(_Wl_)⁄8 = 12,200 × 8 × 12⁄8 = 155,000 inch-pounds Therefore, _bd_^2 = 775. An 8 × 10 inch beam will fulfill the conditions closely. Substituting these dimensions in the beam formula _f_ = (_Mc_)⁄_I_ = (155,000 × 5 × 12)⁄8 × 1000 = 1,160 pounds per square inch tension in outer fiber. The results of the computations for other rangers are shown in Table 60. 4. _Size of Cross Braces._—The cross braces act as columns. The dimensions of the cross braces are determined by trial in such a manner that the vertical dimension of the brace is equal to the vertical dimension of the ranger and the compressive stress in pounds per square inch is computed from the expression, _S_ ⪙ _S__{1}(1 − _l_⁄(60_d_)),[94] TABLE 60 COMPUTATIONS FOR SHEETING AND BRACING FOR TRENCH SHOWN IN FIG. 111 Material is moist sand weighing 110 pounds per cubic foot, with an angle of repose of 30°. Lumber is yellow pine, with working stress as given in Table 59. Working stresses for columns given as _S_(1 − _l_⁄(60_d_)). ──────────────────────────────┬─────────────────────────────────────────────── Sheeting 2 inches × 12 Inches │ Cross Braces ──────────┬───────────┬───────┼───────────┬──────┬──────┬──────────┬────────── │ │Maximum│ │ │ │ │ │ │ Fiber │ │ │ │ │ │ │Stress,│ │ │ │ Actual │Allowable │ Maximum │Pounds │ │ │ │Intensity,│Intensity, │ Bending │ per │ │Total │ │Pounds per│Pounds per │ Moment, │Square │ Depth and │Load, │Size, │ Square │ Square Depth │Inch-Pounds│ Inch │Description│Pounds│Inches│ Inch │ Inch ──────────┼───────────┼───────┼───────────┼──────┼──────┼──────────┼────────── │ │ │end at 26′│ │ │ │ 23′–26.75′│ 9100│ 1140│ 9″│ 6,445│ 4 × 8│ 202│ 784 │ │ │int. at 26′│ │ │ │ 19′–23′│ 8800│ 1100│ 9″│12,890│ 4 × 8│ 403│ 784 │ │ │end at 23′│ │ │ │ 13′–17.5′│ 8550│ 1070│ 0″│ 6,393│ 4 × 8│ 200│ 784 │ │ │int. at 23′│ │ │ │ 8′–13′│ 7160│ 900│ 0″│12,785│ 4 × 8│ 400│ 784 │ │ │end at 19′│ │ │ │ 0′–6′│ 3000│ 375│ 0″│ 3,930│ 4 × 8│ 123│ 784 │ │ │int. at 19′│ │ │ │ │ │ │ 0″│ 7,860│ 4 × 8│ 240│ 784 │ │ │end at 17′│ │ │ │