A test of your common sense

Hi Taz,Taking this as a standard engineering load diagram for "pinned end" loading and assuming no distributed load for the weight of the beam:

• The load at A is P and the load at D is P (reactions)
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• The sheer load is P from A to B, 0 from B to C and -P from C to D
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• The bending load is 0 at A, increasing linearly to PL at B, then steady at PL to C, and then decreasing linearly back to 0 at D.

The deflection will be greatest in the middle, following the next order of curves (bending is the integration of the sheer curve, deflection is the integration of the bending curve).Combined sheer and bending stress will be greatest at the load points, B and C.With a distributed load for the beam weight, there would be added sheer and bending loads:

• The load at A and D is 1.5wL (reactions)
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• The sheer load is 1.5wL at A decreasing linearly (-wx) to 0 at 1.5L and continuing to decrease to -1.5wL at D
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• The bending stress increases from 0 at A to a maximum of 9wL^{^2}/8 at the middle and then decreases back to 0 at D

Thus the greatest sheer load is at the ends, and the greatest bending stress is in the middle.Where the beam fails depends on the relative amounts of P and w and whether it is more sensitive to failure in sheer or bending, and of course the condition of the beam and the end foundations .... and whether or not a butterfly farts in Mexico ....This is based on what I know from my education and experience, as much as I know 1+1=2, and this is why my "common sense" is likely different from yours ... and why there really is no "common" sense of things at all.A better term would be common ignorance ... Enjoy.Edited by RAZD, : addedEdited by RAZD, : /listEdited by RAZD, : No reason given.Edited by RAZD, : ...

Hi Heathen Indeed, and this is part of your "common knowledge" even though not everyone knows it or understands your explanation ...This is part of the "technical language" of structural/stress engineering, where the symbols used represent whole phrases and contexts that someone not educated as an engineer do not know and have no way of knowing.For instance, I can open my 4th editionSteel Manual (1967) to page 2-122 and look at diagram #9 and see this very problem, along with the formulas for stresses and deflections. (if you don't have the same edition, the page and diagram number are likely different, but the diagram will be the same).We also know that these diagrams are idealized renditions of common problems (hence the triangle pin and roller at the ends) and that assist in finding reasonable solutions. Indeed. This is why learning the technical "language" of a field is critical if you are going to discuss it intelligently.Enjoy.

Hi Taz, The engineer/s use these diagrams to assess all the potential failure locations and modes, and then designs the beam to withstand each of the stresses.At the ends you have vertical sheer loads and bearing loads. The foundations (triangle and roller) have bearing loads.At the load positions you have vertical sheer (from loading) and horizontal sheer (from bending), bending and bearing loads.What the diagram tells the engineer is that the stresses in between these points are less than those at these points, so they only need to asses the stresses at these 4 locations to design the beam ... usually with a factor of safety.Where the beam actually fails is due more to the characteristics of the beam -- is it flexible like rubber or fragile like glass -- and on what is deemed to be failure (how much deflection is allowed, ultimate versus yield strengths) than on the loads.Enjoy.

Hi Stile, Correct, it would also prevent the end from rising under load. What it means is that there is no induced stress from tension load that would occur with two pinned ends under deflection.Enjoy.

Hi xongsmith Correct -- it uses the technical language of engineering and not the common language of non-engineers.Engineers understand what is included and what is excluded in the diagram, while your objections are basically that you don't know what is included and excluded, you don't know the language. Which in engineering technical language would be represented by the triangle and roller diagram. Your example is specific, the engineering one is generalized, so that it can be applied to more instances than just a board over cinderblocks.Enjoy.Edited by RAZD, : .