Floor vibration

An evaluation of steel-framed floors, pedestrian bridges and linear stairs for vibration from people, by AISC Design Guide 11, 2nd Ed. (2016). Pick one evaluation per calculation: walking on a building floor, a pedestrian bridge, a rhythmic activity, sensitive equipment or occupants, or a linear monumental stair. The steel stair calculation leaves vibration to this type on purpose, because Design Guide 34 refers to this Guide.

The Guide gives recommendations, not code limits. Each limit, damping ratio and driving force is your input with the Guide's value prefilled.

Inputs of the floor vibration #

Slab and day-to-day loads. Concrete above the deck, deck height, unit weight and f'c set the dynamic modular ratio (1.35 Ec, Section 3.2) and the slab weight. The loads are expected, not design, loads (Section 3.3): 4 psf for mechanical and ceiling; Table 3-1 for live load, 11 psf in a paper office, 6 to 8 in an electronic one, 6 in a residence, 0 in assembly areas and malls.

Beam or joist. A W-shape with its composite moment of inertia computed, an open-web joist (Section 3.5: chord properties, Cr, Eq. 3-7), or It entered. Effective slab width is the spacing up to 0.4 of the span. A panel at a free edge takes Cj = 1.0 with the typical beam's section, as Example 4.3 does; enter It to evaluate an edge member by Section 3.2. The beam panel weight takes your choice of factor: 1.5 where continuous or shear connected with an adjacent span over 0.7 of this one, 1.3 for joist bottom chords extended before the concrete; joists on seats do not take 1.5.

Girder. A W-shape, It entered, or none where the beams bear on walls. Joist seats use Eq. 3-11 and Cg = 1.6; beams into the web use the full composite section and Cg = 1.8. Floor width and length are the distances over which the framing repeats. Enter a joist girder's Ig from Eq. 3-10; it is not computed.

Damping. The sum of Table 4-2 (0.01 structure, ceiling and ductwork, fit-out, partitions) or entered.

Walking. The occupancy sets 0.5 %g or 1.5 %g (Table 4-1), or enter your own; Po is prefilled at 65 lb.

Pedestrian bridge. Span, weight, vertical and lateral stiffness, Po (92 lb), walkers and whether they march, damping (0.01 for bare framing), running as an option with your limit.

Rhythmic activity. Activity (Table 5-2), the participants' weight (less when they use part of the span), the total weight, column shortening for taller buildings, and the limit from Table 5-1.

Sensitive equipment or occupants. How the limit is given, the generic VC list of Table 6-2 or your value, the walking speed of Table 6-1, and the locations of equipment and walker for the mode shape of Eq. 6-2. Section 6.2 occupants use Eq. 6-9.

Linear stair. Stringers by shape and count or It entered, stair weight, rise and run, damping (engineer's judgment; 0.01 for a bare stair, 0.03 to 0.04 with a soffit and frictional treads and guards), walker and observer on the diagonal or 1.0 on the safe side, and whether a rapid descent may be perceptible (4.5 %g rather than 3 %g) and whether groups are to be evaluated.

Auto-design varies the W-shapes of the beam and girder among up to 18 sizes around each, lightest framing first. It does not check strength: run the beam's own calculation on the result.

Checks performed #

Limitations #

Closed-form predictions for regular framing. Not covered: finite element analysis (Chapter 7), the transmission of vibration across joists (Section 8.3), trusses by Eq. 3-6, joist girders by Eqs. 3-7 to 3-10 (enter Ig), unequal girders in one bay beyond entering the governing one, high-frequency floors under Section 2.2 other than Chapter 6, stairs other than a linear flight. Strength is not checked. Floors on cold-formed joists have no path here: the Guide is written for steel beams and open-web joists.

Verification examples #

Verification status: 88 values compared in 16 examples (16 published, 0 hand calculations from the cited equations): 87 within tolerance, 1 recorded deviations. Code basis: the provisions it uses were read in the target edition.

Against the Guide's own worked examples, 4.1 to 4.6, 5.1, 5.2 and 6.1 to 6.4, intermediate values included. Example 4.1 gives fn 3.99 Hz, W 109,000 lb and 0.49 %g; 4.2 gives 5.37 Hz, 65,700 lb, 0.503 %g, slightly over the limit as printed. 4.5 gives 2.69 %g walking and 12.8 %g running; 4.6 gives 7.02 and 4.73 Hz, 1.44, 2.08 and 6.23 %g; 5.2 gives 40.1 %g. Example 6.1 gives 9,890 mips at midbay and 7,350 mips scaled; 6.4 gives 2,220 and 6,780 mips.

Example 6.3 reads its velocities from Figure 6-15 to two digits rather than computing them, so those values carry a wider tolerance, and one is a recorded deviation. The peak velocity, narrowband and one-third octave acceleration equations appear in no example; they are checked by hand against the printed equations in the test file.

The AISC Design Guide 11 copy in the library has an errata page at its end that is for Design Guide 9, not 11; its Examples 5.1 and 5.4 are that guide's. No errata list for Design Guide 11 itself was found, apart from the Rev. 9/19 marks in the text.