Analysis of Trusses, Arches, Beams, Cables & Frames | Structural Analysis - Civil Engineering (CE) PDF Download

Trusses

Degree of Static Indeterminacy

• D_S = m+r_e – 2j where, D_S = Degree of static indeterminacy m = Number of members, r_e = Total external reactions, j = Total number of joints
• D_S = 0 ⇒ Truss is determinate
  If D_se = + 1 & D_si = –1 then D_S = 0 at specified point.
• D_S > 0 ⇒ Truss is indeterminate or dedundant.

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
represents member.
(ii) M₁ & M₂ are non collinear and F_ext = 0
⇒ M₁ & M₂ carries zero force.

Indeterminate Truss

Final force in the truss member

sign convn → +ve for tension, –ve for compression
where,
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'.

Deflection of Truss

Where, y_C = 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

Δ_AB = Δ_B - Δ_A
P_AB = AE/L[Δ_EX - Δ_AX)cos θ + (Δ_By - Δ_Ay) sin θ]
where, Δ_AB = Axial deflection of member AB.
P_AB = Force in member AB (Axial force)