Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev

Structural Analysis

GATE : Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev

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

  • DS = m+re – 2j where, DS = Degree of static indeterminacy m = Number of members, re = Total external reactions, j = Total number of joints
  • DS = 0 ⇒ Truss is determinate
    If Dse = + 1 & Dsi = –1 then DS = 0 at specified point.
  • 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.
Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev(ii) M1 & M2 are non collinear and Fext = 0
⇒ M1 & M2 carries zero force.
Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev

Indeterminate Truss

Final force in the truss member

Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev
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

Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev
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

Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRev
Where, yC = 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

Analysis of Trusses, Arches, Beams, Cables & Frames GATE Notes | EduRevΔAB = ΔB - ΔA
PAB = AE/L[ΔEX - ΔAX)cos θ + (ΔBy - ΔAy) sin θ]
where, ΔAB = Axial deflection of member AB.
PAB = Force in member AB (Axial force)

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