13
Strength of Materials
Prepared by, Jenifer S
STRESS
• Resistance force offered by the material
per unit area
• Applied force or system of forces that
tends to deform a body
• Stress distribution may or may not be
uniform, depending on the nature of the
loading conditionSTRAIN
• When the external force applied in the
material it tends to go some deformation
• Difference between the change in
dimension of the object to the original
dimension of the object
Normal Stress(𝜎)
Result of load applied perpendicular to a member
Shear Stress (𝜏)
Results when a load is applied parallel to an area
Normal Strain (ε)
Ratio between change in dimension to original
dimension
Shear strain (γ)
Change in angle
States of Stress:
• Simply a general state of stress at a point involves all the
normal stress components, together with all the shear stress
components and it remains under equilibrium
• Six components to specify the state of stress at a point
(i.e) 𝜎x , 𝜎y , 𝜎z , 𝜏xy , 𝜏yz , 𝜏zx
States of Strain:
• Homogenous strain always deforms circles and spheres into
strain ellipses and strain ellipsoids, respectively. The strain
ellipsoid completely defines the State of strain
• εx , εy , εz , γxy , γyz , γzx
Stress transformation equation,
[𝜎’] = [q] [𝜎] [q]ᵀ
Strain transformation
ε’ = RAR¯¹ε
Where,
R – Reuter’s matrix
Mohr’s Circle
• 2-D graphical representation of the transformation
law for the Cauchy stress tensor
• Used to determine graphically the stress components
acting on a rotated coordinate system
• Locus of points that represent the state of stress on
individual planes at all their orientations, where the
axes represent the principal axes of the stress
element
• Can be applied to any symmetric 2x2 tensor matrix,
including the strain and moment of inertia tensors.
• s
Derivation of Mohr's circle parametric equations - Equilibrium of forces
Derivation of Mohr's circle parametric equations - Tensor transformation
SUBSCRIBE TO
