# Convention for spring symbols with lateral force

If you draw a diagram with a spring, is there any convention about how it should behave with lateral loads? I guess it might be either:

• Rigid
• Free
• Elastic with bending and/or shear stiffness
• Pin jointed - Initially free but as the spring rotates, it increases stiffness due to its orientation changing. Here's an example where it looks like we're supposed to neglect any bending or shearing of the springs. For instance, if the object moves in the y direction, only the 3 bottom springs would deflect and we wouldn't consider the bending stiffness of the other 3 springs. Is that right and common? From http://ecoursesonline.iasri.res.in/mod/page/view.php?id=126222

• This usually assumes small movement where the deflection is negligible.
– SF.
Jan 15, 2019 at 9:10
• Even small displacements will be affected by their lateral stiffness. So are you saying that we treat lateral stiffness of such springs as zero? The 4th bullet point in the question? Jan 15, 2019 at 18:52
• Yes, simultaneously considering their deflection angle as zero (e.g. imagine the springs to be near-infinitely long). Or alternatively consider them to be allowed frictionless lateral motion. ( ╧ instead of ┴ attachment at base.)
– SF.
Jan 15, 2019 at 19:39

The convention for an idealized spring in such a schematic is that the lateral stiffness is zero but also that it does not move out of its original orientation with respect to its base (i.e., it does not tilt). The idealized spring is characterized by only one parameter: the axial stiffness. (It is thus assumed that the axial deflections are sufficiently small that the stiffness is constant and displacement independent. This assumption holds for small perturbations of any stable solid.)

Since the lateral stiffness is zero, other constraints must limit a body's motion in the directions orthogonal to the spring axis. This can be seen in your second schematic, in which each degree of freedom is constrained by the axial stiffness of one or more springs. In contrast, your first diagram is not well defined: the block should accelerate to the right for any positive $$F$$, which then results in a discrepancy because a real spring would naturally resist such acceleration. To indicate this resistance, you'd either add a pseudospring with horizontal orientation or move away from lumped components altogether, perhaps modeling the spring using the method of compliant joints or by finite element analysis.

A good source of sample schematics for springs and rigid bodies is vibration textbooks, e.g., Tongue's Principles of Vibrations. Thorough and rigorous textbooks will emphasize that the block in your first diagram must be constrained (e.g., by walls) from moving left or right or in or out of the screen/page.

Initially it will be constrained by torsional resistance of the cross section of the spring and will behave like a column laterally loaded, or a cantilever beam with a concentrated load.

But at large deflections the compound reaction of torque and linear expansion of the spring will interact to the applied force.

Here is a sketch of different degrees of freedom of a joint as you asked. There are some other degrees of freedom such as guided, semi fixed with spring constrains. Or a joint free to move laterally but not rotationally.

• So fixed at both ends? Do you have any references such as examples of them used that way? To be clear, you talking about the diagram convention, not real life physics, right? Jan 15, 2019 at 0:33
• Not fixed at both ends. Free on top, fixed on the bottom. And to answer the second part of your question: I mean real engineering cases. In fact it could be more intricate in real life applications. For example: My side yard gate is equipped with a spring attached to the gate at 45 degrees, loaded with both compression and torque. And when someone opens the gate it closes the gate automatically. Jan 15, 2019 at 1:29
• I'm only interested in the convention for drawing diagrams because I need to draw a more complicated arrangement of springs and be clear about which joints can rotate and which cannot. Ideally, I'd like to see it used fixed at both ends (top fixed to the object) in a text book or fairly high quality website. Jan 15, 2019 at 3:57
• I'm asking about the spring symbol, not the support symbols. Jan 15, 2019 at 7:55