Applied Mechanics- Stress and Strain

STRESS

Tensile stress (ot) Compressive stress (Oc) Shear stress (T)

STRESS ( ) When a material is subjected to an external force, a resisting force is set up within the component. the forces distributed over a given section is called the stress at a point. engineering stress or conventional stress . The internal resistance force per unit area acting on a material or intensity of . It uses original cross section area of the specimen and also known as Therefore, P/A

P is expressed in Newton (N) and A, original area, in square meters (m2), the stress will be expresses in N/ m2. This unit is called Pascal (Pa). . As Pascal is a small quantity, in practice, multiples of this unit is used. . 1 kPa 103 Pa 103 N/ m2 1 MPa 1 GPa 109 Pa 109 N/ m2 (kPa Kilo Pascal) (MPa = Mega Pascal) (GPa Giga Pascal) 106 Pa = 106 N/ m2 = 1 N/mm2

Tensile stress (ot) due to the external force. A member subjected to an external force tensile P and tensile stress . If > 0 the stress is tensile, ie. The fibres of the component tend to elongate distribution due to the force is shown in the given figure. AL Lo Bar is under tension Tensile Stress- A

Compressive stress ( shorten due to the external force. stress distribution due to the force is shown in the given figure. . If < 0 the stress is compressive. i.e. The flores of the component tend to . A member subjected to an external compressive force P and compressive AL Lo Bar is under compression Compressive Stress- A

. Shear stress ( . When forces are transmitted from one part of a body to other, the stresses developed in a plane parallel to the applied force are the shear stress. Shear stress acts parallel to plane of interest. Forces P is applied transversely to the member AB as shown. . The corresponding internal forces act in the plane of section C and are called shearing forces. The corresponding average shear stress () T = Area Shear Stress Section plane A 2 A Cross Section Area Applied Force f ar A) Pure shear

compressional stress tensional stress shear stress

Normal stress Intensity of force, or force per unit area, acting normal to AA Symbol used for normal stress, is o (sigma) lim AF

AVERAGE NORMAL STRESS IN AXIALLY LOADED BAR Examples of axially loaded bar Usually long and slender structural members Truss members, hangers, bolts Prismatic means all the cross sections are the same Internal force Cross-sectional aca Region of uniform deformti of bar Extemal force (al

Average normal stress distribution Rz xz -average normal stress at any point on cross sectional area P internal resultant normal force A x-sectional area of the bar

MAXIMUM AVERAGE NORMAL STRESS For problems where internal force P and x-sectional A were constant along the longitudinal axis of the bar, normal stress = P/A is also constan If the bar is subjected to several external loads along its axis, change in x-sectional area may occur. Thus, it is important to find the maximum average normal stress. To determine that, we need to find the location where ratio P/A is a maximum