Question

P8.008 A beam is subjected to equal 18.2 kip-ft bending moments. Assume $t_1=t_2=t_w=2$ in., $d=17$ in., $b_1=5$ in., and $b_2=8$ in. The cross-sectional dimensions of the beam are illustrated. Determine: (a) the distance $\bar{y}$ to the centroid (measured from the bottom), the moment of inertia $I_z$ about the $z$ axis, and the controlling section modulus $S_z$ about the $z$ axis. (b) the bending stress $\sigma_H$ at point H (positive if tension, negative if compression). (c) the bending stress $\sigma_K$ at point K (positive if tension, negative if compression). (d) the maximum bending stress $\sigma_{max}$ produced in the cross section (positive if tension, negative if compression). Answers: (a) $\bar{y} = \underline{\qquad}$ in., $I_z = \underline{\qquad}$ in.$^4$, $S_z = \underline{\qquad}$ in.$^3$. (b) $\sigma_H = \underline{\qquad}$ psi. (c) $\sigma_K = \underline{\qquad}$ psi. (d) $\sigma_{max} = \underline{\qquad}$ psi.

          P8.008
A beam is subjected to equal 18.2 kip-ft bending moments. Assume $t_1=t_2=t_w=2$ in., $d=17$ in., $b_1=5$ in., and $b_2=8$ in. The cross-sectional dimensions of the beam are illustrated. Determine:
(a) the distance $\bar{y}$ to the centroid (measured from the bottom), the moment of inertia $I_z$ about the $z$ axis, and the controlling section modulus $S_z$ about the $z$ axis.
(b) the bending stress $\sigma_H$ at point H (positive if tension, negative if compression).
(c) the bending stress $\sigma_K$ at point K (positive if tension, negative if compression).
(d) the maximum bending stress $\sigma_{max}$ produced in the cross section (positive if tension, negative if compression).
Answers:
(a) $\bar{y} = \underline{\qquad}$ in., $I_z = \underline{\qquad}$ in.$^4$, $S_z = \underline{\qquad}$ in.$^3$.
(b) $\sigma_H = \underline{\qquad}$ psi.
(c) $\sigma_K = \underline{\qquad}$ psi.
(d) $\sigma_{max} = \underline{\qquad}$ psi.

P8.008
A beam is subjected to equal 18.2 kip-ft bending moments. Assume t1=t2=tw=2 in., d=17 in., b1=5 in., and b2=8 in. The cross-sectional dimensions of the beam are illustrated. Determine:
(a) the distance y̅ to the centroid (measured from the bottom), the moment of inertia Iz about the z axis, and the controlling section modulus Sz about the z axis.
(b) the bending stress at point H (positive if tension, negative if compression).
(c) the bending stress at point K (positive if tension, negative if compression).
(d) the maximum bending stress σmax produced in the cross section (positive if tension, negative if compression).
Answers:
(a) y̅ = in., Iz = in.^4, Sz = in.^3.
(b) = psi.
(c) = psi.
(d) σmax = psi.

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