Answer:
σ = 3.402 KPa , γ = 0.25 , G = 13.608 KPa
Explanation:
Given:-
- The dimension of gelatin block = ( 120 x 120 x 40 ) mm
- The applied force, F = 49 N
- The displacement of upper surface, x = 10 mm
Find:-
Find the shearing stress, shearing strain and shear modulus.
Solution:-
- The shear stress is the internal pressure created in an object opposing the applied action ( Force, moment, bending, or torque ).
- A force of F = 49 N was applied parallel to the top surface of the gelatin block.
- The shear effect results in a stress in the gelatin block.
- The formulation of stress ( σ ) is given below:
σ = F / A
Where,
A : The surface area of the object that experiences the shear force.
- The top surface have the following dimensions:
A = ( 0.120 )*( 0.120 ) = 0.0144 m^2
Therefore,
σ = 49 / 0.0144
σ = 3.402 KPa
- The shear strain ( γ ) is the measurement of change in dimension per unit depth of the block.
- The top surface undergoes a displacement of ( x ). The height of the top surface of the gelatin block is L = 40 mm.
Hence,
γ = x / L
γ = 10 / 40
γ = 0.25
- The shear modulus or the modulus of rigidity ( G ) is a material intrinsic property that signifies the amount of resistive stress to any cause of deformation.
- It is mathematically expressed as a ratio of shear stress ( σ ) and shear strain ( γ ):
G = σ / γ
G = 3.402 / 0.25
G = 13.608 KPa
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