Question

Find the mathematical equation for SF distribution and BM diagram for the beam shown in figure 1.​

Answer 1

i) SF:
`v(x) = ((w_0* x )^2)/(2L)`

ii) BM :
`= ((w_0*x)^3)/(6L)`

Step-by-step explanation:

Let's take,

`(y)/(w_0) = (x)/(L)`

Making y the subject of formula, we have :

`y = (x)/(L) * w_0`

For shear force (SF), we have:

This is the area of the diagram.

`v(x) = (1)/(2) * y = (1)/(2) * (x)/(L) * w_0`

`= ((w_0* x )^2)/(2L)`

The shear force equation =

`v(x) = ((w_0* x )^2)/(2L)`

For bending moment (BM):

`BM = v(x) * (x)/(3)`

`= ((w_0* x )^2)/(2L) * (x)/(3)`

`= ((w_0*x)^3)/(6L)`

The bending moment equation =

`= ((w_0*x)^3)/(6L)`