### Trusses

#### Degree of Static Indeterminacy

*D*=_{S}*m*+*r*– 2_{e}*j*where,*D*= Degree of static indeterminacy_{S}*m*= Number of members,*r*= Total external reactions, j = Total number of joints_{e}*D*= 0 ⇒ Truss is determinate_{S}

If*D*= + 1 &_{se}*D*= –1 then_{si}*D*= 0 at specified point._{S}*D*> 0 ⇒ Truss is indeterminate or dedundant._{S}

#### Truss Member Carrying Zero forces

(i) *M _{1}*,

*M*,

_{2}*M*meet at a joint

_{3}*M _{1}* &

*M*are collinear

_{2}⇒ *M _{3}* carries zero force

where *M _{1}, M_{2}, M_{3}*

represents member.

(ii) *M _{1} & M_{2}* are non collinear and

*F*= 0

_{ext}⇒ *M _{1} & M_{2}* carries zero force.

#### Indeterminate Truss

(i) 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

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

where, Δ* _{AB}* = Axial deflection of member AB.

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

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