lecture21 - Lecture21Columns July25,2003 CVEN444...

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    Lecture 21 – Columns Lecture 21 – Columns July 25, 2003 CVEN 444
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    Lecture Goals Lecture Goals Columns Interaction Diagrams Using Interaction Diagrams
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment    Interaction Diagram   Interaction Diagram Consider an square column (20 in x 20 in.) with 8 #10 ( ρ = 0.0254) and f c = 4 ksi and f y = 60 ksi. Draw the interaction diagram.
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Given 8 # 10 (1.27 in 2 ) and f c = 4 ksi and f y = 60 ksi ( 29 ( 29 2 2 st 2 2 g 2 st 2 g 8 1.27 in 10.16 in 20 in. 400 in 10.16 in 0.0254 400 in A A A A ρ = = = = = = =
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Given 8 # 10 (1.27 in 2 ) and f c = 4 ksi and f y = 60 ksi ( 29 ( 29 ( 29 ( 29 ( 29 0 c g st y st 2 2 2 0.85 0.85 4 ksi 400 in 10.16 in 60 ksi 10.16 in 1935 k P f A A f A = - + = - + = ( 29 n 0 0.8 1935 k 1548 k P rP = = = [ Point 1 ]
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Determine where the balance point, c b .
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Determine where the balance point, c b . Using similar triangles, where d = 20 in. – 2.5 in. = 17.5 in., one can find c b b b b 17.5 in. 0.003 0.003 0.00207 0.003 17.5 in. 0.003 0.00207 10.36 in. c c c = + = + =
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Determine the strain of the steel ( 29 ( 29 b s1 cu b b s2 cu b 2.5 in. 10.36 in. 2.5 in. 0.003 10.36 in. 0.00228 10 in. 10.36 in. 10 in. 0.003 10.36 in. 0.000104 c c c c ε - - = = = - - = = =
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Determine the stress in the steel ( 29 ( 29 s1 s s1 s2 s s1 29000 ksi 0.00228 66 ksi 60 ksi compression 29000 ksi 0.000104 3.02 ksi compression f E f E ε = = = = = =
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Compute the forces in the column ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 c c 1 s1 s1 s1 c 2 2 s2 0.85 0.85 4 ksi 20 in. 0.85 10.36 in. 598.8 k 0.85 3 1.27 in 60 ksi 0.85 4 ksi 215.6 k 2 1.27 in 3.02 ksi 0.85 4 ksi 0.97 k neglect C f b c C A f f C β = = = = - = - = = - = -
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Compute the forces in the column ( 29 ( 29 2 s s s n c s1 s2 s 3 1.27 in 60 ksi 228.6 k 599.8 k 215.6 k 228.6 k 585.8 k T A f P C C C T = = = = + + - = + - =
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    Example: Axial Load vs. Moment  Example: Axial Load vs. Moment     Interaction Diagram    Interaction Diagram Compute the moment about the center ( 29 c s1 1 s 3 2 2 2 2 0.85 10.85 in.
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lecture21 - Lecture21Columns July25,2003 CVEN444...

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