1 Precast Concrete
2 Precast Concrete Design
Seismic design of precast concrete using the NEHRP Recommended Provisions
Review of design examples to illustrate the application of the provisions
3 Requirements for Precast Concrete Systems
Precast seismic systems used in structures assigned to Seismic Design Category C must be intermediate or special moment frames, or intermediate precast or special structural walls.
Precast seismic systems used in structures assigned to Seismic Design Category D must be special moment frames, or intermediate precast (up to 40 feet) or special structural walls.
Precast seismic systems used in structures assigned to Seismic Design Category E or F must be special moment frames or special structural walls.
Prestress provided by prestressing steel resisting earthquake-induced flexural and axial loads in frame members must be limited to 700 psi or fc/6 in plastic hinge regions. These values are different from the ACI 318 limitations, which are 500 psi or fc/10.
4 Requirements for Precast Concrete Systems
An ordinary precast structural wall is defined as one that satisfies ACI 318 Chapters 1-18.
An intermediate precast structural wall must meet additional requirements for its connections beyond those defined in ACI 318 Section 21.4. These include requirements for the design of wall piers that amplify the design shear forces and prescribe wall pier detailing and requirements for explicit consideration of the ductility capacity of yielding connections.
A special structural wall constructed using precast concrete must satisfy the acceptance criteria defined in Provisions Section 9.6 if it doesnt meet the requirements for special structural walls constructed using precast concrete contained in ACI 318 Section 21.10.2.
5 Requirements for Precast Concrete Systems: Design Examples
The example in Section 8.1 illustrates the design of untopped and topped precast concrete floor and roof diaphragms of the five-story masonry buildings
The example in Section 8.2 illustrates the design of an intermediate precast concrete shear wall building in a region of low or moderate seismicity. The precast concrete walls in this example resist the seismic forces for a three-story office building.
The example in Section 8.3 illustrates the design of an intermediate precast concrete shear wall for a single-story industrial warehouse building.
The example in Section 8.4 shows a partial example for the design of a special moment frame constructed using precast concrete per ACI 318 Section 21.8.
6 8.1 HORIZONTAL DIAPHRAGMS
7 HORIZONTAL DIAPHRAGMS
Structural diaphragms are horizontal or nearly horizontal elements, such as floors and roofs, that transfer seismic inertial forces to the vertical seismic force-resisting members.
Precast concrete diaphragms may be constructed using topped or untopped precast elements depending on the Seismic Design Category.
Reinforced concrete diaphragms constructed using untopped precast concrete elements are not addressed specifically in the Standard, in the Provisions, or in ACI 318.
Topped precast concrete elements, which act compositely or noncompositely for gravity loads, are designed using the requirements of ACI 318 Section 21.11.
8 Horizontal Diaphragm Examples
This example illustrates untopped precast floor and roof diaphragm design for five-story masonry buildings located in
Birmingham, Alabama, on soft rock (Seismic Design Category B)
New York, New York (Seismic Design Category C).
9 Diaphragm Forces for Birmingham Building
The weight tributary to the roof and floor diaphragms (wpx) is the total story weight (wi) at
Level i minus the weight of the walls parallel to the direction of loading.
Roof:
Total weight = 861 kips
Walls parallel to force = (45 psf)(277 ft)(8.67 ft / 2) = -54 kips
wpx = 807 kips
Floors:
Total weight = 963 kips
Walls parallel to force = (45 psf)(277 ft)(8.67 ft) = -108 kips
wpx = 855 kips
10 Diaphragm Design Forces
Standard equation 12.10-1
11 Diaphragm Design Forces
Calculations for Fpx are provided in Table 8.1-2.
12 Diaphragm Design Forces
The minimum value of Fpx = 0.2SDSIwpx
= 0.2(0.24)1.0(807 kips) = 38.7 kips (roof)
= 0.2(0.24)1.0(855 kips) = 41.0 kips (floors)
The maximum value of Fpx = 0.4SDSIwpx
= 2(38.7 kips) = 77.5 kips (roof)
= 2(41.0 kips) = 82.1 kips (floors)
Note that the calculated Fpx in Table 8.1-2 is substantially larger than the specified maximum limit value of Fpx.
.
