Degree of Static Indeterminacy
Truss Member Carrying Zero forces
(i) M1, M2, M3 meet at a joint
M1 & M2 are collinear
⇒ M3 carries zero force
where M1, M2, M3
(ii) M1 & M2 are non collinear and Fext = 0
⇒ M1 & M2 carries zero force.
Final force in the truss member
sign convn → +ve for tension, –ve for compression
S = Final force in the truss member
K = Force in the member when unit load is applied in the redundant member
L = Length of the member
A = Area of the member
E = Modulus of elasticity
P = Force in the member when truss become determinate after removing one of the member.
P = Zero for redundant member.
Lack of Fit in Truss
Q = Force induce in the member due to that member which is 'Δ' too short or 'Δ' too long is pulled by force 'X'.
Where, yC = Deflection of truss due to effect of loading & temp. both.
If effect of temperature is neglected then
yc = ∑PkL/AE
α = Coefficient of thermal expansion
T = Change in temperature
T = +ve it temperature is increased
T = -ve it temperature is decreased
P & K have same meaning as mentioned above.
Stiffness Method for Truss
ΔAB = ΔB - ΔA
PAB = AE/L[ΔEX - ΔAX)cos θ + (ΔBy - ΔAy) sin θ]
where, ΔAB = Axial deflection of member AB.
PAB = Force in member AB (Axial force)