is called the stress on that section and is denoted by the Greek letter ° (sigma). The stress in a member of cross-sectional area A subjected to an axial load P is then obtained by dividing the magnitude P of the load by the area A: A P Stress = = σ The internal force ° F acting on a small area ° A can be resolved into three components: one normal to the plane and two parallel to the plane. The normal component divided by ° A gives the normal stress (usually denoted by ± (sigma)), and parallel components divided by the area ° A give the shear stress (usually denoted by ² (tau)). Hence, ± = A F z Δ Δ (normal stress component) ² = A F x Δ Δ (shear stress component) ² = A F y Δ Δ (shear stress component) Units : Stress = ) ( 2 2 2 Pa pascal m N m s m kg Area Force = = = However, stress is normally expressed in Mega Pascal, where 1 x 10 6 Pa = 1 MPa i.e. 2 6 2 10 mm N m N = × Other units used for stress are kilo pascal, i.e. pascal x 10 3 = 2 m kN and giga pascal, i.e. pascal x 10 9 ° F x ° F y Area ° A x y z ° F ° F z A P
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Stress Civ E 270 Khattak, N 2 Average Normal Stress Consider an axially loaded prismatic bar with axial loads being applied to the ends of the member. If we cut an imaginary section through the bar by passing a plane (as shown in the figure), for equilibrium of the bottom segment, the internal force acting on the cross sectional area must be equal in magnitude and opposite in direction to the external force acting at the bottom of the bar. If we assume that the axial force at any cross section along the length of the bar remains constant then we can safely assume that the internal force can be distributed uniformly across any cross section of the bar by dividing the external force P by the cross sectional area. Hence, Average Normal Stress = ± ave. = A P If the axial force is a tensile force, the normal stress that is caused by the tensile force is called the tensile stress . Similarly, if the axial force is compressive, it will cause a compressive stress .
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