13 Static Analysis of Diaphragms
14 Static Analysis of Diaphragms
The uniform diaphragm demands are proportional to the distributed weights of the diaphragm in different areas
W1 = [67 psf (72 ft) + 48 psf (8.67 ft)4](153 kips / 863 kips) = 1,150 lb./ft
W2 = [67 psf (72 ft)](153 kips / 863 kips) = 855 lb./ft
15 Critical regions of the diaphragm to be considered in this design
16 Critical regions of the diaphragm to be considered in this design
Joint 1: Maximum transverse shear parallel to the panels at panel-to-panel joints
Joint 2: Maximum transverse shear parallel to the panels at the panel-to-wall joint
Joint 3: Maximum transverse moment and chord force
Joint 4: Maximum longitudinal shear perpendicular to the panels at the panel-to-wall connection (exterior longitudinal walls) and anchorage of exterior masonry wall to the diaphragm for out-of-plane forces
Joint 5: Collector element and shear for the interior longitudinal walls
17 Joint Forces
Joint 1 Transverse forces:
Shear, Vu1 = 1.15 kips/ft (36 ft) = 41.4 kips
Moment, Mu1 = 41.4 kips (36 ft / 2) = 745 ft-kips
Chord tension force, Tu1 = M/d = 745 ft-kips / 71 ft = 10.5 kips
Joint 2 Transverse forces:
Shear, Vu2 = 1.15 kips/ft (40 ft) = 46 kips
Moment, Mu2 = 46 kips (40 ft / 2) = 920 ft-kips
Chord tension force, Tu2 = M/d = 920 ft-kips / 71 ft = 13.0 kips
18 Joint Forces
Joint 3 Transverse forces:
Shear, Vu3 = 46 kips + 0.86 kips/ft (24 ft) 38.3 kips = 28.3 kips
Moment, Mu3 = 46 kips (44 ft) + 20.6 kips (12 ft) - 38.3 kips (24 ft) = 1,352 ft-kips
Chord tension force, Tu3 = M/d = 1,352 ft-kips / 71 ft = 19.0 kips
Joint 4 Longitudinal forces:
Wall force, F = 153 kips / 8 = 19.1 kips
Wall shear along wall length, Vu4 = 19.1 kips (36 ft)/(152 ft / 2) = 9.0 kips
Collector force at wall end, Tu4 = Cu4 = 19.1 kips - 9.0 kips = 10.1 kips
19 Joint 4 Out-of-Plane Forces
The Standard has several requirements for out-of-plane forces. None are unique to precast diaphragms and all are less than the requirements in ACI 318 for precast construction regardless of seismic considerations. Assuming the planks are similar to beams and comply
with the minimum requirements of Standard Section 12.14 (Seismic Design Category B and greater), the required out-of-plane horizontal force is:
0.05(D+L)plank = 0.05(67 psf + 40 psf)(24 ft / 2) = 64.2 plf
20 Joint 4 Out-of-Plane Forces
According to Standard Section 12.11.2 (Seismic Design Category B and greater), the minimum anchorage for masonry walls is:
400(SDS)(I) = 400(0.39)1.0 = 156 plf
According to Standard Section 12.11.1 (Seismic Design Category B and greater), bearing wall anchorage must be designed for a force computed as:
0.4(SDS)(Wwall) = 0.4(0.39)(48 psf)(8.67 ft) = 64.9 plf
21 Joint 4 Out-of-Plane Forces
Standard Section 12.11.2.1 (Seismic Design Category C and greater) requires masonry wall anchorage to flexible diaphragms to be designed for a larger force. Due to its geometry, this diaphragm is likely to be classified as rigid. However, the relative deformations of the wall and diaphragm must be checked in accordance with Standard Section 12.3.1.3 to validate this assumption.
Fp = 0.85(SDS)(I)(Wwall) = 0.85(0.39)1.0[(48 psf)(8.67 ft)] = 138 plf
(Note that since this diaphragm is not flexible, this load is not used in the following calculations.)
22 Joint 5 Forces
Joint 5 Longitudinal forces:
Wall force, F = 153 kips / 8 = 19.1 kips
Wall shear along each side of wall, Vu5 = 19.1 kips [2(36 ft) / 152 ft]/2 = 4.5 kips
Collector force at wall end, Tu5 = Cu5 = 19.1 kips - 2(4.5 kips) = 10.1 kips
Joint 5 Shear flow due to transverse forces: Shear at Joint 2, Vu2 = 46 kips
Q = A d: A = (0.67 ft) (24 ft) = 16 ft2 , d = 24 ft
Q = (16 ft2) (24 ft) = 384 ft3
I = (0.67 ft) (72 ft)3 / 12 = 20,840 ft4
Vu2Q/I = (46 kip) (384 ft3) / 20,840 ft4 = 0.847 kip/ft maximum shear flow
Joint 5 length = 40 ft
Total transverse shear in joint 5, Vu5 = 0.847 kip/ft) (40 ft)/2 = 17 kips
23 Diaphragm Design and Details Joint 1
24 Diaphragm Design and Details Joint 1
Chord reinforcement, As1 = Tu1/?fy = (10.5 kips)/[0.9(60 ksi)] = 0.19 in2 (The collector force from the Joint 4 calculations at 10.1 kips is not directly additive.)
Shear friction reinforcement, Avf1 = Vu1/??fy = (41.4 kips)/[(0.75)(1.0)(60 ksi)] = 0.92 in2
Total reinforcement required = 2(0.19 in2) + 0.92 in2 = 1.30 in2
ACI tie force = (1.5 kips/ft)(72 ft) = 108 kips; reinforcement = (108 kips)/(60 ksi) = 1.80 in2
Provide four #5 bars (two at each of the outside edges) plus four #4 bars (two each at the interior joint at the ends of the plank) for a total area of reinforcement of 4(0.31 in2) + 4(0.2 in2) = 2.04 in2.
25 Diaphragm Design and Details Joint 1
26 Diaphragm Design and Details Joint 2
27 Diaphragm Design and Details Joint 2
28 Diaphragm Design and Details Joint 4
29 Diaphragm Design and Details Joint 4
30 Topped Precast Concrete Units for Five-Story Masonry Building Located in Los
Angeles
For Seismic Design Category C and higher, Standard Section 12.10.2.1 requires that collector elements, collector splices and collector connections to the vertical seismic force- resisting members be designed in accordance with Standard Section 12.4.3.2, which combines the diaphragm forces times the overstrength factor (W0) and the effects of gravity forces.
The seismic design force of 463 kips is distributed as in Section 8.1.1.6 (Figure 8.1-1 shows the distribution). The force is three times higher than that used to design the untopped diaphragm for the New York design due to the higher seismic demand.
Collector elements will be designed for 2.5 times the diaphragm force based on the overstrength factor (?0).
31 Topped Precast Concrete Units for Five-Story Masonry Building
32 Topped Precast Concrete Units for Five-Story Masonry Building
Edge Detail
33 Topped Precast Concrete Units for Five-Story Masonry Building
Interior Details
34 Three-Story Office with Intermediate Precast Concrete Shear Walls
35 Three-Story Office with Intermediate Precast Concrete Shear Walls
Seismic Parameters
36 Structural Design Considerations
Precast Shear Wall System. This system is designed to yield in bending at the base of the precast shear walls without shear slip at any of the joints. The remaining connections (shear connectors and flexural connectors away from the base) are then made strong enough to ensure that the inelastic action is forced to the intended location.
The basic load combinations require that seismic forces and gravity loads be combined in accordance with the factored load combinations presented in Standard Section 12.4.2.3.
