CALCS PROC018
RIGID BODY EQUALIBRIUM 2D

NOTATION

detAdeterminant, equation solution term
Kpx Kpy Kpzcoeffiecient, equation solution
M1zmoment, caused by applied forces about datum
Npnumber of applied forces
P1x P1yforce, applied, resolved components
Px Pyforce-resolved parallel to axes
P2 P3 P4force-reaction, vector sum
sumPxforce sum
sumMzmoment sum
thetaangle, orientation of force (deg.)
x ycoordinates, reaction forces points of action on body
x1 y1coordinates, applied force point of action on body

APPLICATION

Planar triangle of forces or any statically determinate load system

OUTPUT

reactive loads P2 P3 & P4

SEE ALSO

BAS002 & PROC017

THEORY

Statics

GUIDANCE

Array DIM Px(Np),Py(Np),Mz(Np),X(Np),Y(Np) statement must be added at prog start, for the applied forces. Add additional input data X(2), X(3), Y(2), Y(3), P1.2, P1.3, etc when more than one applied load is being used (see example).

INPUT FORMAT

LET Np=:X(1)=:Y(1)=:Px(1)=:Py(1)=:theta2=RAD():theta3=RAD():theta4=RAD():X2=:X3=:X4=:Y2=:Y3=:Y4=:PROC018

EXAMPLE

Call Statement

LET Np=2:X(1)=31:X(2)=24:Y(1)=10:Y(2)=7:Px(1)=7:Px(2)=5:Py(1)=-25:Py(2)=-20:theta2=45:theta3=110:theta4=160:X2=-3:X3=2:X4=8:Y2=-2:Y3=-1:Y4=6:PROC018

Output

PROC018 RIGID BODY EQUALIBRIUM, 2D, Rev 230995
Kpx2= COS(theta2)= 0.5253
Kpx3= COS(theta3)= -0.999
Kpx4= COS(theta4)= -0.9756
Kpy2= SIN(theta2)= 0.8509
Kpy3= SIN(theta3)= -0.04424
Kpy4= SIN(theta4)= 0.2194
Kmz2= -COS(theta2)*Y2+SIN(theta2)*X2= -1.502
Kmz3= -COS(theta3)*Y3+SIN(theta3)*X3= -1.088
Kmz4= -COS(theta4)*Y4+SIN(theta4)*X4= 7.609
detA2= sumMz*(Kpx3*Kpy4-Kpx4*Kpy3)-Kmz3*(sumPx*Kpy4-Kpx4*sumPy)+Kmz4*(sumPx*Kpy3-Kpx3*sumPy)= -34.17
detA3= Kmz2*(sumPx*Kpy4-Kpx4*sumPy)-sumMz*(Kpx2*Kpy4-Kpx4*Kpy2)+Kmz4*(Kpx2*sumPy-sumPx*Kpy2)= 1090
detA4= Kmz2*(Kpx3*sumPy-sumPx*Kpy3)-Kmz3*(Kpx2*sumPy-sumPx*Kpy2)+sumMz*(Kpx2*Kpy3-Kpx3*Kpy2)= -1230
detA= Kmz2*(Kpx3*Kpy4-Kpx4*Kpy3)-Kmz3*(Kpx2*Kpy4-Kpx4*Kpy2)+Kmz4*(Kpx2*Kpy3-Kpx3*Kpy2)= 7.714
Px2= -Kpx2*detA2/detA= 2.327
Px3= -Kpx3*detA3/detA= 141.2
Px4= -Kpx4*detA4/detA= -155.5
Py2= -Kpy2*detA2/detA= 3.769
Py3= -Kpy3*detA3/detA= 6.253
Py4= -Kpy4*detA4/detA= 34.98
P2= ABS(detA2/detA)= 4.43
P3= ABS(detA3/detA)= 141.3
P4= ABS(detA4/detA)= 159.4
END018