Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads
- Beams - Supported at Both Ends - Continuous and Point Loads
- Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads
- Beams - Fixed at Both Ends - Continuous and Point Loads
Beam Fixed at One End and Supported at the Other - Single Point Load
M A = - F a b (L + b) / (2 L2) (1a)
where
M A = moment at the fixed end (Nm, lbf ft)
F = load (N, lbf )
M F = R b b (1b)
where
M F = moment at point of load F (Nm, lbf ft)
R b = support load at support B (N, lbf )
Deflection
δ F = F a3 b2(3 L + b) / (12 L3 E I) (1c)
where
δ F = deflection (m, ft)
E = Modulus of Elasticity (Pa (N/m2), N/mm2, psi)
I = Area Moment of Inertia (m4, mm4, in4 )
Support Reactions
R A = F b (3 L2- b2) / (2 L3 ) (1d)
where
R A = support force in A (N, lbf )
R B = F a2(b + 2 L ) / (2 L3 ) (1f)
where
R B = support force in B (N, lbf )
Beam Fixed at One End and Supported at the Other - Continuous Load
M A = - q L2/ 8 (2a)
where
M A = moment at the fixed end (Nm, lbf ft)
q = continuous load (N/m, lbf /ft)
M1 = 9 q L2/ 128 (2b)
where
M1 = maximum moment at x = 0.625 L (Nm, lbf ft)
Deflection
δ max = q L4 / (185 E I) (2c)
where
δ max = max deflection at x = 0.579 L (m, ft)
δ 1/2 = q L4 / (192 E I) (2d)
where
δ 1/2 = deflection at x = L / 2 (m, ft)
Support Reactions
R A = 5 q L / 8 (2e)
R B = 3 q L / 8 (2f)
Beam Fixed at One End and Supported at the Other - Continuous Declining Load
M A = - q L2/ 15 (3a)
where
M A = moment at the fixed end (Nm, lbf ft)
q = continuous declining load (N/m, lbf /ft)
M1 = q L2/ 33.6 (3b)
where
M1 = maximum moment at x = 0.553 L (Nm, lbf ft)
Deflection
δ max = q L4 / (419 E I) (3c)
where
δ max = max deflection at x = 0.553 L (m, ft)
δ 1/2 = q L4 / (427 E I) (3d)
where
δ 1/2 = deflection at x = L / 2 (m, ft)
Support Reactions
R A = 2 q L / 5 (3e)
R B = q L / 10 (3f)
Beam Fixed at One End and Supported at the Other - Moment at Supported End
M A = -M B / 2 (4a)
where
M A = moment at the fixed end (Nm, lbf ft)
Deflection
δ max = M B L2/ (27 E I) (4b)
where
δ max = max deflection at x = 2/3 L (m, ft)
Support Reactions
R A = 3 M B / (2 L) (4c)
R B = - 3 M B / (2 L) (4d)
Related Topics
• Beams and Columns
Deflection and stress in beams and columns, moment of inertia, section modulus and technical information.
• Mechanics
The relationships between forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.
• Statics
Forces acting on bodies at rest under equilibrium conditions - loads, forces and torque, beams and columns.
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