37 Base Shear
Equation 12.8-2:
except that it need not exceed the value from Standard Equation 12.8-3 computed as:
where T is the fundamental period of the building computed using the approximate method of
Standard Equation 12.8-7:
Therefore, use Cs = 0.0708, which is larger than the minimum specified in Standard
Equation 12.8-5:
Cs = 0.044(SDS)(I) ? 0.01 = 0.044(0.283)(1.0) = 0.012
The total seismic base shear is then calculated using Standard Equation 12.8-1 as: V = CsW =
(0.0708)(5,364) = 380 kips
38 Vertical Distribution of Seismic Force
39 Overturning Moment Longitudinal
40 Overturning
Using the load combinations described above, the vertical loads for combining with the overturning moment are computed as:
Pmax = 1.26D + 0.5L + 0.2S = 397 kips
Pmin = 0.843D = 239 kips
The tension reinforcement can be found from a simple couple.
The effective moment arm is:
jd = 25 - 1.5 = 23.5 ft
41 End Reinforcement
The required reinforcement is:
As = Tu/?fy = (107 kips)/[0.9(60 ksi)] = 1.98 in2
Use two #9 bars (As = 2.0 in2) at each end with Type 2 couplers for each bar at each panel joint. Since the flexural reinforcement must extend a minimum distance, d, (the flexural
depth) beyond where it is no longer required, use both #9 bars at each end of the panel at all three levels for simplicity
At this point a check per ACI 318 Section 16.5 will be made. Bearing walls must have vertical ties with a nominal strength exceeding 3 kips per foot and there must be at least two ties per panel. With one tie at each end of a 25-foot panel, the demand on the tie is:
Tu = (3 kip/ft)(25 ft)/2 = 37.5 kips
The two #9 bars are more than adequate for the ACI requirement.
42 Shear Connections and Reinforcement
Panel joints often are designed to resist the shear force by means of shear friction, but that technique is not used for this example because the joint at the foundation will open due to
flexural yielding.
Alternatively, the joint can be designed with direct shear connectors that will prevent slip along the joint. That concept is developed here.
43 Shear Connection Force
The design shear force is based on the yield strength of the flexural connection. The flexural strength of the connection can be approximated as follows:
Therefore, the design shear, Vu, at the base is 1.5(1.41)(190 kips) = 402 kips.
44 Shear Connection Detail
45 Shear Connection Design
Assembly with two face plates measuring 3/8" Χ 4" Χ 12" connected by a C8x18.75 and with diagonal #5 bars as shown in the figure. In the field, weld an L4Χ3Χ5/16 Χ 0'-8", long leg horizontal, on each face. The shear capacity of this connection is checked as follows:
Shear in the two loose angles:
?Vn = ?f(0.6Fu)tl(2) = (0.75)(0.6)(58 ksi)(0.3125 in.)(8 in.)(2) = 130.5 kip
Weld at toe of loose angles:
?Vn = ?(0.6Fu)tel(2) = (0.75)(0.6)(70 ksi)(0.25 in./(?2)(8 in.)(2) = 89.1 kip
Weld at face plates, using Table 8-8 in AISC Manual (13th edition):
?Vn= 0.75(1.73)(1.0)(4)(8)(2) = 83.0 kip
Bearing of concrete at steel channel:
fc = f(0.85f'c) = 0.65(0.85)(5 ksi) = 2.76 ksi
46 Shear Connection Design
The bearing will be controlled by bending in the web: compute the width (b) of flange loaded at 2.76 ksi that develops the plastic moment in the web:
Mp = ?Fytw2/4 = (0.9)(50 ksi)(0.4872 in2)/4 = 2.67 in-kip/in.
Mu = fc[(b-tw)2/2 - (tw/2)2/2] = 2.76[(b - 0.243 in.)2 - (0.243 in.)2]/2
setting the two equal results in b = 1.65 inches.
Therefore, bearing on the channel is:
?Vc = fc(2 - tw)(l) = (2.76 ksi)[(2(1.65) - 0.487 in.](6 in.) = 46.6 kip
To the bearing capacity on the channel is added the four #5 diagonal bars, which are
effective in tension and compression;
? = 0.75 for shear is used here:
?Vs = ?fyAscos? = (0.75)(60 ksi)(4)(0.31 in2)(cos45°) = 39.5 kip Thus, the total capacity for transfer to concrete is:
?Vn = ?Vc + ?Vs = 46.6 + 39.6 = 86.1 kip
47 Shear Connection Design: Foundation Plate
In the foundation, provide an embedded plate 1/2" Χ 12" Χ 1'-6" with six 3/4-inch-diameter headed anchor studs.
The capacity of the plate in the foundation is governed by the headed anchor studs. Capacity in shear for anchors located far from an edge of concrete, such as these and with sufficient embedment to avoid the pryout failure mode is governed by the capacity of the steel, which is required by ACI 318 Section D3.3.4:
?Vsa =? n Ase futa = (0.65)(6 studs)(0.44 in2 per stud)(60 ksi) = 103 kip
48 Shear Connection Summary
The various shear capacities of the connection are as follows:
Shear in the two loose angles: 130.5 kip
Weld at toe of loose angles: 89.1 kip
Weld at face plates: 83.0 kip
Transfer to concrete: 86.1 kip
Headed anchor studs at foundation: 103 kip
The number of embedded plates (n) required for a panel is:
n =402/83.0 = 4.8
Use five connection assemblies, equally spaced along each side (4'-0" on center works well to avoid the end reinforcement). The plates are recessed to position the #5 bars within the thickness of the panel and within the reinforcement of the panel.
Consider how much moment capacity is added by these connection to the vertical uplift at the joint
49 One-Story Precast Shear Wall Building
This example illustrates the design of a precast concrete shear wall for a single-story building in a region of high seismicity.
The precast concrete building is a single-story industrial warehouse building (Occupancy
Category II) located in the Los Angeles area on Site Class C soils.
