Deflection of beam, reinforced in the center section, multiple Ix values.
Deflection of beam, reinforced in the center section, multiple Ix values.
(OP)
I'm designing a beam for a point load, and to keep compressive stress down, I have to add a stiffener in the center portion, according to the attachment. Is there a way to calculate deflection for this application?






RE: Deflection of beam, reinforced in the center section, multiple Ix values.
However, I would use Risa 3D to model it and input the loads to get the deflection.
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
use the double integration method, section the beam where the section changes,
another idea is to solve the beam bending moments (they don't change with I), then analyze the two different inertias as two different beams ...
the outer beams are loaded by the external reaction only ... easy enough to calc displacements,
the inner beams deflects relative to its ends (where there's shear and moment into the smaller beam) ... easy enough to calc displacements,
i think you'll use the slope and the end of the smaller (outer) beam as a boundary condition for the inner (larger) beam.
add the two together.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
First, draw the M diagram and the M/EI diagram for the real beam.
Then, consider the M/EI diagram as a variable load on the conjugate beam. The resulting shear at any point on the conjugate beam represents the rotation at the same point on the real beam. The resulting moment at any point on the conjugate beam represents the deflection at the same point on the real beam.
The Conjugate Beam Method is simply an extension of Moment-Area principles.
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
You forgot to mention our other old favorite, and that’s Newmark’s Numerical Integration Methods. Much like the Conjugate Beam Method, in fact.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
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: Deflection of beam, reinforced in the center section, multiple Ix values.
If moment of inertia is I in the middle and kI in both ends, the center deflection can be calculated as:
Δ = PL3/48EI + (Pa3/6EI)(1/k-1)
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
On the other hand, if it takes more than about a minute to create and solve a single simply supported beam in an FEA program then this would be a good exercise to use in getting some practice at using the program.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
there is a place for canned beam solvers ... really complicated loadings and geometries, or for checking your hand calcs (or using your hand calcs to check the canned answer).
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
In your formula, what is k-1 in the denominator?
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
Point taken.
However, the OP did stipulate a point load, but not the location. That adds a different dimension to the problem, and considering the ramifications with other different loading situations, I would defer to the computer here 95% of the time just for the flexibility of analysis, knowing things can change. Setting the program up in RISA takes very little time.
Mike McCann
MMC Engineering
http://mmcengineering.tripod.com
RE: Deflection of beam, reinforced in the center section, multiple Ix values.
The load P appears to be at midspan of the beam, although admittedly its location is not dimensioned. I have no quarrel with those who prefer to use RISA or any similar software to solve the problem, but I echo rb1957's earlier comment:
BA
RE: Deflection of beam, reinforced in the center section, multiple Ix values.