Calculator with trigonometry functions
Step 1: Free Body Diagram
The picture given has a force unknown at point E in the Y-direction facing up, force given at points G and F in the Y-direction facing down, forces unknown at point A in the X and Y-direction pointing to the right and up, length given for each beam, and unknown angle theta between each beam.
Step 2: Finding Theta
Adjacent side: side between theta angle and 90 degree angle
Hypotenuse side: side opposite the 90 degree angle
cos(theta) = (Adjacent side length/Hypotenuse side length)
simplified---> theta = cos^(-1)(Adjacent/Hypotenuse)
Step 3: Summing Moment About Point a to Find Ey
Select point A and all force vectors that do not directly pass through point A. To sum a moment about point A, multiply the magnitude of each of force vectors by the perpendicular distance from that vector to point A. Add those values together and set equal to zero. When adding together imagine you are walking in a counter-clockwise circle around point A, the forces that would be acting against you when you are walking parallel to them (the two forces given at point G and F) need to have a negative sign put in front of them.
Your equation should look like:
(Ey)(3 x length of beam) - (force at point F)(2 x length of beam) - (force at point G)(length of beam) = 0
Plug in known values and solve for force Ey.
Step 4: Draw Sectional Free Body Diagram
Step 5: Take Moment About Point F
a^2 + b^2 = c^2 Where c=Hypotenuse (given beam length), a=line ED' (given beam length divided by 2), and b is unknown length
Solve for b.
Now to solve for the moment about point F use the same process as solving for moment about point A.
The equation used should be:
(Ey)(length of beam) - (Fcd)(b) = 0
Solve for Fcd. Since this is a positive value the force is a compression force.
Step 6: Sum of the Forces in the Y-Direction
To find the force acting on beam CF sum up all the forces acting in the Y-direction.
To find the force of Fcf acting in the y-direction use the equation:
Fcf (y-direction) = Fcf * sin(theta)
Now sum all the forces acting in the y-direction and set equal to zero. If any for is pointing down put a negative sign in front of it. Your equation should look like:
Ey - (given force at point F) - (Fcf * sin(theta)) = 0
Solve for Fcf. Since this is a negative value the force acting on beam CF is in tension.
Step 7: Sum of the Forces in the X-Direction
To find the force acting on beam GF sum up all the forces acting in the X-direction.
To find the force of Fcf acting in the x-direction use the equation:
Fcf (x-direction) = Fcf * cos(theta)
Now sum all the forces acting in the x-direction and set equal to zero. If any force is pointing left put a negative sign in front of it. Your equation should look like:
Fgf + Fcd + (Fcf * cos(theta)) = 0
Solve for Fgf. Since this is a negative value the force acting on beam GF is in tension.
You have now found all the forces in the required beams.