how to draw axial force diagram

Centric Force Diagrams and Torque Diagrams

Every bit an alternative to splitting a body in half and performing an equilibrium assay to find the internal forces and moments, nosotros tin likewise use graphical approaches to plot out these internal forces and moments over the length of the torso. Where equilibrium analysis is the most straightforward approach to finding the internal forces and moments at one cantankerous department, the graphical approaches are the virtually straightforward approaches to find the internal forces or the internal moments across the entire length of a axle, shaft, or other body. This may be useful in circuitous loading scenarios where it may non exist obvious where the maximum internal forces or internal moments exist. As a merchandise off even so, we will need to plot out each type of internal load separately (one plot for internal axial forces, one for internal shear forces, one for internal torques, and one for internal bending moments).

Complex Loading of a Beam — In complex loading situations, such every bit the loads on this horizontal ceiling axle, it may be difficult to know where the internal forces and internal moments will be greatest. By plotting out the internal forces and moments, we volition be able to more easily identify these maximum internal loads and nosotros can design the beam accordingly to withstand these loads.

Internal forces in 3D — The internal centric force (N) and the internal toque (T) deed along the length of the beam or shaft.

In this section, we volition exist focusing on the methods used to generate the plots for the internal centric forces, and the internal torques. This will be the force and moment acting along the length of the axle or shaft. The axial force plot is used primarily for vertical columns or cables supporting multiple loads along its length. The torque diagram is used primarily for shafts supporting multiple inputs and outputs. Each of these plots volition have a different practical application, only nosotros have grouped them together here because the process used to generate each of the two plots is very similar.

Creating the Axial Force Diagram

The axial forcefulness diagram will plot out the internal axial (normal) forces within a beam, cavalcade, or cable that is supporting multiple forces along the length of the beam itself. This can be thought of as the internal tension or compression forces. The most relevant practical scenarios that match this description volition be main back up columns in a multi-story building, or hanging cables that are used to back up multiple loads.

Main support collumns in a multi-story building — The master vertical support columns in this building will support multiple load forces that act along the length of the column Image by Jun Seita CC-By-NC ii.0.

To create the axial force plot for a body, we volition use the following process.

Solve for all external forces acting on the trunk.
Depict out a free body diagram of the body horizontally. In the instance of vertical structures, rotate the body so that it sits horizontally and all the forces act horizontally
Lined up below the gratuitous body diagram, depict a prepare of axes. The ten-axis volition correspond the location (lined up with the costless body diagram above), and the y-axis volition represent the internal centric forces, with positive numbers indicating tension and negative numbers indicating compression.
Starting at zero at the left side of the plot, you will move to the right, pay attention to forces in the free body diagram higher up. As you motion right in your plot, keep steady except...
- Spring upwards by the magnitude of the forcefulness for any forces in our complimentary body diagram to the left.
- Spring downwards by the magnitude of the force for any forces to the right.
- You tin can ignore whatsoever moments or vertical forces applied to the torso.
Past the time you get to the correct end of the plot, yous should always wind up coming back to zero. If y'all don't air current up back at zero, become back and cheque your previous piece of work.

A free body diagram with the axial force diagram. — The free body diagram of a support column (rotated to exist horizontal). Is shown above the respective axial force diagram for that column

To read the plot, yous simply need to notice the location of interest from the free body diagram higher up, and read the corresponding value on the y-axis from your plot. Again, positive numbers correspond an internal tension at that location and negative numbers represent an internal pinch at that location.

Creating the Torque Diagram

The torque diagram volition plot out the internal torsional moment within a shaft that is supporting multiple inputs and/or outputs along its length. The most relevant practical scenarios that friction match this clarification are shafts within complex gear or pulley driven systems.

A line shaft delivering power via multiple pulleys — This line shaft has a single input delivering torques to multiple outputs via pulleys. Image by Wtshymanski CC-BY-SA 4.0

To create the torque diagram for a shaft, nosotros will use the following process.

Solve for all external moments interim on the shaft.
Draw out a costless body diagram of the shaft horizontally, rotating the shaft if necessary, so that all torques deed around the horizontal centrality.
Lined up below the gratuitous body diagram, describe a set of axes. The 10-centrality volition represent the location (lined up with the free body diagram above), and the y-axis will represent the internal torsional moment, with positive numbers indicating an internal torsional moment vector to the correct and negative numbers indicating an internal torsional moment to the left.
Starting at zero at the left side of the plot, you lot will move to the right, pay attention to moments in the gratis body diagram above. Equally you motility right in your plot, go on steady except...
- Jump upwards by the magnitude of the moment for whatsoever torques in our free body diagram where the moment vector would point left.
- Jump downwards by the magnitude of the moment for any torques in our free torso diagram where the moment vector would point right.
- You tin can ignore any forces in the free torso diagram or moments not nearly the 10 axis.
Past the time you go to the correct finish of the plot, you should always wind up coming back to zip. If you lot don't current of air upward back at zero, go back and check your previous work.

A free body diagram of a shaft with the torque diagram. — A free body diagram of a shaft is shown above the corresponding toque diagram. Recollect to use the right hand dominion to determine if the moment vector is pointing to the right or left.

To read the plot, you lot only demand to take the find the location of interest from the complimentary body diagram above, and read the respective value on the y-axis from your plot.

Worked Problems:

Question 1:

A wooden beam is subjected to the forces shown below (forces applied at base of vector). Draw the axial force diagram for the beam.

Problem 1 Diagram

Solution:

Question 2:

A cable is anchored to the ceiling and subjected to the forces shown below (assume are forces practical at base of the vector). Draw the centric force diagram for the cable.

Problem 2 Diagram