Q-1Design the cross section of a rectangular beam carrying 1.0 kip-ft distributed load having a simple span of 10 ft. The beam will be made with 3000 psi normal weight concrete (stone chips) only i.e. no tension reinforcement will be provided.

 Solution:

Given, W=1kip/ft, f’c = 3000 psi

Moment, 𝑀𝑚𝑎𝑥= 𝑤𝐿28 = 1×1028 = 12.5 k-ft = 150 kip-in

Modulus of Rupture, fr = 7.5√𝑓′𝑐 = 7.5×√3000 psi = 410 psi=0.410ksi

Let, Breadth, b = 10 inch

Modulus of Rupture, fr = 6𝑀𝑚𝑎𝑥𝑏ℎ2

ℎ=√6𝑀𝑓𝑟×𝑏 = √6×1500.410×10= 14.8 inch ≈15 inch

∴ Cross section of Beam = 10” × 15”

From the above design, it is clear that a small portion of tensile stress can be carried by concrete and with such consideration a structural member can be designed as well. But, this process is associated with some limitations. Concrete is a brittle materials and if no reinforcement is provided, sudden failure will be expected when the first crack occurs, thus giving no warning. Therefore, design of structural member without reinforcement is not suggested by Any Code.