# Applying forces from the inside of a bar

I was reading Schaum's Outline: Strength of Materials (fifth edition) when I came across this solved example problem from the Tension and Compression chapter:

The solution was clear to me, however what I was wondering about, is the problem itself. Since the bar is uniform and made of same material, I'm unable to figure out how one would apply forces 'internally' in the rod, like the $$15kN$$ and $$10kN$$ forces shown in Fig. 1-9 (a).

I would imagine it to be something like applying a shearing force on the lateral faces of the bar (assuming it has some thickness) at the points shown in the figure which then result in internal forces. Is this how it's done or there's some other way without shearing the lateral surfaces of the bar?

• Have you heard of St. Venant's principle? That says that (except in a few special situations) the exact way a load is applied only has a local effect on the response of the structure. So in real life engineering, the answer to your question about how the loads were applied is "it doesn't matter." Jun 10 '21 at 16:53

In real application, representative to the case you are presenting, there is usually no internal application of forces (Of course you can conceive cases that this is not true). So essentially what you are imagining that there is a shear force externally and then the force is uniformly distributed internally. The bottom line is that type of exercises is that you assume that the forces are magically and automatically distributed to the cross-section.

IMHO the following is an example -representative of the problem in the OP - i.e. a problem of tag of war

This can be simplified as (I've offset the forces so that they are visible).

So the forces are applied on the external surface of the rope. In this scenario - if you are after stresses on each section of the rope -, it is adequate to assume that the forces are uniformly distributed on the cross-section of the rope.

The mechanism or the increase in stresses, is difficult(/if not impossible) to calculate analytically, and the difference it would make on the stresses would be -in the majority of the cases- minimal.

• But what about a 6" shell going through a gun barrel? high pressure behind and low pressure in front... An interesting problem to evaluate the rate of change of stress in the barrel as the shell moves. Jun 10 '21 at 10:43
• I am thinking of constricting bolted attachments with loads applied. Or, perhaps a fabrication of weldment where the loads are applied to the plates that project at those interfaces with load attacments (and only deflection is sought). Alternatively, external weldments were applied to the bar with loads. In either case this simplification might be a first order solution. Jun 10 '21 at 11:05
• @SolarMike It was my understanding that the OP talked about a solid bar. IMHO, the gun barrel and projectile is a two part system. I would argue that even then the developed tensile stresses on the gun barrel, are developed only due to the applied pressure at the face opposite the projectile. In that specific case - gun barrel- (which IMHO is not representative of the problem in the OP), if your point is that there are normal forces (instead of tangential), yes you right. Jun 10 '21 at 11:30
• @JimClark your scenario about application of internal forces is a lot more appropriate than the gun barrel example. The question is, would that make such a difference at the resulting stresses on each segment of the rope? And, some might argue (I won't) that the weldment or the extruded plates are not part of the uniform bar of the original problem. Jun 10 '21 at 11:41