Especificación funcional y desarrollo (B1)
CONTROL DE EDICIONES
DESCRIPCIÓN BÁSICA DEL PRODUCTO/SERVICIO
FOR PEDESTRIAN BRIDGES
The following presents recommended criteria and analysis examples for indoor and outdoor pedestrian bridges.
The evaluation criterion for floors can also be used to determine the vertical vibration acceptance of pedestrian bridges supported by beams or joists and girders. Recom- mended tolerance acceleration limits are shown in Table 4-4. A reduction factor of 0.7 is recommended in Section 2.2 for establishing the driving force because pedestrian bridges are one-way systems, and the walker and the potentially affected sensor can be relatively close together. The resulting Po value is 92 lb, assuming there is only one walker. Bachmann and Ammann (1987) have suggested that for marching by a group, the dynamic loading is the number of walkers, n, times that of a single walker, that is, nPo. And, for a group of random walkers, it is n times that for a single walker, nPo.
The recommended damping ratio for pedestrian bridges is 0.01, assuming there is only bare structural framing. If a soffit or other element that increases damping exists, the ratio should be increased. The effective weight, W, is taken as the total weight of the bridge. The acceleration limit for outdoor footbridges should not be used for quiet areas like crossovers in hotel or office building atria. The maximum
step frequency is 2.2 Hz, so the maximum lateral forcing frequency is 1.1 Hz. Synchronization of walking with lat- eral sway will not occur if the natural frequency of lateral vibration exceeds 1.1 Hz. Thus, it is recommended that the natural frequency of lateral vibration be not less than 1.3 Hz (AASHTO, 2009).
Designers of pedestrian bridges are cautioned to pay atten- tion to the location of the concrete slab relative to the beam height. If the concrete slab is located between the beams (because of clearance considerations), the pedestrian bridge will vibrate at a much lower frequency and at larger ampli- tude than if the slab is located above the supporting mem- bers, because of the lower transformed moment of inertia.
4.3 RECOMMENDED EVALUATION CRITERIA
FOR LINEAR MONUMENTAL STAIRS
Evaluation of linear monumental stairs for walking vibration tolerance consists of three checks (see Section 2.3): (1) that the vertical natural frequency of the stair is greater than 5 Hz, (2) that lateral natural frequency is greater than 2.5 Hz, and (3) that the vertical acceleration due to a descending indi- vidual or group is less than the relevant tolerance limit for people standing on the stairs. Recommended step frequen- cies for normal and rapid descents and acceleration tolerance limits for people standing on the stairs—not the walkers— are shown in Table 4-5. Because stair descent accelerations are always greater than ascent accelerations, only descents need to be considered in design.
The procedures recommended in the following can be used to analyze linear flights of stairs, such as shown in Figure 4-4(a). The procedures can also be adapted using engineering judgment for stairs, such as the one shown in Figure 4-4(b). The finite element method in Chapter 7 should be used for more complex slender stairs.
Table 4-3. Floor Lengths and Floor Widths for Figure 4-2 Framing Bay Floor Width, ft Floor Length, ft
A 90 105
B 120 70
C 120 105
Table 4-4. Recommended Tolerance Limits for Pedestrian Bridges
Type Acceleration Limit ao/g × 100%*
Indoor 1.5%
Outdoor 5.0%
A. FLOOR SLAB
Determine uniformly distributed weight, total depth, deck height, and effective depth, de.
Calculate n = Es
/
(1.35Ec).B. JOIST PANEL MODE
Calculate Ij (see Section 3.4 if trusses or Section 3.5 if open web joists). Calculate wj and Δ = w L E I 5 384 j j j s j 4 . Calculate fj=0.18 g Δj.
Determine Ds for slab and deck or estimate usingDs=
(
12de3)
12n.Calculate Dj = Ij
/
S.CalculateBj=Cj
(
D Ds j)
Lj ≤(q)4
(floor width).
Cj = 2.0 for interior panels; 1.0 for edge panels.
Calculate Wj = wjBjLj (× 1.5 if continuous or web connected or 1.3 if joist bottom chords are extended, and an adjacent beam or girder span is greater than 0.7 times the joist or beam span of the bay).