The precast wall panels used in this building are typical DT wall panels.
Walls are designed using the ACI category of intermediate precast structural walls.
50 One-Story Precast Shear Wall Building
51 One-Story Precast Shear Wall Building
52 Intermediate precast concrete wall panels
The intent of the intermediate precast structural wall requirements is to provide yielding in
a dry connection for bending at the base of each precast shear wall panel while maintaining significant shear resistance in the connection.
The flexural connection for a wall panel at the base is located in one DT leg while the connection at the other leg is used for compression. Per ACI 318 Section 21.4, these connections must yield only in steel elements or reinforcement
All other elements of the connection (including shear resistance) must be designed for 1.5 times the force associated with the flexural yield strength of the connection.
53 System Force Calculations
Flexible diaphragm
Equivalent lateral force method
Load combinations
Earthquake forces
Building weight
Base shear
Horizontal distribution without torsion for flexible diaphragm
54 Longitudinal Direction Design
55 Tension and Shear Forces at the Panel Base
Design each precast shear panel to resist the seismic overturning moment by means of a ductile tension connector at the base of the panel.
A steel angle connector will be provided at the connection of each leg of the DT panel to the concrete footing.
The horizontal leg of the angle is designed to yield in bending as needed in an earthquake.
ACI 318 Section 21.4 requires that dry connections at locations of nonlinear action comply with applicable requirements of monolithic concrete construction and satisfy both of the following:
Where the moment action on the connection is assumed equal to 1.5My, the co- existing forces on all other components of the connection other than the yielding element shall not exceed their design strength.
The nominal shear strength for the connection shall not be less than the shear associated with the development of 1.5My at the connection.
56 Longitudinal Direction
The maximum tension for the connection at the base of the precast panel to the concrete footing is governed by the seismic overturning moment and the dead loads of the panel and the roof.
At the base:
ME = (4.25 kips)(20 ft) = 85.0 ft-kips
Dead loads:
SD = 2(1.08) + 7.73 = 9.89 kips
1.4D = 13.8 kips
0.7D = 6.92 kips
Compute the tension force due to net overturning based on an effective moment arm, d, of
4.0 feet (the distance between the DT legs). The maximum is found when combined with
0.7D:
Tu = ME/d - 0.7D/2 = 85.0/4 - 6.92/2 = 17.8 kips
57 Size the Yielding Angle
58 Size the Yielding Angle
The location of the plastic hinge in the angle is at the toe of the fillet (at a distance, k, from the heel of the angle.) The bending moment at this location is:
Mu = Tu(3.5 - k) = 17.8(3.5 - 1.1875) = 41.2 in.-kips
Using ACI 318 Section 21.4.3, the tension force for the remainder of this connection and the balance of the wall design are based upon a probable strength equal to 150 percent of the yield strength. Thus:
59 Size the Yielding Angle
The amplifier, required for the design of the balance of the connection, is:
The shear on the connection associated with this force in the angle is:
Check the welds for the tension force of 27.0 kips and a shear force 6.46 kips.
60 Size the Yielding Angle
The Provisions Section 21.4.4 (ACI 318 21.4.3) requires that connections that are designed to yield be capable of maintaining 80 percent of their design strength at the deformation
induced by the design displacement. For yielding of a flat bar (angle leg), this can be checked by calculating the ductility capacity of the bar and comparing it to Cd.
61 Welds to Connection Angle
Welds will be fillet welds using E70 electrodes.
For the base metal, ?Rn = ?(Fy)ABM.
For which the limiting stress is ?Fy = 0.9(50) = 45.0 ksi.
For the weld metal, ?Rn = ?(Fy)Aw = 0.75(0.6)70(0.707)Aw.
For which the limiting stress is 22.3 ksi.
Size a fillet weld, 6.5 inches long at the angle to the embedded plate in the footing. Using an elastic approach:
Resultant force =
Aw = 27.8/22.3 = 1.24 in2
t = Aw/l =1.24 in2 / 6.5 in. = 0.19 in.
For a 3/4 inch angle leg, use a 5/16 inch fillet weld. Given the importance of this weld,
increasing the size to 3/8 inch would be a reasonable step
62 Welds to Connection Angle
It is conservative to limit the maximum strain in the bar to esh = 15ey. At this strain, a flat
bar would be expected to retain all its strength and thus meet the requirement of maintaining
80 percent of its strength.
Assuming a plastic hinge length equal to the section thickness:
Since the ductility capacity at strain hardening is 0.112/0.012 = 9.3 is larger than Cd = 4 for this system, the requirement of Provision Section 21.4.4 (ACI 318 Sec. 21.4.3) is met.
63 Base Connection Detail
64 Special Moment Frame Constructed Using Precast Concrete
As for special concrete walls, the Standard does not distinguish between a cast-in-place and a precast concrete special moment frame in Table 12.2-1.
ACI 318 Section 21.8 provides requirements for special moment frames constructed using precast concrete.
That section provides requirements for designing special precast concrete frame systems using either ductile connections (ACI 318 Sec. 21.8.2) or strong connections (ACI 318
Sec. 21.8.3.)
65 Ductile Connectors
For moment frames constructed using ductile connections, ACI 318 requires that plastic hinges be able to form in the connection region. All of the requirements for special moment frames must still be met, plus there is an increased factor that must be used in developing the shear demand at the joint.
It is interesting to note that while Type 2 connectors can be used anywhere (including in a plastic hinge region) in a cast-in-place frame, these same connectors cannot be used closer than h/2 from the joint face in a ductile connection. The objective of Type 2 connectors is that they relocate the yielding away from the connector, into the bar itself.
66 Ductile Connectors
67 Strong Connections
ACI 318 also provides design rules for strong connections used in special moment frames. The concept is to provide connections that are strong enough to remain elastic when a plastic hinge forms in the beam.
