A beam A B C with an overhang from B to C supports a uniform load of 3 kN / m throughout its len

(a) The maximum bending moment occurs at point B. The bending moment at B due to the uniform loa

Question

A beam $A B C$ with an overhang from $B$ to $C$ supports a uniform load of $3 \mathrm{kN} / \mathrm{m}$ throughout its length (see figure). The beam is a channel section with dimensions as shown in the figure. The moment of inertia about the $z$ axis (the neutral axis) equals $210 \mathrm{cm}^{4}$ (a) Calculate the maximum tensile stress $\sigma_{t}$ and $\max$ imum compressive stress $\sigma_{c}$ due to the uniform load. (b) Find required span length $a$ that results in the ratio of larger to smaller compressive stress being equal to the ratio of larger to smaller tensile stress for the beam. Assume that the total length $L=a+b=6 \mathrm{m}$ remains unchanged.

          A beam $A B C$ with an overhang from $B$ to $C$ supports a uniform load of $3 \mathrm{kN} / \mathrm{m}$ throughout its length (see figure). The beam is a channel section with dimensions as shown in the figure. The moment of inertia about the
$z$ axis (the neutral axis) equals $210 \mathrm{cm}^{4}$
(a) Calculate the maximum tensile stress $\sigma_{t}$ and $\max$ imum compressive stress $\sigma_{c}$ due to the uniform load.
(b) Find required span length $a$ that results in the ratio of larger to smaller compressive stress being equal to the ratio of larger to smaller tensile stress for the beam. Assume that the total length $L=a+b=6 \mathrm{m}$ remains unchanged.

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