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. -
Statics
Loads - forces and torque, beams and columns.
Related Documents
-
Aluminum I-Beams
Dimensions and static properties of aluminum I-beams - Imperial units. -
American Standard Beams - S Beam
American Standard Beams ASTM A6 - Imperial units. -
American Standard Steel C Channels
Dimensions and static parameters of American Standard Steel C Channels -
American Wide Flange Beams
American Wide Flange Beams ASTM A6 in metric units. -
Area Moment of Inertia - Typical Cross Sections I
Typical cross sections and their Area Moment of Inertia. -
Area Moment of Inertia - Typical Cross Sections II
Area Moment of Inertia, Moment of Inertia for an Area or Second Moment of Area for typical cross section profiles. -
Area Moment of Inertia Converter
Convert between Area Moment of Inertia units. -
Beam Loads - Support Force Calculator
Calculate beam load and supporting forces. -
Beams - Fixed at Both Ends - Continuous and Point Loads
Stress, deflections and supporting loads. -
Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads
Supporting loads, moments and deflections. -
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
Supporting loads, stress and deflections. -
Beams Natural Vibration Frequency
Estimate structures natural vibration frequency. -
British Universal Columns and Beams
Properties of British Universal Steel Columns and Beams. -
Cantilever Beams - Moments and Deflections
Maximum reaction forces, deflections and moments - single and uniform loads. -
Continuous Beams - Moment and Reaction Support Forces
Moments and reaction support forces with distributed or point loads. -
Drawbridge - Force and Moment vs. Elevation
Calculate the acting forces and moments when elevating drawbridges or beams. -
Floor Joist Capacities
Carrying capacities of domestic timber floor joists - Grade C - metric units. -
Floors - Live Loads
Floors and minimum uniformly distributed live loads. -
HE-A Steel Beams
Properties of HE-A profiled steel beams. -
HE-B Steel Beams
Properties of HE-B profiled steel beams. -
Normal Flange I-Beams
Properties of normal flange I profile steel beams. -
Section Modulus - Unit Converter
Convert between Elastic Section Modulus units. -
Square Hollow Structural Sections - HSS
Weight, cross sectional area, moments of inertia - Imperial units -
Steel Angles - Equal Legs
Dimensions and static parameters of steel angles with equal legs - imperial units. -
Steel Angles - Equal Legs
Dimensions and static parameters of steel angles with equal legs - metric units. -
Steel Angles - Unequal Legs
Dimensions and static parameters of steel angles with unequal legs - imperial units. -
Steel Angles - Unequal Legs
Dimensions and static parameters of steel angles with unequal legs - metric units. -
Stress
Stress is force applied on cross-sectional area. -
Three-Hinged Arches - Continuous and Point Loads
Support reactions and bending moments. -
Trusses
Common types of trusses. -
W Steel Beams - Allowable Uniform Loads
Allowable uniform loads. -
W-Beams - American Wide Flange Beams
Dimensions of American Wide Flange Beams ASTM A6 (or W-Beams) - Imperial units. -
Weight of Beams - Stress and Strain
Stress and deformation of vertical beams due to own weight.