68 Strong Connection Example
A single-bay frame is designed to meet the requirements of a precast frame using strong connections at the beam-column interface.
Reinforcing the beam with three #10 bars top and bottom, the nominal moment strength of the beam is:
69 Strong Connection Example
This is the moment strength at the plastic hinge location. The strong precast connection must be designed for the loads that occur at the connection when the beam at the plastic hinge location develops its probable strength. The moment strength at the beam-column interface (which also is the precast joint location) must be at least:
70 Strong Connection Example
Therefore, the design strength of the connection must be at least: Using #14 bars in the column side of the Type 2 coupler:
which is greater than the load at the connection (843 ft-kips) when the plastic hinge develops.
71 Examples for Seismic Design of Precast Concrete
Diaphragms in moderate and high seismic design categories
Intermediate precast concrete shear walls in moderate and high seismic design categories
Special moment frames constructed using precast concrete with emulation details
72 Seismic Design of Precast Concrete
Precast concrete designs must reflect the jointed nature of the material assembly
Precast concrete code requirements include detailing to add ductility and redundancy to allow comparison with (emulation of) monolithic cast-in-place concrete
Special moment frames constructed using precast concrete with emulation details include requirements beyond monolithic construction for bar splices
73 Seismic Design of Precast Concrete
Precast concrete designs that recognize certain benefits of the jointed nature of the construction are recognized by ACI 318, but are currently beyond the scope of the provisions.
Special moment-resisting frames using a hybrid system are covered under ACI 374.1-05 and TI.2-03.
Special precast concrete shear walls using unbonded post-tensioning are covered under ACI ITG 5.1 and ITG 5.2.
74 Questions
Title slide
The presentation will cover examples of application of the provisions for earthquake
design to precast concrete systems.
Precast Concrete Design -1
Overview slide:
Scope of the chapter: This chapter illustrates the seismic design of precast
concrete members using the NEHRP Recommended Provisions (referred to
herein as the Provisions) for buildings in several different seismic design
categories.
Scope of the presentation: The presentation does not repeat the text that
describes provisions or procedures, but instead is focused on design examples
which illustrate these points through the applications of those provisions.
Precast Concrete Design -2
Introduction slide 1: three slides cover the introduction of the chapter
In the introduction, a brief summary of the requirements for precast concrete
systems from the provisions is presented to set the context for the following design
examples. The first introductory slide describes the precast concrete systems that
must be used in increasingly severe seismic design categories. The terminology in
the provisions now characterizes relative seismic risk using seismic design
categories instead of seismic zones or the ACI terminology of low, moderate and
high seismic risk. The system descriptions link the ACI 318 provision detailing
requirements to the level of seismic risk.
This introductory slide also introduces limitations imposed on the level of average
effective prestressing stress for precast concrete systems that are prestressed.
The limitation is imposed because prestressing strand lacks the range of post-yield
ductility of mild steel reinforcement. Flexural stress that is sufficient to cause
cracking in highly prestressed concrete components may cause sudden and brittle
failure.
Precast Concrete Design -3
Introduction slide 2: three slides cover the introduction of the chapter
The second introductory slide covers precast concrete wall requirements in the
progression of severity of seismic risk.
Precast Concrete Design -4
Introduction slide 3: three slides cover the introduction of the chapter
The third introductory slide briefly describes the examples that will be covered in
the presentation. These diaphragm examples are related to content in Chapter 10
of P751 that covers the design of masonry wall buildings.
Precast Concrete Design -5
Horizontal diaphragms examples; 1st slide shows the floor plan that is used for the
example. The layout is the same used in Chapter 10, Sec. 10.2, which illustrates
the design of a five-story masonry residential building. The plan dimensions of the
floor are 152 ft x 72 ft. The interior portion of the plan includes walls spaced at 24 ft
in the transverse direction. The 40 ft bays at either end of the plan include walls
spaced at 24 ft in the longitudinal direction.
Precast Concrete Design -6
Horizontal diaphragms: slide gives four basic points on precast concrete
diaphragms including:
Definition
Precast construction types with or without cast-in-place concrete topping
Code criteria
The slide notes that there is an absence of specific criteria for diaphragm design
without concrete topping. In fact, ACI 318 lacks direct criteria for the design of
diaphragms in precast or cast-in-place concrete in regions of low or moderate
seismic risk (SDC A, B or C.) The provisions for precast concrete diaphragms in
ACI 318 are included in Chapter 21 only applicable to SDC D, E and F.
Precast Concrete Design -7
First slide to introduce the design of untopped precast diaphragms using hollow
core floor plank. The design is linked to the Chapter 10 masonry wall example for
SDC B using Birmingham., Alabama. The use of seismic acceleration parameters
for New York for SDC C differs from Chapter 10.
Precast Concrete Design -8
Weight used for the diaphragm design is given for floor and roof. The weight used
for the design of the diaphragm does not include the weight of walls parallel to the
direction of loading because the wall weight does not contribute to the inertial force
in the floor. That must be collected and distributed to the walls,
Precast Concrete Design -9
Equation 12.10-1 for the calculation of diaphragm design forces is provided in this
slide. Note that this equation is different from the equation for the vertical
distribution of base shear used for the design of the lateral force-resisting system.
That distribution must also be considered in the design of the diaphragm
Precast Concrete Design -10
The table with the values of the calculated diaphragm forces is given for the
Birmingham example.
Precast Concrete Design -11
The slide presents the calculation of the maximum and minimum limits for
diaphragm design forces. The maximum diaphragm design forces from the
provisions are significantly less than calculated by Eq. 12.10-1, and these governs
the design forces.
Precast Concrete Design -12
The load and reaction diagram from the example is shown to illustrate the support
provides by the walls to a continuous beam. The uniform diaphragm loads vary by
building segment because the transverse walls on the ends are included in the
distributed weights, but the supporting walls in the center section are not included in
the diaphragm load.
