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## The rigid beam is supported by the three suspender bars. bars ab and ef are made of aluminum and bar cd is made of steel. if each bar has a

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The rigid beam is supported by the three suspender bars. bars ab and ef are made of aluminum and bar cd is made of steel. if each bar has a cross-sectional area of 450 mm2, determine the maximum value of p if the allowable stress is (σallow)st = 200 mpa for the steel and ( σallow)al = 150 mpa for the aluminum. est = 200 gpa and eal = 70 gpa.

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Physics
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2021-09-05T15:31:17+00:00
2021-09-05T15:31:17+00:00 1 Answers
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## Answers ( )

Answer:Pmax = 67.5 KN

Explanation:We need to calculate the maximum allowable value of P for both aluminum and steel bars.

FOR STEEL BARS:Since,

(σallow)st = (Pmax)st/Awhere,

(σallow)st = maximum allowable stress of steel bar = 200 MPa = 2 x 10⁸ Pa

A = Cross-sectional area of steel bar = 450 mm² = 0.45 x 10⁻³ m²

(Pmax)st = Maximum allowable force for steel bar = ?

Therefore,

2 x 10⁸ Pa = (Pmax)st/0.45 x 10⁻³ m²(Pmax)st = (2 x 10⁸ Pa)(0.45 x 10⁻³ m²)(Pmax)st = 9 x 10⁴ N = 90 KNFOR Aluminum BARS:Since,

(σallow)al = (Pmax)al/Awhere,

(σallow)al = maximum allowable stress of Al bar = 150 MPa = 1.5 x 10⁸ Pa

A = Cross-sectional area of Aluminum bar = 450 mm² = 0.45 x 10⁻³ m²

(Pmax)al = Maximum allowable force for Aluminum bar = ?

Therefore,

1.5 x 10⁸ Pa = (Pmax)al/0.45 x 10⁻³ m²(Pmax)al = (1.5 x 10⁸ Pa)(0.45 x 10⁻³ m²)(Pmax)al = 6.75 x 10⁴ N = 67.5 KNSince,

(Pmax)al < (Pmax)st

Therefore,

The maximum allowable force will be:

Pmax = (Pmax)alPmax = 67.5 KN