Beam ABCD has sliding support at A, roller supports at C and D, and a pin connection at B (see figure). Assume that the beam has a rectangular cross-section (b = 4 in., h = 12 in.). Uniform load q acts on ABC and a concentrated moment is applied at D. Let load variable q = 1750 lb/ft, and assume that dimension variable L = 4 ft. First, use statics to confirm the reaction moment at A and the reaction forces at C and D, as given in the figure. Then find the ratio of the magnitudes of the principal stresses (σ₁ /σ₂ ) just left of support C at a distance d = 8 in. up from the bottom.

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4.5qL² A 3L 9 B 3L Pin connection (moment release); h 9.875qL 4L d Te 2qL² D 0800 3.875qL