A cast iron beam 10 m long is supported on top of two supports positioned at distances a and b from the ends. The beam c

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A cast iron beam 10 m long is supported on top of two supports
positioned at distances a and b from the ends. The beam carries a
uniformly distributed load w in N/m (including its own weight). The
allowable stresses are 20 MN/m2 for bending in tension and 80 MN/m2
in compression. The inverted T-beam section has a moment of inertia
of 36 × 106 mm4 with neutral axis located 180 mm from the top and
50 mm from the bottom of the section.
a. Determine the positive moment capacity.
b. Calculate the negative moment capacity.
c. If a=1.0 m and b=1.6 m, find the safe value of w.
d. If the two supports are symmetrically positioned at distances
x from the ends, find the value of x and w so that w is a
maximum.