Fixed-pinned beam - Couple moment Mo at any point Calculator
Formula
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Beam Formulas
Beam Deflection, Slope, Moment, Shear, and Reactions
Property |
Formula |
Deflection (yAC) |
yAC=−M0x4EIL3[2b2L−(L−x)(L2−b2)] |
Deflection (yCB) |
yCB=−M0a(L−x)4EIL3[−4L3−((L−x)2−3L2)(L+b)] |
Slope (θAC) |
θAC=−M0x4EIL3[4b2L−(2L−3x)(L2−b2)] |
Slope (θCB) |
θCB=−M0a4EL3[4L3−3(L+b)(x2−2Lx)] |
Moment (MAC) |
MAC=−M02L3[2b2L−(L−3x)(L2−b2)] |
Moment (MCB) |
MCB=3M0a2L3(L+b)(L−x) |
Shear (VAB) |
VAB=−3M0a2L3(L+b) |
Reaction (RA) |
RA=−3M0a2L3(L+b) |
Reaction (RB) |
RB=3M0a2L3(L+b) |
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 |