Question

A simply supported beam of span 3.0 m has a cross-section 120 mm × 180 mm. If the permissible stress in the material of the beam is 10 N/mm² , determine 

(i) maximum udl it can carry 

(ii) maximum concentrated load at a point 1 m from support it can carry. Neglect moment due to self weight.

Answer 1

Here b = 120 mm, d = 180 mm, I = \(\frac1{12}\) bd³ , y_max = \(\frac d2\)

∴ Moment carrying capacity of the section 

= f_per × Z 

= 10 × 648000 N-mm 

(i) Let maximum udl beam can carry be w/metre length as shown in Fig.

In this case, we know that maximum moment occurs at mid span and is equal to M_max = \(\frac{wL^2}8\) 

Equating it to moment carrying capacity, we get,

(ii) Concentrated load at distance 1 m from the support be P kN. Referring to Fig.

Equating it to moment carrying capacity, we get

\(\frac{2P}3\) × 10⁶ = 10 × 648000

∴ P = 9.72 kN-m.