A beam of span L meters simply supported by the ends, carries a central load W. The beam section is shown in figure. If the maximum shear stress is 450 N/cm2 when the maximum bending stress is 1500 N/cm2. Calculate the value of the centrally applied point load W and the span L. The overall height of the I section is 29 cm.

W = 11,416.6879 N

L ≈ 64.417 cm

Explanation:

The maximum shear stress, , is given by the following formula;

= 1 cm = 0.01

h = 29 cm = 0.29 m

= 25 cm = 0.25 m

b = 15 cm = 0.15 m

= The centroidal moment of inertia

= 1/12*(0.15*0.29^3 - 0.15*0.25^3 + 0.01*0.25^3) = 1.2257083 × 10⁻⁴ m⁴

Substituting the known values gives;

= 1.2257083 × 10⁻⁴ m⁴

From which we have;

Which gives;

W = 11,416.6879 N

= 1500 N/cm² = 15,000,000 N/m²

= 15,000,000 × 1.2257083 × 10⁻⁴ ≈ 1838.56245 N·m²

From Which we have;

L ≈ 0.64417 m ≈ 64.417 cm.