Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads

Supporting loads, moments and deflections.

Sponsored Links

Beam Fixed at One End and Supported at the Other - Single Point Load

Beam fixed at one end and supported at the other - single point load Bending Moment

M A = - F a b (L + b) / (2 L2)                               (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 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, lb f )

R B = F a2(b + 2 L ) / (2 L3 )                                 (1f)

where

R B = support force in B  (N, lb f )

Beam Fixed at One End and Supported at the Other - Continuous Load

Beam fixed at one end and supported at the other - continous load Bending Moment

M A = - q L2/ 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 L2/ 128                              (2b)

where

M 1 = maximum moment at x = 0.625 L  (Nm, lb f 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

Beam fixed at one end and supported at the other - continous declining load Bending Moment

M A = - q L2/ 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 L2/ 33.6                              (3b)

where

M 1 = maximum moment at x = 0.553 L (Nm, lb f 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

Beam fixed at one end and supported at the other - moment at the 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 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)

Sponsored Links

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.

Related Documents

Sponsored Links

Search

Search is the most efficient way to navigate the Engineering ToolBox.

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about

Citation

This page can be cited as

  • The Engineering ToolBox (2003). Beams - Fixed at One End and Supported at the Other - Continuous and Point Loads . [online] Available at: https://www.engineeringtoolbox.com/beams-fixed-end-d_560.html [Accessed Day Month Year].

Modify the access date according your visit.

3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter

















































3.15.9

Sponsored Links
.