Does anyone have the formulae for working out the DEFLECTION of a BUILT IN BEAM with TWO POINT LOADS 1

[keithtop]

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

 

[JStephen]

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).

 

[rb1957]

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

 

[johnbridge231]

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-design.html

 

[oldrunner]

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.

 

[IDS]

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/continuous-beam-spreadsheet-with-units/

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/

 

[desertfox]

Hi keithtop

Try this link:-

http://web.mst.edu/~mecmovie/chap10/m10_08_cant_twoP.swf