Consider a pin-jointed structure as shown in Figure 4.13 and subjected to external force P 1 , P 2 and P 3 . Let the vertical displacement of point C , is required. Under the action of the real external load, let the axial force in typical member be and therefore, the deformation of the member
( L and AE are the length and axial rigidity of typical member).
Apply a unit vertical load at C and substituting in Eq. (4.12) leads to
(4.14)
The basic steps to be followed for finding the displacements of the pin-jointed structure are
Compute the axial force in various members (i.e. ) due to applied external forces.
Compute the axial force in various members (i.e. ) due to unit load applied in the direction of required displacement of the point.
Compute the product for all members.
The summation will provide the desired displacement.
The axial force shall be taken as positive if tensile and negative if compressive.
The positive implies that the desired displacement is in the direction of applied unit load and negative quantity will indicate that the desired displacement is in the opposite direction of the applied unit laod.
is required. Under the action of the real external load, let the axial force in typical member be 
and therefore, the deformation of the member
( L and AE are the length and axial rigidity of typical member). 
) due to applied external forces. 
) due to unit load applied in the direction of required displacement of the point. 
for all members. 
will provide the desired displacement. 
implies that the desired displacement is in the direction of applied unit load and negative quantity will indicate that the desired displacement is in the opposite direction of the applied unit laod. 
