The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is

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Two steel truss members AC and BC, each having cross sectional area of 100 mm², are subjected to a horizontal force F as shown in the figure. All the joints are hinged.

ME-GATE-2012

The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is

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Answer 1

F2 S.C Madhu 22.05.20 D1

Given:

Area = 100 mm² = 100 × 10^-6 m²

$\frac{T_{1}}{\sin 120^{\circ}} = \frac{T_{2}}{\sin 135^{\circ}} = \frac{F}{\sin 105^{\circ}}$

$\frac{T_{1}}{\sin 120^{\circ}} = \frac{F}{\sin 105^{\circ}}$

T1 = 0.8965F

$\frac{T_{2}}{\sin 135^{\circ}} = \frac{F}{\sin 105^{\circ}}$

T2 = 0.732F

Maximum force is,

F_max = Max(T₁,T₂) = T₁ = 0.8965F

$M a x i m u m s t r e s s = \frac{F_{m a x}}{a r e a} = \frac{0.8965 F}{100 \times 10^{- 6}} = \frac{0.8965 F}{100} M P a$

Now,

Maximum stress ≤ 100 MPa

$\frac{0.8965 F}{100} M P a \leq 100 M P a$

$F \leq \frac{100 \times 100}{0.8965}$

F ≤ 11.154 kN

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The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100 MPa is

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