NEW 375 Lecture08(2) - Statically Indeterminate problems...

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Statically Indeterminate problems
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Given: Cross-section Areas: Modulus of Elasticity EXAMPLE PROBLEM 1. BEHAVIOR OF A REINFORCED CONCRETE COLUMN UNDER AXIAL LOADING 2 2 2 1 . 20 3 . 4 4 . 24 in A in A in A A A Con St Ccon St g = = = + = psi E psi E Con St 6 7 10 3 10 9 . 2 × = × = Cross- section
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FIND: Con St Con St P P σ σ , , EXAMPLE δ cross-section
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STEP 1: FORCE and EQUIBRIUM ? ? 50 = = = = Con St P P k F P St P St P Con P Con P = + = + Con St P P P + = Con St P P + = 50 (Eq.1) NOTE:Two unknowns
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δ STEP 2: DEFORMATION / GEOMETRY OF FIT Con St δ δ δ = = ASSUMING NO SLIDE BETWEEN CONCRETE AND STEEL BARS, THEY ARE SUBJECTED TO COMPRESSION SIMULTANEOUSLY . THEREFORE (Eq. 2)
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STEP 3: APPLY FORCE-DEFORMATION RELATIONSHIP: Con Con St St EA PL EA PL = = δ δ = Con Con Con Con St St St St A E L P A E L P = 3 30 1 . 20 3 . 4 Con St P P (Eq. 3) (Eq. 4) Substitute Eq. 3 & 4 into Eq. 2 con st δ δ = (Eq. 2) (Eq. 5)
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k P P k k P k P P Con St Con Con Con 1 . 34 14 . 2 9 . 15 14 . 3 50 50 14 . 2 = = = = = + k P Con 9 . 15 = k P St 1 . 34 = INTO Equation 1: k P P Con St 50 = + SUBSTITUTE Equation 5: SOLVE SIMULTANEOUS EQUATIONS
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