C. GIRDER PANEL MODE For each girder:
Calculate Ig (Section 3.4 if a truss; Section 3.5 if a joist girder; Section 3.5 if open web joists are supported). Calculate wg andΔ = w L E I 5 384 g g g s g 4
with correction if only one beam is supported at midspan (see Section 3.1). Calculate =fg 0.18 gΔg and Dg = Ig
/
Lj.Use average of supported joist span lengths, if different, for Lj.
If girder frequencies are different, base remainder of calculations on the girder with lower frequency. For interior panel, calculate
Bg=C D Dg
(
j g)
Lj≤1/4
(q) (floor length)
Cg = 1.8 if shear connected; 1.6 if not. For edge panel, calculateB = ⎛⎝2⎞⎠L
3
g j.
Calculate Wg = wgBgLg(× 1.5 if girder is continuous over the top of supporting columns and an adjacent girder span is greater than 0.7 times the girder span in the bay).
D. COMBINED PANEL MODE Calculatefn=0.18 g
(
Δj+Δg)
. If Bj > Lg, reduce Δg by Lg/
Bj ≥ 0.5 (Equation 4-6). Calculate = + Δ Δ Δ Δ Δ Δ + + W j W W j g j g j g g . Estimate β using values from Table 4-2.Calculate β
(
)
= − a g P W exp 0.35f p o n where Po = 65 lb or as modified for a particular design (see Section 4.1.1).
Comparea
g
ptoa
g
o from Table 4-1.
Natural Frequencies
Stair vertical or lateral natural frequency can be determined using Equation 3-1 with slightly different definitions as follows: f gE I W L π 2 n s t s s3 2 = ⎛ ⎝⎜ ⎞ ⎠⎟ (4-7) where
EsIt = stringer vertical flexural stiffness, including string- ers and any other elements that provide stiffness; stair lateral flexural stiffness, lb-in.2
Ls = stringer length measured along the diagonal between supports, in.
Ws = weight of stair, lb
fn = fundamental natural frequency, Hz g = acceleration of gravity = 386 in./s2
If the stair is supported on girders, the vertical com- bined mode or system frequency can be estimated using the Dunkerley relationship as shown in Equation 3-2.
Acceptance Criterion
The acceleration acceptance criterion, Inequality 4-8, for vertical vibration of linear stairs is similar to that for floors but somewhat more complex as explained in Section 2.3. The criterion states that the stair is satisfactory if the peak acceleration, ap, due to a stair descent as a fraction of the acceleration of gravity, g, does not exceed the acceleration tolerance limit, ao in %/g, from Table 4-5:
a g e RQ W e a g 0.62 cos 1 p f s W R o 2 100 n
(
)
= θ β ϕ ϕ − ≤ −γ − β (4-8) where Q = assumed bodyweight = 168 lb R = calibration factor (see Table 4-5) Ws = weight of stair, lbβ = damping ratio
ϕW= unity normalized mode shape value at the excitation (walker)
ϕR = unity normalized mode shape value at the response
(potentially affected observer) location
θ = stair inclination from horizontal, measured with respect to support points, degrees
γ = 0.29 for normal descents = 0.19 for rapid descents
Because the vertical natural frequency is greater than 5 Hz and maximum assumed step frequency for normal descents from Table 4-5 is 2.5 Hz, the harmonic number, h, is greater than 2 and the calibration factor, R, is 0.7 as specified in Sec- tion 2.3. Similarly, if the vertical frequency is less than 8 Hz, the harmonic number is 2 for rapid descents and R = 0.5. If the natural frequency is greater than 8 Hz, the harmonic number is 3 or greater and R = 0.7.
Engineering judgment is required when estimating the damping ratio. Davis and Murray (2009) reported a damping ratio of 0.01 for a stair with no nonstructural components, treads that are isolated from each other, and guardrails that are connected without the potential for frictional interfaces. Table 4-5. Vertical Acceleration Tolerance Limits and Parameters
Step Frequency, Hz Acceleration Tolerance Limit, ao, %g Calibration Factor, R Walking Load Parameter, γ Remarks ≤ 2.5 1.7 0.7 0.29 Normal descents 2.5–4.0 3.0 0.5 if fn < 8 Hz
0.7 if fn > 8 Hz 0.19 Rapidly descending individual—not perceptible
2.5–4.0 4.5 0.5 if fn < 8 Hz
0.7 if fn > 8 Hz 0.19
Rapidly descending individual—perceptible; rapidly descending group
(a) Linear stair
(b) Linear stair with intermediate landing Fig. 4-4. Linear stairs.