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Stiffness (k) =
Rotation(╬╕)/Moment(M)
Rotation(╬╕)
Moment(M)/2Rotation(╬╕)
Moment(M)/Rotation(╬╕)
Moment(M)/Rotation(╬╕)
Stiffness (k) is defined as the measure of the resistance offered by an elastic body to deformation. In the context of structural mechanics, it represents the moment required to produce a unit rotation at a specific joint.
Stiffness (k) is defined as the measure of the resistance offered by an elastic body to deformation. In the context of structural mechanics, it represents the moment required to produce a unit rotation at a specific joint.
k=╬╕MтАЛ тАФ definition of rotational stiffness
M=L4EIтАЛтЛЕ╬╕ тАФ stiffness for a member with far end fixed
When an external moment (M) is applied to a structural member, it induces a rotation (╬╕). The stiffness (k) is the proportionality constant in the relationship M=kтЛЕ╬╕, which simplifies to k=╬╕MтАЛ. This parameter is fundamental in the slope-deflection method and matrix stiffness analysis for indeterminate structures.
Stiffness is a property of the structure's geometry and material (E and I).
It is independent of the load applied and purely a structural characteristic.
Higher stiffness implies higher resistance to deformation for a given moment.
Essential for analyzing indeterminate structures.
Used to compute distribution factors in Moment Distribution Method.
Does not account for non-linear material behavior directly.
Assumes linear elastic response (Hooke's law).
Continuous beam analysis.
Frame analysis in building design.
Vibration analysis of structures.
Stiffness is inversely proportional to flexibility (Flexibility=k1тАЛ=M╬╕тАЛ).
Option A represents flexibility, not stiffness.
D is correct тАФ Stiffness (k) is the ratio of the applied moment (M) to the resulting rotation (╬╕)at the same point.
Remember that stiffness is defined as 'Force or Moment per unit displacement/rotation', whereas flexibility is 'Displacement or Rotation per unit force/moment'.