# Analysis of Trusses, Arches, Beams, Cables and Frames-2

By Vishwajeet Sinha|Updated : January 1st, 2017

### Trusses

#### Degree of Static Indeterminacy

1. DS = m+re – 2j where, DS = Degree of static indeterminacy m = Number of members, re = Total external reactions, j = Total number of joints
2. DS = 0 ⇒ Truss is determinate
If Dse = + 1 & Dsi = –1 then DS = 0 at specified point.
3. DS > 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 Fext = 0

M1 & M2 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, yC = 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, ΔAB = Axial deflection of member AB.

PAB = Force in member AB (Axial force)

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