. The Locomotive. ^ q 11 i 11 ! 1 p. Figs. 8 and 9. — Illustrating the Stresses in a Solid Plate. The forces R and 5 are as yet unknown, and we must determine themfrom the condition that the triangle is in equilibrium. We proceed, first, tofind R, by resolving all the forces acting upon the triangle so as to findthe component of each that is perpendicular to ab. The total force acting uponthe edge ab in this direction is Rlt (t being the thickness of the plate). Thelength of be is / sin x, and hence the total force acting upon be, and per-pendicularly to be, is fit smx; whence it follows that
. The Locomotive. ^ q 11 i 11 ! 1 p. Figs. 8 and 9. — Illustrating the Stresses in a Solid Plate. The forces R and 5 are as yet unknown, and we must determine themfrom the condition that the triangle is in equilibrium. We proceed, first, tofind R, by resolving all the forces acting upon the triangle so as to findthe component of each that is perpendicular to ab. The total force acting uponthe edge ab in this direction is Rlt (t being the thickness of the plate). Thelength of be is / sin x, and hence the total force acting upon be, and per-pendicularly to be, is fit smx; whence it follows that the component, per-pendicular to ab, of the total force acting on be, is fit sin2 x. Similarly, thelength of ac is / cos x, and the total force acting on ac (and perpendicularly toit) is Fit cos x; and the component of this, perpendicular to ab, is Fit cos2 order that the triangular piece of plate, abc, may be in equilibrium, we musttherefore have Rlt = Fit cos2 x + fit sin2 x, orR = F cos2 x + / sin2 x. (1) When we know the
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