Three-Hinged Arch - Continuous Load
Mm = (q L2 / 8) (4 (xm / L - (xm / L)2) - ym / yc) (1a)
Mm = moment at m (Nm, lbf ft)
q = continuous load (N/m, lbf/ft)
xm = x-coordinate for m (m, ft)
ym = y-coordinate for m (m, ft)
yc = y-coordinate for center hinge (m, ft)
L = horizontal distance between the supports (m, ft)
Cartesian coordinates related to a center located in the hinge of support no. 1.
R1y = R2y
= q L / 2 (1b)
R = support force (N, lbf)
R1x = R2x
= q L2 / (8 yc) (1c)
Three-Hinged Arch - Half Continuous Load
Mm = (q L2 / 16) (8 (xm / L - (xm / L)2) - 2 xm / L - ym / yc) (2a)
R1y = 3 q L / 8 (2b)
R2y = q L / 8 (2c)
R1x = R2x
= q L2 / (16 yc) (2d)
Three-Hinged Arch - Horizontal Continuous Load
Mm = (q L2 / 2) (xm / L - 3 xm / L + (xm / L)2) (3a)
Mk = (q L2 / 4) (2 (L - xk) / L - yk / yc) (3b)
Mk = moment at k (Nm, lbf ft)
yk = y-coordinate for k (m, ft)
xk = x-coordinate for k (m, ft)
R1y = - q yc2 / (2 L) (3c)
R2y = q yc2 / (2 L) (3d)
R1x = - 3 q yc / 4 (3e)
R2x = q yc / 4 (3f)
Three-Hinged Arch - Eccentric Point Load
Mm = (F a / 2) (2 (b / a) (xm / L) - ym / yc) (4a)
Mk = (F a /2) (2 (L - xk) / L - yk / yc) (4b)
R1y = F b / L (4c)
R2y = F a / L (4d)
R1x = R2x
= F a / (2 yc) (4f)
Deflection and stress, moment of inertia, section modulus and technical information of beams and columns.
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
Loads - forces and torque, beams and columns.
Typical cross sections and their Area Moment of Inertia.
Stress, deflections and supporting loads.
Supporting loads, moments and deflections.
Supporting loads, stress and deflections.
Maximum reaction forces, deflections and moments - single and uniform loads.
Moments and reaction support forces with distributed or point loads.
Calculate buckling of columns.
The Mass Moment of Inertia vs. mass of object, it's shape and relative point of rotation - the Radius of Gyration.
Stiffness is resistance to deflection.
Properties of structural lumber.
Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.