Analysis of Trusses, Arches, Beams, Cables and Frames Notes for Civil Engineering Exams

By Vishwajeet Sinha|Updated : October 6th, 2021


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


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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Vishwajeet SinhaVishwajeet SinhaMember since Jun 2016
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