Precast Concrete Design -13
Based on the assumption that the diaphragm in this example is rigid, the reaction
forces on the four transverse walls are taken as equal. The slide shows the
calculation of the uniform lateral force in each section of the building based on the
diaphragm load for each section.
Precast Concrete Design -14
The plan view of the floor is repeated with the dimensions removed and the critical
regions for design identified with the numbered circles and arrows for reference to
detailed sections.
Precast Concrete Design -15
The slide bullet points describe the five critical regions shown in the previous slide.
These locations are used in the design example for the calculation of forces and to
illustrate the reinforcing detailing.
Precast Concrete Design -16
Calculations for joint forces at critical regions 1 and 2 are given. These calculations
follow simple principles of statics.
Precast Concrete Design -17
Calculation for joint forces at critical regions 3 and 4 (longitudinal) are given.
Precast Concrete Design -18
The slide repeats text from the Guide covering out-of-plane effects. Three slides are
included to show the requirements and calculations for out-of-plane forces at Joint
4. The first slide shows the calculation for minimum out-of-plane horizontal force.
Precast Concrete Design -19
The second slide for out-of-plane forces at joint 4 gives the calculations for
minimum masonry wall anchorage and minimum bearing wall anchorage
Precast Concrete Design -20
The third slide for Joint 4 illustrates the force calculation if the diaphragm is
considered flexible
Precast Concrete Design -21
Force calculations for Joint 5 are shown for longitudinal and transverse forces. The
transverse force effect is shear flow, calculated using VQ/I to determine the total
joint force.
Precast Concrete Design -22
The floor plan is shown with Joint 1 highlighted to identify the application of the
following calculations. This joint is the first interior transverse joint away from the
transverse wall between the outer and inner floor plates.
Precast Concrete Design -23
Calculations for Joint 1 reinforcement are provided. The design must provide
sufficient reinforcement for chord forces as well as shear friction connection forces.
The section of bars and placement is given. The selection of bars is given to satisfy
the steel area calculation.
Precast Concrete Design -24
Figures from the example that illustrate the placement of reinforcement are
provided in this slide. At the interior joint, two horizontal bars are place in the
grouted joint between the ends of plank and parallel with the support beam. In the
second figure, the flange of the plank is broken at he edge to open the edge core
and permit placement of #4 bars and grout in the core, filling the profile and joint to
the finished floor.
Precast Concrete Design -25
Floor plan with highlighting for joint 2 is shown to identify joint. This joint is the joint
between the outside diaphragm and the transverse wall between the outside and
inside floor plates.
Precast Concrete Design -26
Detail at Joint 2 is shown to show the placement of reinforcing in the masonry wall
an in an opened core of the hollow core plank. Note the detail shows diagonal bars
to transfer forces mostly in tension and compression rather than by dowel shear or
shear friction. The block just below the bearing in the masonry wall is a bond beam
with two #5 bars grouted in as part of the diaphragm reinforcement.
Precast Concrete Design -27
Floor plan is shown with Joint 4 highlighted. This joint is between the outside
diaphragm plank and the outside longitudinal wall,
Precast Concrete Design -28
Detail at Joint 4 is shown to illustrate the placement of reinforcing at the end of
plank and in the masonry walls for a dry system. The top flange in the end of the
hollow core plank is broken way to permit access to the cores so that the cores at
the end of the plank, the bearing space in the wall beyond the plank, and the bond
beam below the bearing of the plank can be reinforced and grouted.
Precast Concrete Design -29
The example for a topped precast floor is introduced with requirements of the
provisions for higher seismic design categories. The seismic force for this example
is compared to the SDC B example. Note also that it is the diaphragm force used
to determine the collector and transfer requirement, and not the distributed lateral
force used for the vertical elements of the lateral force-resisting system.
Precast Concrete Design -30
The floor plan showing walls and the diaphragm layout is shown for the SDC D
example. This is the same building layout used in the earlier examples but the joints
between the hollow core plank in the interior areas of the floor have been removed.
This reflects the presence of cast-in-place concrete topping with welded wire
reinforcement to carry diaphragm forces, so the location of these interior joints is
not a design consideration.
Precast Concrete Design -31
The detail along an edge of the hollow core plan with topping is shown to illustrate
the placement of reinforcement. (Calculation of diaphragm design forces follow the
same procedures used in the earlier example, and are not repeated due to limits in
time. Figures are provided to show the differences in reinforcement with the topped
system.) In this section, the flange above the outside core in the plan is broken
away to open the core to permit placement of the edge reinforcement. The cast-inplace
concrete topping covers the top flange and also fills the core void with the
reinforcing bars.
Precast Concrete Design -32
Two details at interior joints with topping are shown to illustrate the placement of
reinforcement. (Calculation of diaphragm design forces follow the same procedures
used in the earlier example, and are not repeated due to limits in time. Figures are
provided to show the differences in reinforcement with the topped system.) At the
interior support beam, the space between the ends of the hollow core plank has the
reinforcing bars. The cast-in-place concrete topping concrete fills this joint and fills
part of the ends of the hollow cores as it flows away from the joint. Sometimes
plastic or crumpled paper dams are stuffed into the cores to limit the flow of the
joint concrete beyond the end of the plank. At the wall support, the wall cores are
shown reinforced and grouted for the plank bearing. The space between the ends
of the plank is grouted and excess concrete flows into the cores. The topping
concrete with transverse reinforcement is above this. The upper level of masonry
wall is built above the floor toppping and is ties to the wall below with vertical
reinforcement.
Precast Concrete Design -33
Design example for intermediate precast walls in three-story office in Seismic
Design Category B. These walls can be used up to any height in Seismic Design
Categories B and C but are limited to 40 feet for Seismic Design Categories D, E,
and F.
