# deflection pp

Beam deflection due to a point load with two pin jointed supports at either end.

Controller: **CodeCogs**

doubledeflection_pp( | double | L | |

double | a | ||

double | W | ||

double | x | ||

double | EI` = 1` | ) |

This function is used to calculate the deflection along a beam that is subjected to a single perpendicular point load

*W*. The deflection of the beam is calculated using the principal of virtual work, applying a unit load of 1N at the location where the deflection is required and solving where*M(x*) are the moment along the beam due to the applied unit load*W*, while*M_u(x*) is the moment due to the applied virtual point load at the location*x*.Purchase a Licence for more information.

## Example

Calculate the deflection along a 9m long solid plank of wood (100mm x 50m) wood due to a person that weights 70kg who stands 3m from either end. In graphical form the deflection (negative is downwards) is given by:#include<stdio.h> #include<codecogs/engineering/structures/deflection_pp.h> int main() { double E=10e9; // approximate strength of wood. double I=1.042e-6; // I=b*h^3/12. double L=9; double a=3; double W=70*9.81; // Force in Newtons for(int x=0;x<=L;x++) printf("\n deflection(x=%d)=%lf",x, Engineering::Structures::deflection_pp(L, a, W, x, E*I)); return 0; }Output:

deflection(x=0)=0.000000 deflection(x=1)=0.322188 deflection(x=2)=0.600441 deflection(x=3)=0.790825 deflection(x=4)=0.860389 deflection(x=5)=0.820115 deflection(x=6)=0.691972 deflection(x=7)=0.497927 deflection(x=8)=0.259947 deflection(x=9)=0.000000

### Parameters

L The length of the beam. [m] a The location of the point load applied to the beam. [m] W The point load applied at location *a*in a direction perpendicular to the main beam. [N]x The point at which the deflection should be calculated EI The Modulus of Elasticity (E) multiplied with the Second Moment of Area (I) for the specified beam. See Young's Modulus for example values. [N/m^2]

##### Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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