When analyzing a beam it is important to know what forces are acting on it in order to ensure a safe structural design. When examining each force, it is important to take into account the magnitude and the direction that the force is acting in. In this Instructable, you are going to learn how to see what the net, or total, force is acting on a two-dimensional beam in the y-direction (vertical direction). If you know the load, or net force, acting on a beam you are then able to implement supports for the beam that allow it to safely support the given net force. Knowing this information can be valuable when looking and the structural design of real life objects. For example, when designing a beam for an overpass you will have to know the net force of the cars acting on it so that you can know what type of load your supports will have to uphold.
Step 1: Analyze the Given Forces
To start off, you will look at the beam and see what direction that forces are acting in. If the force (represented by an arrow) is going down, the force will have a negative value. On the other hand, if the force is directed upwards, it will have a positive value. Going back to the overpass example, the cars on the overpass would exert a downward (negative) force on the beams that compose the overpass.
Step 2: Write Down the Given Information
It is important to keep track of the information that you are given. Write down the forces and their accompanying number value and sign (positive or negative). As you can see in the graphic, the name of the force is written down along with the sign, the value, and the unit system of the force. In this case, the unit of force is represented by N (Newtons), a unit of force. It is important to keep track of the unit that the problem is being worked in because the numerical value changes depending on the unit system that the problem is worked in.
Step 3: Adding the Forces to Find the Net Force
Next, you will add all of the forces that you just wrote down together. As seen in the accompanying picture, -50N+45N-20N= -25N. Depending on the forces given, an answer that is positive, negative, or zero is an acceptable answer. In this case, the net force is negative because there is a bigger total negative force acting on the beam than the total positive force.
Step 4: Interpreting the Net Force in the Y-direction
Upon summing the forces you will calculate a numerical value that is either positive, zero, or negative. If the result of the addition is positive, then the net force is acting on the beam in an upwards direction. If the net force calculated is equal to zero, then that means the forces acting upwards and downwards cancel each other out. This means that the beam is in equilibrium. Lastly, if the net force is negative, then it is acting in a downwards direction.
The three outcomes each have different implications when used in real world engineering applications. If the beam is in equilibrium then no additional support is needed. If the net force is upwards or downwards then supports will be needed in one of the two directions.