Strength of Material (Part-2) (General Engineering) (SSC JE)

Resilience–The total strain energy stored in a body is commonly known as resilience. Whenever, the straining force is removed from the strained body, the body is capable of doing work. Hence, the resilience is also defined as the capacity of a strained body for doing work on the removal of the straining force.

Proof resilience–The maximum strain energy stored in a body is known as proof resilience. The strain energy stored in the body will be maximum, when the body is stressed upto elastic limit.

Modulus of resilience–It is defined as the proof resilience of a material per unit volume.
Modulus of resilience = Proof resilience/Volume of the body

Engineering stress-strain curve of mild steel for tension under static loading–
• Straight line (Proportional region, Hooke's law is valid)
A - Limit of proportionality
B - Elastic limit
C - Upper yield point
C' - Lower yield point
E - Ultimate point or maximum stress point
F - Fracture point
OA - Straight line
OB - Elastic region
BC - Elasto plastic region
CD - Perfectly plastic region
DE - Strain hardening
EF - Necking region

In symmetrical beam sections the maximum shear stress is in the centroid axis fiber.

Mohr circle is a circle which represents the relation between normal stress and shear stress for a plane of a 2 dimensional stressed body.
• It is helpful in finding maximum and minimum principal stresses maximum shear stress etc.
• It is 2 dimensional graphical representation.
• It is used to determine stresses on an oblique section of a body subjected to–
• Direct tensile stress is two mutually perpendicular directions.
• Direct tensile stress is two mutually perpendicular directions accompanied by a simple shear stress.
• Direct tensile stress in one plane accompanied by a shear stress.

Mohr’s circle–
• The transformation equation for plane stress can be represented in graphical form by a plot known as Mohr's circle.
• It also provides a means for calculating principle stresses, maximum shear stresses and stresses on inclined planes.
• Mohr's circle represents the transformation of the second order tensor. The Mohr circle can be applied to any symmetric tensor matrix including the strain and moment of inertia tensors.
• Mohr's circle is valid not only for stresses but also for other quantities of a similar mathematical nature, including strains and moments of inertia.
• Stress at a point area moment of inertia is 2nd order tensor which can be represented by 3 × 3 matrix.