ACI 318 Section 21.4.2 requires that yielding between wall panels or between wall
panels and the foundation be restricted to steel elements. However, the Provisions
are more specific in their means to accomplish the objective of providing reliable
post-elastic performance. Provisions Section 21.4.3 (ACI 318 Sec. 21.4.4) requires
that connections that are designed to yield be capable of maintaining 80 percent of
their design strength at the deformation induced by the design displacement.
Alternatively, they can use Type 2 mechanical splices.
This precast concrete building is a three-story office building (Occupancy
Category II) in southern New England on Site Class D soils. The structure utilizes
10-foot-wide by 18-inch-deep prestressed double tees (DTs) spanning 40 feet to
prestressed inverted tee beams for the floors and the roof. The DTs are to be
constructed using lightweight concrete. Each of the above-grade floors and the roof
are covered with a 2-inch-thick (minimum), normal-weight cast-in-place concrete
topping. The vertical seismic force-resisting system is to be constructed entirely of
precast concrete walls located around the stairs and elevator/mechanical shafts.
The only features illustrated in this example are the rational selection of the seismic
design parameters and the design of the reinforcement and connections of the
Precast Concrete Design -34
precast concrete shear walls.
The first slide shows the plan of the building. The plan is 150 ft long and 120 ft long with
interior stairs and interior elevator cores.
Precast Concrete Design -34
The precast walls are estimated to be 8 inches thick for building mass calculations.
These walls are normal-weight concrete with a 28-day compressive strength, f'c, of
5,000 psi. Reinforcing bars used at the ends of the walls and in welded connectors
are ASTM A706 (60 ksi yield strength). The concrete for the foundations and
below-grade walls has a 28-day compressive strength, f'c, of 4,000 psi.
Design example for intermediate precast walls in three-story office. Slide shows the
seismic parameters from the Table in the example.
Precast Concrete Design -35
The slide provides the description of the intent of design for the intermediate
precast concrete wall system. The design develops a ductile mechanism for energy
dissipation, and then designs other connection elements in the load path to remain
elastic.
Although it would be desirable to force yielding to occur in a significant portion of
the connections, it frequently is not possible to do so with common configurations of
precast elements and connections. The connections are often unavoidable weak
links. Careful attention to detail is required to assure adequate ductility in the
location of first yield and to preclude premature yielding of other connections.
Precast Concrete Design -36
Calculation of base shear from the equivalent lateral force equations of the
provisions is shown with the values determined in the example. Note that this force
is substantially larger than a design wind would be. If a nominal 20 psf were
applied to the long face and then amplified by a load factor of 1.6, the result would
be less than half this seismic force already reduced by an R factor of 4.
Precast Concrete Design -37
Vertical distribution of base shear is shown in the example calculations for the
entire structure.
The seismic lateral force ,Fx, at any level is determined in accordance with
Standard Section 12.8.3.
Since the period, T, is less than 0.5 seconds, k = l in both building directions. The
total lateral forces are calculated as:
Roof: Cvr = 0.50; Fr = 190 kips
Third Floor: Cv3 = 0.333; F3 = 127 kips
Second Floor: Cv2 = 0.167; F2 = 63 kips
Since torsion is assumed to be carried by the walls in the transverse direction, the
forces to each of two walls (as shown in the slide) in the direction under
consideration is half the total, and these are the forces illustrated in the figure.
Precast Concrete Design -38
The free-body diagram for one longitudinal wall is shown in Figure 8.2-4. The
tension connection at the base of the precast panel to the below-grade wall is
governed by the seismic overturning moment and the dead loads of the panel and
supported floors and roof. In this example, the weights for an elevator penthouse,
with a floor and equipment load at 180 psf between the shafts and a roof load at
20 psf, are included. The weight for the floors includes double tees, ceiling, and
partitions (total load of 70 psf) but not beams and columns. Floor live load is 50 psf,
except 100 psf is used in the elevator lobby. Roof snow load is 30 psf.
Precast Concrete Design -39
Calculation of tension reinforcing considering the gravity load effects, reduced by
.9-SDS is shown.
Precast Concrete Design -40
Design shear panels to resist overturning by means of reinforcing bars at each end
with a direct tension coupler at the joints.
The results of the calculation for overturning and selection of the end reinforcing is
covered on this slide.
Although the transverse direction walls are covered in the guide, they are not
covered here in the interest of time.
Precast Concrete Design -41
Notes on base shear design for the guide are covered here.
The joint opening would concentrate the shear stress on the small area of the dry-
packed joint that remains in compression. This distribution can be affected by the
shims used in construction. With care taken to detail the grouted joint, shear friction
can provide a reliable mechanism to resist this shear.
Precast Concrete Design -42
Base shear design is based 1.5 times the strength of the yielding connection in
accordance with the provisions.
Precast Concrete Design -43
The base shear connection is shown in the figure and is to be flexible vertically but
stiff horizontally in the plane of the panel. The vertical flexibility is intended to
minimize the contribution of these connections to overturning resistance, which
would simply increase the shear demand.
The figure illustrates a welded connection with an embedded plate with tail bars
developed in the wall and a foundation plate anchored with headed anchor studs.
The connection is made with two face plates, one on each side of the wall.
Precast Concrete Design -44
All of the links in the load path should be checked . The slide shows the
calculations for shear strength of the connection by checking this load path.
Precast Concrete Design -45
The bearing strength is considered in the load path, and the calculations for the
bearing strength limit of the connection are included.
Precast Concrete Design -46
Design for anchorage to concrete of the foundation embed plate is covered.
Precast Concrete Design -47
Shear connection design summary is given and the selection of the number of
connections is shown in this slide.
The total demand moment, for which the entire system is proportioned, is 5,320 ftkips.
Thus, these connections will add approximately 5 percent to the resistance,
and ignoring this contribution is reasonable. If a straight plate measuring 1/4 inch
by 8 inches (which would be sufficient) were used and if the welds and foundation
embedment did not fail first, the tensile capacity would be 72 kips each, a factor of
42 increase over the angles, and the shear connections would have the unintended
effect of more than doubling the flexural resistance, which would require a much
higher shear force to develop a plastic hinge at the wall base.
