Question

a horizontal beam simply supported in a span of 10m carries a total load of 100kg. the load distribution varies parabolically from zero at each end to maximum at mid span. Calculate the values of B.M at intervals of 1m and plot the B.M diagram. State the values of
A. Maximum B.M
B. Shearing force at quarter span

Answer 1

We know that equation of parabola whose end point lying on x axis will be

$y^2=4(a_1-a)(x-a_1)$ ,

here value of $a_1=10$

and value of a=0

$y^2=4(10)(x-10)=40x-400$

here load is 100 kg

beam is simply supported

$R_A+R_B=1000$

since maximum load is in middle and distributed uniformly both sides so we can say that

$R_A=R_B=500$

$M_x=1000- \frac{(y^2+400)}{40}$

Now for maximum bending moment

$M_x=1000-\frac{425}{40}\times 5$

M= 946.875 Nm

(ii) Shear force at quarter span

$S=\frac{dM}{dx}= 2\times 100\times 2.5= 500 N$