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Draw the shear force diagram and bending moment diagram for the beam loaded as shown in fig
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written 6.0 years ago by | • modified 6.0 years ago |
S.F.D
B.M.D $\sum F_y=0$
$V_B+V_E=20*4+50+25*2$
$V_B+V_E+180$
and taking moment about E,
$\sum M_E = 0$
$-20*4*(\frac{4}{2}+5+5+2)+V_b*(5+5+2)-50*(5+2)-(25*2)*\frac{2}{2} = 0$
$V_B=126.67KN$
Now, $V_G = 180-V_B = 53.33KN$
B.M analysis:
BM in the section AB, distance * from A
$BM_x = -20*\frac{x^2}{2}$
At x = 0,
$BM_A = 0$
At x = 4,
$BM_B = -20*\frac{4^2}{2} = -160KNm$
$BM_c = -20*4(\frac{4}{2}+5)+126.67*5$
$BM_c = 73.30KNm $
$BM_E = 0$
BM in the section DE, distance x from E
$BM_x = 53.33*x-25\frac{x^2}{2}$
At x = 2
$BM_D = 53.33*2-25*\frac{2^2}{2} = 56.66$
${BM_C = 53.33*(5+2)-25*2*(\frac{2}{2}+5) }_{from- end-E} = 73.33KN$