The Mechanics of Construction, EtcDughton, Bull & Company, 1861 |
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Page 91
... lowest point . If ρ be the radius of curvature at any point ( x , y ) of the elastic curve which contains the centres of gravity of the cross sections of the beam after deflection ; then by ( 1 ) Art . 22 , 1 I ΕΙ = or P = M P EI ' But ...
... lowest point . If ρ be the radius of curvature at any point ( x , y ) of the elastic curve which contains the centres of gravity of the cross sections of the beam after deflection ; then by ( 1 ) Art . 22 , 1 I ΕΙ = or P = M P EI ' But ...
Page 197
... lowest point of the chain , the axis of x being horizontal and that of y vertical . Let PT , a tangent at any point P of the curve , meet the vertical axis of y in T " . Let AM = x and MP = y , be the coordinates of any point B N A y x ...
... lowest point of the chain , the axis of x being horizontal and that of y vertical . Let PT , a tangent at any point P of the curve , meet the vertical axis of y in T " . Let AM = x and MP = y , be the coordinates of any point B N A y x ...
Page 198
... lowest point of the chain . But more of this as we proceed . Now the arc AP , after it has assumed its permanent state of equilibrium , may be considered as a rigid body kept at rest by three forces , viz . the tension t acting at P in ...
... lowest point of the chain . But more of this as we proceed . Now the arc AP , after it has assumed its permanent state of equilibrium , may be considered as a rigid body kept at rest by three forces , viz . the tension t acting at P in ...
Page 200
... lowest point of the curve being the origin , and the horizontal tangent at the lowest point the axis of x . The following is another convenient form of the equation of the common catenary in reference to the same coordinate axes . By ...
... lowest point of the curve being the origin , and the horizontal tangent at the lowest point the axis of x . The following is another convenient form of the equation of the common catenary in reference to the same coordinate axes . By ...
Page 201
... point P of the catenary is ds t - Ва dx But by ( 2 ) and ( 6 ) , Art . 133 , ds ( s2 + a2 ) $ α = = dx and hence t ... lowest point A of the curve . The quantity a , as defined in a preceding paragraph , is the length of a uniform chain ...
... point P of the catenary is ds t - Ва dx But by ( 2 ) and ( 6 ) , Art . 133 , ds ( s2 + a2 ) $ α = = dx and hence t ... lowest point A of the curve . The quantity a , as defined in a preceding paragraph , is the length of a uniform chain ...
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Common terms and phrases
angle axle beam breadth c₁ catenary centre of gravity centre of pressure chain circular arch coefficient of resistance coefficient of safety common catenary compression cosec cross section cubic foot curve of pressure cylinder deflection Denote density determined diameter dimensions Edition equal equation equilibrium exterior forces extrados extremity F. A. Paley Fcap feet fibre find the thickness fixed formula fracture h₁ Hence horizontal line horizontal position horizontal thrust inertia intrados king-post length lever arm load lowest point modulus of elasticity moment of inertia moments neutral axis parabola parallel perpendicular plane preceding prism PROP r+ h r₁ radius rafter rectangular roof section HK segmental arch sin² springing line stability straining force supported supposed surcharge thickness of pier tie-beam torsion trapezoid triangle vertical pressure weight Wherefore
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