Question

For the beam and loading shown, use discontinuity functions to compute: (a) the slope Os of the beam at B, and (b) the deflection VA of the beam at A. Assume a constant value of ET = 68000 kN m2 for the beam; WA = 15 kN/m, wg - 41 kN/m, LAB 2.9 m, Lac = 1.9 m,

Answer 1

WB P1- T I ni i i III WA - - wat jy ! 1 We F lag = 2.90 LAB = 2.9M flee elogim Lec = 1.9m ADDED LOAD UPSIDE & DOWNSIDE OF BEAM AS SHOWN WA = 15 kn/m ; e = 40 kN/m El z 68000 kn.m2 WB - WA Wc-WA were ble [ema + loc = love LABt.Lbc = LAC LAB LAB + LBC Ne = 58.034 FROM DOUBLE INTE GRATION METHOD

WA Wc-WA) 23 WB (21-L m 2 LAC 3 2 LBC INTEGRATE ON BOTH SIDES I Wan² [We-WA) a4 - 24LAC WB (O-LAR) + Wc-WB ola E1 + CU- - (2-LAP + 24 LBC 417 . 4 - | nowy z c-myno **sca) - AGAIN INTEGRATE ON BOTH SIDES WA 27 We-WA) Stca I 1118 (A-LAB)" wc-we +0,+ - - + - 120 LAC Igo ge

→ Apply BOUNDARY CONDITIONS AT * = 408 m; dy=0 43.034 7) ****en el cas 40 - La copy na 17.034 1970 : 24 (48) 24 (19) | = -423.043 4 .8 m ; y=0 * 4.974 43.03% (he) 43.034 5 - 41(109) 14.034(.que (4-4) - 423.043 (4-6) + y - 120(4.8) 24. 120 (19) 20 24 2 1532, 543 @ Slope AT B ire. 252.9 m; from to © - 68000 L i ter ) DEFLECTION AT A i-e. 120 m from to @ Voz (1532.543) = 0.022538 m 68000 NVA = 22. 538 mm