Determine the plastic moment capacity fo the beam as shown on figure take load factor

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written 7.9 years ago by

teamques10 ★ 69k

Degree of Indeterminancy , r = 6 – 3 = 3

Number of plastic hinges , n = r + 1 = 3 + 1 = 4

Plastic Hinges Location , N = 6

Number of Independent mechanism = N – r = 6 – 3 = 3

For AB collapse , Θ = δ / 2

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Using Work equation ,

ΣP * δ = Σ Mp * Θ

30 * 4 * 2Θ = Mp * Θ + Mp ( Θ + Θ ) + Mp * Θ

240 * Θ = 4 Mp * Θ

Mp = 60 KN-m …………………………………… (1)

For BC collapse ,

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ΣP * δ = Σ Mp * Θ

24 * δ = Mp * Θ + Mp ( 2Θ ) + Mp * Θ

48 * Θ = 4 Mp * Θ

Mp = 12 KN-m ……………………………………. (2)

For CD collapse ,

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Θ = δ/1 , α = δ / 3

Θ = 3 α

Acc to work equation

ΣP. δ = Σ Mp * Θ

40 * δ = Mp * Θ + 2 Mp * ( Θ + α )

40 * Θ = Mp * Θ + 2 Mp * ( Θ + Θ/3 )

40 * Θ = ( 11 / 3 ) * Mp * Θ

Mp = 10.91 KN-m …………………………………. (3)

Plastic moment = Greatest Mp

From above 3 values , take highest value of Mp ,

Mp = 60 KN-m

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