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

This is an AMP page - Open full page! for all features.

Beams - Fixed at Both Ends - Continuous and Point Loads

Support loads, stress and deflections

Sponsored Links

Beam Fixed at Both Ends - Single Point Load

Bending Moment

MA = - F a b2 / L2                               (1a)

where

MA = moment at the fixed end A (Nm, lbf ft)

F = load (N, lbf)

MB = - F a2 b / L2                              (1b)

where

MB = moment at the fixed end B (Nm, lbf ft)

MF = 2 F a2 b2 / L3                           (1c)

where

MF = moment at the point load (Nm, lbf ft)

Deflection

δF = F a3 b3 / (3 L3 E I)                                  (1d)

where

δF = deflection at point load (m, ft)

E = Modulus of Elasticity (Pa (N/m2), N/mm2, psi)

I = Area Moment of Inertia (m4, mm4, in4)

Support Reactions

RA = F (3 a + b) b2 / L3                                 (1f)

where

RA = support force at fixed end A (N, lbf)

RB = F (a + 3 b) a2 / L3                                 (1g)

where

RB = support force at fixed end B  (N, lbf)

Beam Fixed at Both Ends - Uniform Continuous Distributed Load

Bending Moment

MA = MB

     = - q L2 / 12                                   (2a)

where

M = moments at the fixed ends  (Nm, lbf ft)

q = uniform load (N/m, lbf/ft)

M1 = q L2 / 24                         (2b)

where

M1 = moment at the center (Nm, lbf ft)

Deflection

δmax = q L4 / (384 E I)                                  (2c)

where

δmax = max deflection at center (m, ft)

E = Modulus of Elasticity (Pa (N/m2), N/mm2, psi)

I = Area Moment of Inertia (m4, mm4, in4)

Support Reactions

RA = RB

    =  q L / 2                               (2d)

where

R = support forces at the fixed ends  (N, lbf)

Beam Fixed at Both Ends - Uniform Declining Distributed Load

Bending Moment

MA = - q L2 / 20                                  (3a)

where

MA = moments at the fixed end A  (Nm, lbf ft)

q = uniform declining load (N/m, lbf/ft)

MB = - q L2 / 30                                 (3b)

where

MB = moments at the fixed end B  (Nm, lbf ft)

M1 = q L2 / 46.6                         (3c)

where

M1 = moment at x = 0.475 L (Nm, lbf ft)

Deflection

δmax = q L4 / (764 E I)                                  (3d)

where

δmax = max deflection at x = 0.475 L (m, ft)

E = Modulus of Elasticity (Pa (N/m2), N/mm2, psi)

I = Area Moment of Inertia (m4, mm4, in4)

δ1/2 = q L4 / (768 E I)                                  (3e)

where

δ1/2 = deflection at x = 0.5 L (m, ft)

Support Reactions

RA = 7 q L / 20                               (3f)

where

RA = support force at the fixed end A  (N, lbf)

RB =  3 q L / 20                               (3g)

where

RB = support force at the fixed end B  (N, lbf)

Beam Fixed at Both Ends - Partly Uniform Continuous Distributed Load

Bending Moment

MA = - (q a2 / 6) (3 - 4 a / l + 1.5 (a / L)2)                                  (4a)

where

MA = moment at the fixed end A  (Nm, lbf ft)

q = partly uniform load (N/m, lbf/ft)

MB = - (q a2 / 3) (a / L - 0.75 (a / L)2)                                 (4b)

where

MB = moment at the fixed end B  (Nm, lbf ft)

Support Reactions

RA = q a (L - 0.5 a) / L - (MA - MB) / L                              (4c)

where

RA = support force at the fixed end A  (N, lbf)

RB =  q a2 / (2 L) + (MA - MB) / L                              (4d)

where

RB = support force at the fixed end B  (N, lbf)

Sponsored Links

Related Topics

Related Documents

Sponsored Links

Share

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

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 the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.

Topics

Unit Converters

Temperature

oC
oF


Load Calculator!

Length

m
km
in
ft
yards
miles
naut miles


Load Calculator!

Area

m2
km2
in2
ft2
miles2
acres


Load Calculator!

Volume

m3
liters
in3
ft3
us gal


Load Calculator!

Weight

kgf
N
lbf


Load Calculator!

Velocity

m/s
km/h
ft/min
ft/s
mph
knots


Load Calculator!

Pressure

Pa (N/m2)
bar
mm H2O
kg/cm2
psi
inches H2O


Load Calculator!

Flow

m3/s
m3/h
US gpm
cfm


Load Calculator!

2 8

This website use cookies. By continuing to browse you are agreeing to our use of cookies! Learn more