Beams  Fixed at One End and Supported at the Other  Continuous and Point Loads
Supporting loads, moments and deflections.
 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
Bending Moment
M_{A} =  F a b (L + b) / (2 L^{2}) (1a)
where
M_{A} = moment at the fixed end (Nm, lb_{f} ft)
F = load (N, lb_{f})
M_{F} = R_{b} b (1b)
where
M_{F} = moment at point of load F (Nm, lb_{f} ft)
R_{b} = support load at support B (N, lb_{f})
Deflection
δ_{F} = F a^{3} b^{2} (3 L + b) / (12 L^{3} E I) (1c)
where
δ_{F} = deflection (m, ft)
E = Modulus of Elasticity (Pa (N/m^{2}), N/mm^{2}, psi)
I = Area Moment of Inertia (m^{4}, mm^{4}, in^{4})
Support Reactions
R_{A} = F b (3 L^{2}  b^{2}) / (2 L^{3}) (1d)
where
R_{A} = support force in A (N, lb_{f})
R_{B} = F a^{2} (b + 2 L ) / (2 L^{3}) (1f)
where
R_{B} = support force in B (N, lb_{f})
Beam Fixed at One End and Supported at the Other  Continuous Load
Bending Moment
M_{A} =  q L^{2} / 8 (2a)
where
M_{A} = moment at the fixed end (Nm, lb_{f} ft)
q = continuous load (N/m, lb_{f}/ft)
M_{1} = 9 q L^{2} / 128 (2b)
where
M_{1} = maximum moment at x = 0.625 L (Nm, lb_{f} ft)
Deflection
δ_{max} = q L^{4} / (185 E I) (2c)
where
δ_{max} = max deflection at x = 0.579 L (m, ft)
δ_{1/2} = q L^{4} / (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
Bending Moment
M_{A} =  q L^{2} / 15 (3a)
where
M_{A} = moment at the fixed end (Nm, lb_{f} ft)
q = continuous declining load (N/m, lb_{f}/ft)
M_{1} = q L^{2} / 33.6 (3b)
where
M_{1} = maximum moment at x = 0.553 L (Nm, lb_{f} ft)
Deflection
δ_{max} = q L^{4} / (419 E I) (3c)
where
δ_{max} = max deflection at x = 0.553 L (m, ft)
δ_{1/2} = q L^{4} / (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
Bending Moment
M_{A} = M_{B} / 2 (4a)
where
M_{A} = moment at the fixed end (Nm, lb_{f} ft)
Deflection
δ_{max} = M_{B} L^{2} / (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, moment of inertia, section modulus and technical information of beams and columns. 
Mechanics
Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more. 
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Loads  forces and torque, beams and columns.
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