. Theory of structures and strength of materials. Fig. 14. Fig. is. Let \7i be the line of loads, and let OS, OT he the radiallines from O, the pole, parallel to the tangents at P and A as the origin. Let 0 be the inclination of the tangent at P to the beam,and let the polar distance OV :=/>. wdx = the load upon the portion iMN. Then wdx = ST= SF - TV = p tan 6 - p tan {6 -|- dO) = —pdd, approximately. dO dy smce dx dxIntegrating twice, py = - Z/^^-^ + c,x + c^, t, and c^ being constants of integration. 6 = ^dx CENTRES OF GRAVITY. II If the intensity, w, of the load is constant, wxpy
. Theory of structures and strength of materials. Fig. 14. Fig. is. Let \7i be the line of loads, and let OS, OT he the radiallines from O, the pole, parallel to the tangents at P and A as the origin. Let 0 be the inclination of the tangent at P to the beam,and let the polar distance OV :=/>. wdx = the load upon the portion iMN. Then wdx = ST= SF - TV = p tan 6 - p tan {6 -|- dO) = —pdd, approximately. dO dy smce dx dxIntegrating twice, py = - Z/^^-^ + c,x + c^, t, and c^ being constants of integration. 6 = ^dx CENTRES OF GRAVITY. II If the intensity, w, of the load is constant, wxpy=- —^ + c,x + c,, and the curve is a parabola. 6. Centres of Gravity.—Let it be required to determine the centre of gravity of any plane area symmetrical with re-spect to an axis-ATX. Divide the area into suitable elementaryareas a^, a^, a^, . . having known centres of
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Keywords: ., bookcentury1800, bookdecade1890, bookpublishernewyo, bookyear1896
