The document Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev is a part of the GATE Course Structural Analysis.

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**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)** M_{1}, M_{2}, M_{3} meet at a joint

M_{1} & M_{2} are collinear

⇒ M_{3} carries zero force

where M_{1}, M_{2}, M_{3}

represents member.**(ii)** M_{1} & M_{2} are non collinear and F_{ext} = 0

⇒ M_{1} & M_{2} 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_{A}_{y}) sin θ]

where, Δ_{AB} = Axial deflection of member AB.

P_{AB} = Force in member AB (Axial force)

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