Table 226

Horizontal Force Factor, ap and Rp

1. Elements of structure ap Rp a. Cantilevered parapets 2.5 3.0

b. All interior bearing and nonbearing walls 1.0 3.0

c. Penthouse (not an extension of structural frame) 2.5 4.0

d. Cladding connections 1.0 3.0

2. Nonstructural components a. Ornamentations and appendages 2.5 3.0

b. Floor-supported cabinets and book stacks more than 6 feet in height 1.0 3.0

c. Partitions 1.0 3.0

3. Equipment a. Emergency power supply systems 1.0 3.0

b. Tanks and vessels 1.0 3.0

4. Other components a. Rigid components with ductile material and attachments 1.0 3.0

b. Rigid components with nonductile material and attachments 1.0 1.5

c. Flexible components with ductile material and attachments 2.5 3.0

d. Flexible components with nonductile material or attachments 2.5 1.5

(Condensed from 1997 UBC, Table 16-O.)

where

Fp = lateral force applied to the center of mass of the component ap = in-structure amplification factor that varies from 1.0 to 2.5 (Table 2.26) Ca = seismic coefficient that varies depending on the seismic zone in which the structure is located and the proximity to active earthquake faults. Ca varies from 0.075 to 0.66.

Ip = component importance factor, which depends on the occupancy of the structure and varies from 1.0 to 1.5 Rp = component response modification factor, which varies from 1.5 to 3.0 (Table 2.26)

hx = element or attachment elevation with respect to grade. hx shall not be taken as less than 0. hr = the structure roof elevation, with respect to grade Wp = weight of the component

Upper-and lower-bound limits for Fp are defined as follows: Fp need not exceed 4CaIpWp

Fp shall not be less than 0.7 CaIpWp

The ap factor accounts for the dynamic amplification of force levels for flexible equipment. Rigid components, defined as components including attachments that have a period less than 0.06 seconds, are assigned an ap = 1.0. Flexible components have a period greater than 0.06 seconds, and are assigned an ap = 2.5. The component response modification factor, Rp, represents the energy absorption capability of the component's structure and attachments. Conceptually, the value considers both the overstrength and ductility of the component's structure and attachments. It is believed that in the absence of research, these separate considerations can be adequately combined into a single factor for nonstructural components. In general, the following benchmark values were used:

Rp = 1.5 brittle or buckling failure mode expected

Rp = 3.0 moderately ductile materials and detailing

Rp = 4.0 highly ductile materials and details

Where connection of the component to concrete or masonry is made with shallow expansion, chemical, or cast-in-place anchors, Rp is taken as 1.5. Shallow anchors are defined as those anchors with an embedment length-to-diameter ratio of less than 8. If the anchors are constructed of brittle materials (such as ceramic elements in electrical components), or when anchorage is provided by an adhesive, Rp is taken as 1.0. The term adhesive in this case refers to connections made by using surface application of a bonding agent, and not anchor bolts embedded using expoxy or other adhesives. An example, of anchorage made with adhesive would be base plates for posts glued to the surface of the structural floor in a raised access floor system.

The reduced Rp values, 1.5 for shallow embedment (post installed and cast) anchors and 1.0 for adhesive anchors, are intended to account for poor anchor performance observed after the Northridge earthquake. When anchors are installed into "housekeeping" pads, these pads should be adequately reinforced and positively anchored to the supporting structural system.

The design forces for equipment mounted on vibration isolation mounts must be computed using an ap of 2.5 and an Rp of 1.5. If the isolation mount is attached to the structure using shallow or expansion-type anchors, the design forces for the anchors must be doubled.

Equation (2.50) represents a trapezoidal distribution of floor accelerations within the structure, linearly varying from Ca, at the ground, 4.0 Ca at the roof. The ground acceleration, Ca, is intended to be the same acceleration used as design input for the structure itself and will include site effects.

To meet the need for a simpler formulation, a conservative maximum value for Fp = 4IpWp has been set.

A lower limit for Fp = 0.7CaIpWp is prescribed to ensure a minimal seismic design force. The redundancy factor R has been set equal to unity since the limiting redundancy of nonstructural components has already been accommodated in the selection Rp factors.

The out-of-plane design loads for exterior walls or wall panels that have points of attachment at two or more different elevations may be determined as follows. For the vertical span of a wall between two successive attachment elevations, hx and hx+1, evaluate the seismic force coefficients Fp/Wp at each of the two points, observing the minimum and maximum limits, and compute the average of the two values. The average seismic coefficient times the unit weight of the wall provides the distributed load for the span between the given attachment points, and it should extend to the top of any wall parapet above the roof attachment point at hr.

For a single-story exterior wall, the seismic force coefficient at the base is 0.7CaIp, and at the roof is 1.33CaIp. An average value of 1.02CaIp applies to the unit weight of the wall for the distributed load over the entire wall.

In addition to lateral force requirements, the 1997 UBC specifies that for essential or hazardous facilities, components must be designed for the effects of relative motion, if the component is attached to the structure at several points. An example would be vertical riser in a piping system that runs from floor to floor. The component must accommodate the maximum inelastic response displacement, defined as

Figure 2.63. Equipment anchorage design; air-conditioning unit example.

2.5.4.2. Design Examples

Example 1.

Given. An air-conditioning unit weighing 25 kips will be installed in the mechanical penthouse on the roof of a 10-story building. The dimensions of the unit are shown in Fig. 2.63. The fundamental period of the air-conditioning unit is 0.05 seconds. There are four 1-inch diameter anchor bolts, one at each corner of the unit, embedded in the roof concrete slab. The bolts have an embedment length of 7 inches. The building is in seismic zone 4 and the building site is within 5 kilometers of a type-B seismic source, and located on soil profile type SD.

Required. Using the 1997 UBC provisions, determine the shear and tension demands on the anchor bolts, assuming the bolts will be designed using ASD, allowable stress design.

Solution hx = 120 feet (attachment height of element with respect to grade) hr = 120 feet (roof elevation with respect to grade) Ip = 1.0 (standard occupancy)

ap = 1.0 (in-structure amplification factor, values range from 1.0 to 2.5) (In our case, this is equal to 1.0.)

Rp = 1.25 (component response modification factor varies from 1.25 to 3) In our case, Rp = 1.25, calculated as follows:

The ratio of anchor bolt embedment length to bolt diameter le/d = 7/1 = 7. This is less than 8. Therefore, from footnotes of 1997 UBC, Table 16-N, Rp = 1.25. If the ratio le/d was more than 8, we would have used a higher value of Rp. Ca = 0.66 (seismic coefficient that is dependent on the seismic zone in which the structure is located and its proximity to active faults) Ca varies from a low of 0.075 to a high of 0.66. In our case, Ca = 0.66, calculated as follows:

For soil profile type SD (stiff soil), Ca = 0.44Na, where Na is the near-source factor. Our site is within 2 kilometers of a type A seismic source. Therefore, Na = 1.5 and Ca = 0.44Na = 0.44 x 1.5 = 0.66.

The design lateral force for the equipment using Eq. (2.50) is apCaIp fp =

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