Fixed-fixed beam - Uniformly distributed load Calculator - BEcalc.com

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Fixed-fixed beam - Uniformly distributed load Calculator

Deflection Yab:

Slope θab:

Moment Mab:

Shear Vab:

Reactions Ra:

Reactions Rb:

Formula

Quantity	Formula
Deflection $y_{AB}$	$y_{AB} = \frac{-w_0 x^2 (L - x)^2}{24EI}$
Slope $\theta_{AB}$	$\theta_{AB} = \frac{-w_0 x}{12EI} \left( L^2 - 3Lx + 2x^2 \right)$
Moment $M_{AB}$	$M_{AB} = \frac{-w_0}{12} \left( L^2 - 6Lx + 6x^2 \right)$
Shear $V_{AB}$	$V_{AB} = \frac{w_0}{2} \left( L - 2x \right)$
Reactions $R_A$ and $R_B$	$R_A = R_B = \frac{w_0 L}{2}$

Definitions

Symbol	Physical quantity	Units
E·I	Flexural rigidity	N·m², Pa·m⁴
y	Deflection or deformation	m
θ	Slope, Angle of rotation	-
x	Distance from support (origin)	m
L	Length of beam (without overhang)	m
M	Moment, Bending moment, Couple moment applied	N·m
P	Concentrated load, Point load, Concentrated force	N
w	Distributed load, Load per unit length	N/m
R	Reaction load, reaction force	N
V	Shear force, shear	N

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