Beam Deflection, Stress, Strain Equations and Calculators
Area Moment of Inertia Equations & Calculators
Beam Cubic Parabola Shape Deflection Equation Calculator with Variable Shape Fixed End Single Concentrated Force Applied
 Cross Section: Rectangle: width z variable, depth y constant
 Elevation: Cubic Parabola
 Plan: Cubic Parabola
ALL calculators require a Premium Membership
Preview Calculator
Equations
k (Constant) = z / y
I_{2} = b^{3} d / 30
c = b / 2 S_{s} = I_{2} / c
b_{1} = k h
Deflection at A:
f = ( 6 P / b_{1} E ) ( l / h )^{3}
Where:
E = 
Modulus of Elasticity 
psi 
(N/mm^{2}) 
I = 
Moment of Inertia 
in^{4} 
(mm^{4}) 
P = 
Force 
lbf 
(N) 
f = 
Deflection 
inches 
(mm) 
S_{s}= 
Section Modulus 
in^{3} 
(mm^{3}) 
a, b, c, d, x, l = 
Some distance as indicated 
inches 
(mm) 
References:
 Civil Engineering Formulas, Tyler G. Hicks, PE International Engineering Associates
