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Δ = displacement caused when force is increased by a small amount
P = external force applied
N = internal force in the member force applied
L = length of member
A = cross-sectional area of member
E = Modulus of elasticity
Same symbol is used for partial and total differentiation and they are pretty obvious.
What will be the work done if all three forces are place at once on the beam?
  • a)
    (p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)
  • b)
    (p1 + dp1)(Δ1 + dΔ1) + 1⁄2 (p2)( Δ2 + dΔ2)
  • c)
     1⁄2 (p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)
  • d)
     1⁄2 (p1 + dp1)(Δ1 + dΔ1) + 1⁄2 (p2)( Δ2 + dΔ2)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Δ = displacement caused when force is increased by a small amoun...
Answer: d
Explanation: Now, since all the loads are gradually applied, all will have a factor of half.
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Δ = displacement caused when force is increased by a small amountP = external force appliedN = internal force in the member force appliedL = length of memberA = cross-sectional area of memberE = Modulus of elasticitySame symbol is used for partial and total differentiation and they are pretty obvious.What will be the work done if all three forces are place at once on the beam?a)(p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)b)(p1 + dp1)(Δ1 + dΔ1) +1⁄2(p2)( Δ2 + dΔ2)c)1⁄2(p1 + dp1)(Δ1 + dΔ1) + (p2)( Δ2 + dΔ2)d)1⁄2(p1 + dp1)(Δ1 + dΔ1) +1⁄2(p2)( Δ2 + dΔ2)Correct answer is option 'D'. Can you explain this answer?
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