Short Column Deflection

[kylelo]

A short column is said to depend on material strength only. But you know deflection still occurs. It may be negligible, but I'm computing the corresponding strain of concrete at mid-height with respect to the upper and lower region. If concrete fails at a strain of 0.003 at mid-height. What formula do you use to compute for the strain at the upper region. I'd like to compare them. Please see color diagram of the strains attached herewith.

 

[kylelo]

Thank you.

 

[paddingtongreen]

Guys, you are at cross purposes. JAE, he has an equal eccentricity of the reaction at the base. This does not need an external equalizing moment - no horizontal reactions.

If pinned/pinned JAE is correct when you draw in the horizontal reactions required to make ΣM=0 for the free body.




Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[BAretired]

In the sketch provided, both ends may be considered pinned. Each end has an applied moment of Pn*e. Neglecting deflection, the moment is constant for the full length of column.

The first order deflection at midspan is M.L²/8EI but this provides a variable moment over the height of column, so at mid-height, the moment is Pn(e + δ). But because the moment has increased, the deflection also must be increased, so the moment must be amplified to account for increased deflection.

If the load is sustained over a long period of time, concrete creeps and further increases deflection, again amplifying the magnitude of the moment at mid-height. The exact amount of this amplification is dependent on several factors but can be estimated for purposes of design and is given in the applicable concrete code.

BA