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

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Deflection and stress, moment of inertia, section modulus and technical information of beams and columns. 
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