Question

9. For the beam loaded and supported as shown in Figure (see Week 4), use the integration method to determine (a) The equation of the elastic curve using the xi and x2 coordinates (b) The slope at A. (c) The deflection at C Take E 200 GPa and1- 4 x 108 mm4 30 kN 20 kNm 4 m 2 m

Answer 1

Guven- 3 0 KN 20 KAJ.m m) 2m RA Soluthon O Suppt Reactions - +ve - ve RB 50 KN ve RA + RBご30 - change the doechion of RA e Equation of Elastic Cve dot2 . To find th1 S' Taking Section at distance χ mh,n, C 2 Integrating 1st ω.γ. to χ 2- dod 6 2. 6

③ To Find constants of Integ ratonc, and(q Using boundhy conditions - 6 2. 2. C4 2C1-4 6 2 8.33 x (6-2)3 0 x(c)3 + 6 C, t 2c 1-80 +1ox (c) : 8 C826,88 | CI -103. 36 Put C, and G2 in above equations and and

dol 3 doi This is slope equation oly This s deflection equation ind the slope and deflection: つ Slope al. A : Put χ = 6 m in Slope e9uat.on and Use ωhole eaualhon EL.dy一ー 15χ2-103.3c+ 20γ-25(1-2) 2. EL dy di (A) - 540 lo3 3G 120400 d2 E=200 GPa ニ4X108乂10-12

da (A) EL S6, 64 S 6.64 b) DefFlection at C: Put xo m , in Deflection equation 2 Ft.ycニ5X3-103.36 χ-28 6.72 Но χ EL yc - -286.72 y. - -286,72 28 6.72 200 X lo6 410 DeFlection at C 3.S84 x103 m AnsweS eqation of Elastic Cunve ② Slope at Aニ1.gs.8x1,-づadlan a Defied on at c ус - 3.S84 mm