StructuralMind

Column Design — Verification

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Column Design computes two different kinds of quantity, and each is verified differently. The section capacity is a physical prediction — it states what the section will actually carry. The detailing limits are rules the code lays down. A rule cannot be falsified by a test, because the rule defines what is acceptable. So the first layer is checked against measured columns and the second against the clause itself.

Section capacity

The interaction diagram Column Design uses is the fiber engine of Section Analysis itself. Solving the same column in both macros produces the same mesh fibers, the same bar positions, the same material curves and the same interaction diagram point by point. The comparison was run separately for rectangular and circular sections, and in both the numbers match digit for digit.

In practice this means you can take a column's section into Section Analysis and inspect the same interaction diagram, moment-curvature curve and fiber stress state there. The capacity that enters the strength check in Column Design and the capacity you see there are the same number.

The verification of that capacity against measured columns is on the Section Analysis verification page. Across thirty-nine laboratory specimens, the capacity computed on the design basis never exceeded the moment the specimen carried.

Which diagram the check uses

The strength check uses the code's equivalent rectangular stress block for concrete and the non-hardening elastoplastic diagram for steel. Even when a behaviour curve such as Hognestad or Mander is selected in the request, the strength calculation runs on those two diagrams.

The material factors γc=1.5\gamma_c = 1.5 and γs=1.15\gamma_s = 1.15 are applied to the stress read from the curve after it is built. The modulus of elasticity is not reduced, so the yield strain shifts to fyd/Esf_{yd}/E_s.

Behaviour curves exist to produce the expected behaviour of a section and are used in the Section Analysis macro. A code verdict is produced with the code's own diagram.

Detailing limits

Every rule is checked at three points: comfortably inside the limit, exactly at it, and just outside. The value exactly at the limit is the decisive one, because TS 500's limits are inclusive and a rule written with >> instead of \geq shows up only there. The limit each rule reports is checked as well.

ClauseRuleWhat was checked at the limit
TS 500 §7.4.1Smallest section dimension \geq 250 mm250 mm PASSED, 249 mm FAILED
TS 500 §7.4.1Circular diameter \geq 300 mm300 mm PASSED, 299 mm FAILED
TS 500 §7.4.1Longitudinal bar diameter \geq 14 mm14 mm PASSED. 20 mm corners with 12 mm intermediates FAILED, because the smallest diameter governs
TS 500 §7.4.1 Eq. 7.8ρ0.01\rho \geq 0.01Bracketed from both sides
TS 500 §7.4.1 Eq. 7.9ρ0.04\rho \leq 0.040.0103 PASSED, 0.048 FAILED
TS 500 §7.4.1 Eq. 7.7Nd0.9fcdAcN_d \leq 0.9 f_{cd} A_cExactly at the limit PASSED, 1 kN above FAILED
TS 500 §7.4.1Stirrup diameter \geq 8 mm8 mm PASSED, 6 mm FAILED
TS 500 §7.4.1Mid-zone spacing smin(12ϕ,200)s \leq \min(12\phi, 200)Checked at four diameters. At ϕ\phi14 and ϕ\phi16 the bar term governs (168 and 192 mm), at ϕ\phi20 and ϕ\phi32 the 200 mm cap does
TBDY 2018 §7.3.4Confinement zone spacing smin(bmin/3, 150, 6ϕ)s \leq \min(b_{min}/3,\ 150,\ 6\phi)All three terms made to govern, each on a different section
TBDY 2018 §7.3.4Ductility classHigh ductility uses 6ϕ6\phi and limited ductility 8ϕ8\phi, while the 150 mm cap is unchanged
TBDY 2018 §7.3.4Confinement zone length max(1.5bmax, n/6, 500)\geq \max(1.5 b_{max},\ \ell_n/6,\ 500)Each of the three terms made to govern on a different section

A 50 mm floor is applied beneath the ceilings the spacing rules produce. That floor is not the code's rule; it is there to keep the spacing buildable, and it comes into play on small sections.

When a confinement zone length is entered by hand, the formula is bypassed and the entered value applies even if it falls below the 500 mm floor.

Scope of this calculation

What the results above cover, together with the direction each omission leans.

The shear and capacity-shear formulas take both column ends as hinging. The capacity shear is computed as Ve=(Mp,top+Mp,bot)/nV_e = (M_{p,\text{top}} + M_{p,\text{bot}})/\ell_n. Where the beams framing into the column are weaker and hinge first, the beams' plastic end actions are not distributed to the column ends in proportion to the members' stiffnesses, and the result is on the safe side.

Factored actions, already carrying the overstrength factor, are expected. The combination values entered into Column Design must be the factored ultimate-strength values where they are gravity loads. Likewise, values entered for seismic combinations must already carry the increases the seismic code requires (the equivalent static / modal combination increase, the overstrength factor and the like).

The increased reinforcement ratio limit in a lap splice zone is not applied. TS 500 §7.4.1 raises the ratio limit to 0.06 inside a lap splice zone. The calculation applies ρ0.04\rho \leq 0.04 in all cases, so a column carrying a ratio between 0.04 and 0.06 in its splice zone is reported as FAILED. The deviation is on the safe side.

Second-order effects are not computed. When slenderness exceeds the TS 500 §7.6 threshold no moment magnification is applied; a warning is issued instead and the relevant check is marked FAILED. Columns that require a second-order analysis need that magnification carried out separately.

Biaxial bending comes from the section engine. The interaction curve at a given bending angle is verified to be the one Section Analysis produces. The resolution of the angle sweep belongs to that engine's own scope.

Bottom cover is a separate input. If top and side cover are entered and bottom cover is left empty, 25 mm is used. The bar layout is then not symmetric about the section centroid. Rebuilding the section in another macro requires entering bottom cover as well to reach the same number.

Whether the code's own rules are adequate is not the subject of this page. What is shown here is that the TS 500 and TBDY 2018 rules are applied as written.

Sources

  • TS 500 (2000)
  • TBDY 2018
  • PEER Structural Performance Database (Berry, Parrish & Eberhard, 2004)