Wall and pier rigidity
Finds the lateral stiffness of a concrete or masonry wall with openings, or of solid piers on a line, and each pier's share of a force. Copy the rigidity into Rigid diaphragm torsion or your building model: nothing links them. The type reads Calculated; it has no pass or fail.
Inputs of the wall rigidity #
- What to analyze: one wall with openings, or up to 12 solid piers sharing one displacement.
- Force V at the top: shared by rigidity. The rigidities do not depend on it.
- Material: concrete (Ec by ACI 318-19 19.2.2.1, from f'c and wc), concrete masonry (Em = 900 f'm, TMS 402-22 4.2.2.2), clay masonry (Em = 700 f'm), or E entered.
- G/E: 0.4 prefilled (TMS 402-22 4.2.2.2 and the usual value for concrete).
- Factors on I and on the shear area: 1.0 is the gross section. ACI 318-19 6.6.3.1.1 gives 0.70 uncracked and 0.35 cracked on I for walls; whether the wall cracks is your call. They apply to every part.
- Effective thickness t: the actual thickness of concrete or fully grouted masonry, an equivalent solid thickness for partial grout. Rigidity k uses it; relative R does not.
- Top of the wall: cantilever, or fixed against rotation by a stiff level above. Which it is, is your call: the sources tell you to judge where the inflection point sits.
- Strip at the base, deducted as: where the openings reach the base of a cantilever wall, the strip taken out of the solid wall can be a cantilever (TM 5-809-3 Example 2, a stiffer wall) or fixed at both ends (CMACN 2002, softer). In TM 5-809-3 Example 2 the difference is about 4 %.
- Openings: up to 12, each by its distance from the wall's left end, its sill above the base, width and height. A door has sill 0. An opening reaching the top of a cantilever wall leaves free-standing piers.
- Piers: length, height, thickness, ends (cantilever or fixed), and corner. A corner pier is an L or T: I × 1.5 and a shape factor of 1.0 in shear (TM 5-809-3 7-8).
Checks performed #
| Result | Basis |
|---|---|
| E, G | ACI 318-19 19.2.2.1; TMS 402-22 4.2.2.2; or entered |
| Deflection of a rectangular part: V/(E t) [c (h/L)³ + 1.2/(G/E) (h/L)], c = 4 cantilever, 1 fixed | TM 5-809-3 Eq. 7-11, 7-12; flexure plus shear |
| Wall: solid wall, less the strip with the openings, plus its piers | TM 5-809-3 7-9; CMACN Summer 2002 |
| Piers in a strip: side by side, rigidities add; stacked, deflections add | TM 5-809-3 Example 2 |
| Shear in each pier by rigidity; moment V h for a cantilever, V h / 2 for fixed ends | Statics |
| Advisory: stiffer than the solid wall | The cantilever strip at the base can do this; change it to fixed |
| Advisory: staggered openings | Openings overlapping in height with no clean line between them: the tallest counts over the full band, a softer wall than drawn |
| Advisory: shallow spandrel | Under half the height of the band, the piers are softer than fixed |
The wall is read as a stack of bands: each group of openings overlapping in height is one strip. Inside it, an opening running the band's full height cuts it into piers; a shorter one, such as a window above a sill, stacks a solid strip in series with the piers beside it.
Limitations #
- The method is approximate, and its sources say so: TM 5-809-3 7-8 warns that any simplified method can give inconsistent results and asks for judgment. It ignores the rotation of the parts and assumes where they are fixed. Finite elements are the check for a wall that matters.
- Linear elastic. No cracking beyond the factors you enter, no foundation rotation, no flanges on a wall with openings. No strength check: design the piers in their own calculation.
- Openings are rectangles lined up with the wall.
Verification examples #
Verification status: 34 values compared in 10 examples (10 published, 0 hand calculations from the cited equations): 34 within tolerance, 0 recorded deviations. Code basis: the provisions it uses were read in the target edition.
| Example | Source | Values |
|---|---|---|
| 12 × 20 ft wall, one window | TM 5-809-3 Design Example 1, pp. 7-10, 7-11 | Solid 0.3461 in., total 0.3726 in., k 2.68 |
| 12 × 20 ft wall, door and window | TM 5-809-3 Design Example 2, pp. 7-12, 7-13 | Solid 0.4829 in., total 0.6469 in., four piers, shares 7.6, 24, 68.4 % |
| Chart equations | TM 5-809-3 Figure 7-5a | All four curves at h/d = 1 |
| Two walls with a door | CMACN Masonry Chronicles Summer 2002 | 0.28, 0.315 in.; 1.57, 1.71 in.; R 0.585 |
| Solid walls | Yaw (2022) Table 2 | R 1.2898, 1.1119, 0.3754 |
| Five piers | CMACN Masonry Chronicles Spring 2002 Table 1 | R 1.58 to 0.04 |
TM 5-809-3 reads its deflections off a chart, so its values carry a chart reading, up to about 1 % here. The app computes the chart's equations. CMACN prints Em = 1.5 ksi, evidently 1,500 ksi with the thousands dropped: its deflections are run as printed. None of these is written to TMS 402-22 or ACI 318-19: the method is older than both, and only E and G come from the current codes. No published example has staggered openings, a fixed top or an opening reaching the top; hand calculations cover the last two.