(1) The three-bar truss ABC shown in the figure is constructed of steel pipes having cross- sectional area A = 3900 mm² and modulus of elasticity E = 200 GPa. The inclined bars are L = 2 m long and the horizontal span AB is v2L = 2/2 m. A vertical load P = 500 kN is placed at C, as shown. 1. Determine the three bar forces in terms of P. 2. Obtain the total strain-energy expressions U U and U for AB, BC, and CA, respectively, in terms of P, A, L, and E. 3. Obtain a formula for the total strain energy U stored in the three-bar truss in terms of P, A, L and E. 4. If 8 is the vertical displacement of C , obtain 8 in terms of P, A, L and E via the use of W(work) = U(total strain energy). 5. What is the horizontal displacement &, of B in terms of P, A, L and E? Obtain 8, in mm.
(1) The three-bar truss ABC shown in the figure is constructed of steel pipes having cross- sectional area A = 3900 mm² and modulus of elasticity E = 200 GPa. The inclined bars are L = 2 m long and the horizontal span AB is v2L = 2/2 m. A vertical load P = 500 kN is placed at C, as shown. 1. Determine the three bar forces in terms of P. 2. Obtain the total strain-energy expressions U U and U for AB, BC, and CA, respectively, in terms of P, A, L, and E. 3. Obtain a formula for the total strain energy U stored in the three-bar truss in terms of P, A, L and E. 4. If 8 is the vertical displacement of C , obtain 8 in terms of P, A, L and E via the use of W(work) = U(total strain energy). 5. What is the horizontal displacement &, of B in terms of P, A, L and E? Obtain 8, in mm.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:(1) The three-bar truss ABC shown in the figure is constructed of steel pipes having cross-
sectional area A = 3900 mm² and modulus of elasticity E = 200 GPa. The inclined bars are
L = 2 m long and the horizontal span AB is 2L = 2/2
placed at C, as shown.
1. Determine the three bar forces in terms of P.
2. Obtain the total strain-energy expressions U
m. A vertical load P = 500 kN is
U
BC
and U for AB, BC, and CA,
AB
CA
respectively, in terms of P, A, L, and E.
3. Obtain a formula for the total strain energy U stored in the three-bar truss in terms of P,
A, L and E.
4. If 8 is the vertical displacement of C , obtain 8 in terms of P, A, L and E via the use of
W(work) = U(total strain energy).
5. What is the horizontal displacement &, of B in terms of P, A, L and E? Obtain 8, in mm.
A
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