Stiffness Method for Beams

# Stiffness Method for Beams - Stiffness Method 2-Span Beam...

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Stiffness Method - 2-Span Beam Example (FPP) Span 1 Length L 8 m EI/L_1 5000 kNm Young's Modulus E 200 Second Moment of Area I 200 K12 = 20000 10000 FEM 12 100 kNm 10000 20000 FEM 21 -100 kNm Span 2 Length L 6 m Young's Modulus E 200 EI/L_2 6666.667 kNm Second Moment of Area I 200 FEM 23 90 kNm K23 = 26666.67 13333.33 FEM 32 -90 kNm 13333.33 26666.67 Global Moments Global Deflections 1 2 3 -100 20000 10000 0 d1 10 = 10000 46666.67 13333.33 * d2 90 0 13333.33 26666.67 d3 Restrict 10 = 46666.67 13333.33 * d2 90 13333.33 26666.67 d3 Solve d2 = 0.000025 -1E-005 * 10 d3 -1E-005 4.4E-005 90 d2 = -0.000875 rads d3 0.003813 rads Member 12 Forces M1 = 20000 10000 * 0 M2 10000 20000 -0.000875 M1 = -8.75 kNm M2 -17.5 kNm Member 23 Forces M2 = 26666.67 13333.33 * -0.000875 M3 13333.33 26666.67 0.003813 M2 = 27.5 kNm M3 90 kNm Final Moments Member 12 M1 = -8.75 - -100 = 91.25 M2 -17.5 100 -117.5 Member 23 M2 = 27.5 - -90 = 117.5 M3 90 90 0 Nodal Moments 1 2 3 91.25 117.50 0.00 kNm Tension on: Top Top Btm kN/mm 2 E6 mm 4 kN/mm 2 E6 mm 4

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Stiffness Method for Beams - Stiffness Method 2-Span Beam...

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