Cantilever beam - Couple moment Mo at free end Calculator - BEcalc.com

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Cantilever beam - Couple moment Mo at free end Calculator

Deflection Yab:

Deflection Ymax at x= :

Slope θab:

Moment Mab = Ma = Mb:

Shear Vab = Va = Vb:

Reactions Ra:

Formula

Parameter	Formula
Deflection $y_{AB}$	$y_{AB} = \frac{M_0 x^2}{2EI}$
Deflection at $x = L$ ( $y_{MAx}$ for segment AB)	$y_{MAx} = -\frac{M_0 L^2}{2EI}$
Slope $\theta_{AB}$	$\theta_{AB} = -\frac{M_0 x}{EI}$
Moment $M_{AB}$ ( $M_A = M_B$ )	$M_{AB} = M_A = M_B = -M_0$
Shear $V_{AB}$ ( $V_A = V_B$ )	$V_{AB} = V_A = V_B = 0$
Reactions $R_A$	$R_A = 0$

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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