maximum deflection at zero shear

[cve60069]

Dear all

I have been reading up on deflection, particularly the position of the maximum,and it stated in the Steel Designers Manual (1980-ish edition) that the max deflection occurs where the bending-moment is maximum. Is this so?

Regards

 

[frv]

No. Think of a cantilever.

 

[frv]

Let me rephrase that: not always. (it does happen in certain members with symmetric loads)

 

[paddingtongreen]

It is generally, the cantilever is a special case, but extend a mirror image and the reaction becomes the load, and the applied loads become the reactions and the deflection is correct. If it wasn't true, the differential equations would be screwed up. I hedged, I can't think of a case where it isn't true. but then, my memory is old and worn out.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[hokie66]

That statement is too broad. Take the case of a simple beam with a point load not at midspan. The maximum moment is at the load, but the maximum deflection is between the load and midspan.

 

[IDS]

The maximum deflection occurs where the slope due to deflection is zero. If the loading, flexural stiffness, and support conditions are all symmetrical about this point then this will also be a point of maximum curvature, and hence maximum bending moment, but if any of those factors are not symmetrical the points of maximum deflection and maximum bending moment will not (in general) coincide.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[paddingtongreen]

cve60069, If this is the Crosby Lockwood SDM, what chapter are you referring to. I have a different edition, but that stuff doesn't change much.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[frv]

paddington.. Do you have the AISC 13th Ed. Manual?- Look at the tables for loading cases and deflections. Compare max. moment to maximum deflection locations. It will become obvious that this location does not "generally" coincide. Only for certain symmetric conditions.

 

[rb1957]

max moment always occurs where the shear force changes sign.

max deflection always occurs where the slope is zero (as noted above). mathematically, deflection has a turning pt (or a point of inflection) when the slope is zero ... so a beam can have move than one zero slope, and maximum deflection will be at one of these.

i think it's hard to generalise that max moment occurs at max deflection, unless you're dealing with a beam with a simple loading.

 

[paddingtongreen]

@frv, yes, I realized that, I just didn't bother to take up space to say so. I know now what led me astray, I was thinking of the conjugate beam method as a simple way for the OP to check for himself, and I had the wrong diagram in mind when I answered.

Michael.
Timing has a lot to do with the outcome of a rain dance.