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Fixed-pinned beam - Couple moment Mo at any point Calculator

















Formula

Beam Formulas

Beam Deflection, Slope, Moment, Shear, and Reactions

Property Formula
Deflection (yAC) yAC=M0x4EIL3[2b2L(Lx)(L2b2)]
Deflection (yCB) yCB=M0a(Lx)4EIL3[4L3((Lx)23L2)(L+b)]
Slope (θAC) θAC=M0x4EIL3[4b2L(2L3x)(L2b2)]
Slope (θCB) θCB=M0a4EL3[4L33(L+b)(x22Lx)]
Moment (MAC) MAC=M02L3[2b2L(L3x)(L2b2)]
Moment (MCB) MCB=3M0a2L3(L+b)(Lx)
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
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