Question

Determine the shear and moment along the beam as functions ofx. Also, draw the shear and moment diagrams for the beam. Notes: Always take distance x for any function to start from the very left end of the beam. Show neat sketches of all sections required to develop the shear and moment functions, specifying the function regions. 4 kN/m 2 kN/m 6 kN.m B I 3.0 m 3.0 m 3.0 m

Answer 1

4 kN/m 믄 Free Ay - Reaction 2kN/m 2kW at force By - Reaction force at B cm DJ6kum B 11 12K AN Ay 3.3273797 3m x 3nr 3 m "By 8.5 shear force diagram (KN) + lo 61 9.5 1 12.16466 12 Bencing Moment 6 + + Diagrom (KNM) + oo 1 x=6.3273 26=907- x=6m X50m >(3m take moment at B=0 Ay x6 = 240 x 2 + 1 x 2 x 6 X 8 - 6 Ay = 14.5KNA Equating vertical force Ay +By = 2x9 + 1/2 X 2 X 6 14.5 + By = 24 By = 9.5kN A

shear force and bending moment Equahon as a function of gli for (o&x<3m) (to A Val 2 kN/m - 2 x Shear force (EF.g=0) Iva KN Bencing moment (EM=O) 5 мя Mge= IMx=-22 -2x H x 34 2 KNM for point A put x= 3m VA = -2x3 = -6kN MA= -32= -9kNm V for (3<x<6m) A to 2kN/m 1} (x-3) kun IN J 142 kN/m 6-37177 * 3m Mx Vx = -2%3C + Ay - x ( Ź(x-3))x(x-3) Ay KN Va= -2% +14.5 2x +14.5 - (x-3)2 6 3 MX = - 2xxx2 +Ay(x-3) — *•((x-3))*(x-3)X (*13 (x-3) Mg = -x2 + 14.5(3-3). (2-3) kim 18 for point o put se=6m ND == 2 *6+14.5 -(6-3) Mor -62 +14.5 (6-3) - (6-3)3 IKN 6 kNm 18

for (6m<x<9m) D to B Nx 2 kN/m JŽ (x=3] KN ! ] TT Jakrim 3m 3 m Mic xa 6kNm -(2-6)~? Ay Va = - 2x2 + Ay + Ay - 3x ((x-3))(x-3) KN =-2x +14.5 - (x-3)? 6 Mgen 2xxx} + Ay (x-3)-4x(cx-2)(x+3)(x+3) +6 Mx = -62 +14.5(2-3) - (x-3)3 +6 kim 18 For point B but se=9m (9-3)2 6 Ni= - 2X9 +1465 - = -9.5 KIV MB = -92 +14.519-3) - (9-3)3 +6= 0 kNm Shear force 70 6 18 at x=6.327379m O= -2% +14755 (x-3)2 by het and and trial method = 6.327379m Bending moment at x = 6-32737m M 18 M=12.16466418 kNm c76 (6.321379)2 + 19:5( 6-321319-3) - (6 39379-3)