Question

A simply supported beam (E 512 GPa) carries a uniformly distributed load q 5125 N/m, and a point load P 5 200 N at mid-span. The beam has a rectangular cross section (b 5 75 mm, h 5 200 mm) and a length of 3.6 m. Calculate the maximum deflection of the beam

Answer 1

`\mathbf{\Delta_(max)=0.78 \ mm}`

Step-by-step explanation:

From the given information;

A simply supported beam (E = 12 GPa)

load q = 125 N/m

point load P = 200 N

the rectangular cross section

b = 75 mm

h = 200 mm

length = 3.6 m

The objective is to calculate the maximum deflection of the beam;

Using the formula;

`I = (1)/(E)*bh^3` about the z-axis that goes through the central

`I = (1)/(12)*(75 \ mm)*(200 \ mm)^3`

`I = 5*10^7 \ mm^4`

The length L = 3.6 m = 3600 mm

The maximum deflection of the beam can be calculated by using the formula:

`\Delta _(max) = (5)/(384)* (qL^4)/(EI)+(PL^3)/(48EI)`

`\Delta _(max) = (1)/(12*10^3 (N)/(mm^2)*5*10^7 \ mm^4 )[ (5*(125 \ N)/(100 \ mm)*3600 \ mm^4)/(384)+(200*(3600 \ mm )^3)/(48)]`

Thus; the maximum deflection of the beam is
`\mathbf{\Delta_(max)=0.78 \ mm}`