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Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

(OP)
Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS. I used to have this info., when I was a
student 50 years ago, but obviously cant remember it now. All the info. on the web only gives it with one load in the centre.
I would be very grateful for this because it takes such a long time to surf the web & then you only get the same answers.

Best Regards Keithtop

RE: Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

You can use superposition and just add the deflection at a particular point due to each load.
I think the AISC handbook and perhaps Roark's Formulas For Stress and Strain also have formulas for paired loadings (where loads are symmetrical about center).

RE: Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

superimpose the deflection curves from each point load.

i'm guessing that "built-in" means cantilevered, so M(0) = -Pa
this is easy to integrate twice, because the boundary conditions are slope and deflection at x=0 = 0, so the constants of integration disappear.

you're left with ...
M(x) = -Pa+Px x<a
EI*v(x) = -Pax+Px^2/2 x<a
EI*d(x) = -Pax^2/2+Px^3/6 x<a

for x>a you have EI*d(x) = EI*d(a)+EI*v(a)*(x-a) (ie a constant slope outbd of the point-load).

Quando Omni Flunkus Moritati

RE: Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

simple mechanics....

Analysis and Design of arbitrary cross sections
Reinforcement design to all major codes
Moment Curvature analysis

http://www.engissol.com/cross-section-analysis-des...

RE: Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

Page 33, Steel Designer's Manual by Gray and others. Lower left panel. Fixed end beam diagram with each side distance equal for the same point load.

RE: Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS

For the deflection at x due to a single load at a on a beam fixed at both ends Pilkey gives:

For x < a
-W*b^2*x^2/(6*L^3*E*I)*(3*a*x+b*x-3*a*L)

For x >= a
-W*a^2*(L-x)^2/(6*L^3*E*I)*((3*b+a)*(L-x)-3*b*L)

W = Load
L = Span
b = L-a
See attached diagram.

As others have said, for two loads just add the deflections from two single load calculations.

Alternatively the ConbeamU spreadsheet here:
http://newtonexcelbach.wordpress.com/2012/09/06/co...
has a SSpan function that allows any number of point or distributed loads. You can get fixed end conditions by specifying end moment restraints with a very high stiffness. See the SSSpanU Example sheet for an example which you can plug your own numbers into.

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/

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