Pin-jointed steel structure, Mechanical Engineering

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Pin-jointed steel structure:

Find out the forces in the members of the pin-jointed steel structure.

Solution

Joint D

Suppose f_CDand f_DE both as tensile forces; and also suppose the nature of other members forces as illustrated.

f_CD = 2 t ⇒ ∴ f_CD = 2 t (tension)

and f_DE = 0

Joint C

∠ BCE = ∠ DCE = 45^o (obviously)

f_CD= f_CE cos 45^o⇒ ∴ f_CE = 2 √2

= 2.8284 (comp.)

i.e. CE is a strut

f_CB = f _CE cos 45^o = 2 × √2 × (½) = 2 t (tension)

i.e. CB is a tie.

Joint E

f _EF = f _CE cos 45^o = 2 × √2 × (1/√2) = 2 t (comp.)

f _EB = f _CE cos 45^o = 2 × √2 × (1/√2) = 2 t (tension)

Joint B

∴ f _BE = f_BF cos 45^o (comp.)

f _BE =2 √2 t(comp.)

f _AB - f _FB cos 45^o = f_BC

f _AB = 2 × √2 × (1/√2) = 4t (comp.)

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