Simply supported beam is subjected to a linearly varying distributed load ( ) 0 q x x L 5 q with maximum intensity 0 q at B. The beam has a length L 5 4 m and rectangular cross section with a width of 200 mm and height of 300 mm. Determine the maximum permissible value for the maximum inten- sity, 0 q , if the allowable normal stresses in tension and compression are 120 MPa.

q₀ = 350,740.2885 N/m

Explanation:

Given

σ = 120 MPa = 120*10⁶ Pa

We can see the pic shown in order to understand the question.

We apply

∑MB = 0  (Counterclockwise is the positive rotation direction)

⇒ - Av*L + (q₀*L/2)*(L/3) = 0

⇒ Av = q₀*L/6   (↑)

Then, we apply

Then, we can get the maximum bending moment as follows

then we get  

We get the inertia as follows

We use the formula

σ = M*y/I

⇒ M = σ*I/y

where

If M = Mmax, we have

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