Precast Concrete Design -48
The design example is for a single story building with perimeter shear wall panels.
This example shows the design for intermediate precast concrete walls in SDC D.
The structure has 8-foot-wide by 12.5-inch-deep prestressed double tee (DT) wall
panels. The roof is light gage metal decking spanning to bar joists that are spaced
at 4 feet on center to match the location of the DT legs. The center supports for the
joists are joist girders spanning 40 feet to steel tube columns. The vertical seismic
force-resisting system is the precast/prestressed DT wall panels located around the
perimeter of the building. The average roof height is 20 feet, and there is a 3-foot
parapet.
The slide describes the precast building.
Precast Concrete Design -49
The figure shows a plan of the building. The building is 120 ft long and 96 ft wide.
The precast wall panels used in this building are typical DT wall panels commonly
found in many locations but not normally used in southern California. For these
wall panels, an extra 1/2 inch has been added to the thickness of the deck (flange).
This extra thickness is intended to reduce cracking of the flanges and provide cover
for the bars used in the deck at the base.
The wall panels are normal-weight concrete with a 28-day compressive strength of
f'c = 5,000 psi. Reinforcing bars used in the welded connections of the panels and
footings are ASTM A706 (60 ksi). The concrete for the foundations has a 28-day
compressive strength of f'c = 4,000 psi.
Precast Concrete Design -50
In Standard Table 12.2-1 the values for special reinforced concrete shear walls are
for both cast-in-place and precast walls. In Section 2.2, ACI 318 defines a special
structural wall as a cast-in-place or precast wall complying with the requirements of
21.1.3 through 21.1.7, 21.9 and 21.10, as applicable, in addition to the
requirements for ordinary reinforced concrete structural walls. ACI 318
Section 21.10 defines requirements for special structural walls constructed using
precast concrete, including that the wall must satisfy all of the requirements of ACI
318 Section 21.9.
Unfortunately, several of the requirements of ACI 318 Section 21.9 are problematic
for a shear wall system constructed using DT wall panels. Therefore, these walls
will be designed using the ACI category of intermediate precast structural walls.
Design parameter table for the example building using intermediate precast
concrete walls is given in the slide.
Precast Concrete Design -51
A summary of the requirements and design intent for intermediate precas.t concrete
shear walls is provided.
Yielding will develop in the dry connection at the base by bending in the horizontal
leg of the steel angle welded between the embedded plates of the DT and footing.
The horizontal leg of this angle is designed in a manner to resist the seismic
tension of the shear wall due to overturning and then yield and deform inelastically.
The connections on the two legs of the DT are each designed to resist 50 percent
of the shear. The anchorage of the connection into the concrete is designed to
satisfy the 1.5Sy requirements of ACI 318 Section 21.4.3. Careful attention to
structural details of these connections is required to ensure tension ductility and
resistance to large shear forces that are applied to the embedded plates in the DT
and footing.
Precast Concrete Design -52
Design assumptions and steps in calculation for lateral forces are listed:
The metal deck roof acts as a flexible horizontal diaphragm to distribute seismic
inertia forces to the walls parallel to the earthquake motion (Standard Sec.
12.3.1.1).
The building is regular both in plan and elevation.
The redundancy factor, ., is determined in accordance with Standard
Section 12.3.4.2. For this structure, which is regular and has more than two
perimeter wall panels (bays) on each side in each direction, .
= 1.0. The structural
analysis to be used is the ELF procedure (Standard Sec. 12.8) as permitted by
Standard Table 12.6-1.
Orthogonal load combinations are not required for flexible diaphragms in Seismic
Design Category D (Standard Sec. 12.5.4).
The basic load combinations (Standard Sec. 12.4.2.3) require that seismic forces
and gravity loads be combined in accordance with the following factored load
combinations:
(1.2 + 0.2SDS)D ± rQE + 0.5L+ 0.2S
(0.9 -0.2SDS)D ± rQE + 1.6H
Precast Concrete Design -53
At this flat site, both S and H equal 0. Note that roof live load need not be combined with
seismic loads, so the live load term, L, can be omitted from the equation. Therefore:
1.4D + rQE
0.7D -rQE
These load combinations are for the in-plane direction of the shear walls.
The earthquake force considerations are listed by bullet points due to the limited time for the
presentation. The detailed calculations can be found in the guide.
Precast Concrete Design -53
The total shear along each side of the building is V/2 = 46.75 kips. The maximum
shear on longitudinal panels (at the side with the openings) is:
Vlu = 46.75/11 = 4.25 kips
On each side, each longitudinal wall panel resists the same shear force as shown
in the free-body diagram of the figure, where D1 represents roof joist reactions and
D2 is the panel weight.
Precast Concrete Design -54
Base connection design yielding and design for overstrength of other connection
actions. The slide describes the connection and the actions considered.
Precast Concrete Design -55
Base connection tension from overturning moment and sustained gravity resistance
calculation is shown. Notes that 0.7D comes from the load combination (0.9-0.2SDS)
and 1.4 comes from (0.9+0.2SDS). These factors consider the vertical acceleration
effects.
Precast Concrete Design -56
The angle, which is the ductile element of the connection, is welded between the
plates embedded in the DT leg and the footing. This angle is an L5Χ3-1/2Χ3/4 Χ
0'-6-1/2" with the long leg vertical. The steel for the angle and embedded plates will
be ASTM A572, Grade 50. The horizontal leg of the angle needs to be long enough
to provide significant displacement at the roof, although this is not stated as a
requirement in either the Provisions or ACI 318. This will be examined briefly here.
The angle and its welds are shown in the figure.
Precast Concrete Design -57
Calculation of the bending in connection angle and tension resistance are shown in
the slide.
The calculation shows that the calculated strength is slightly less than the demand,
but providing a stronger angle (e.g., a shorter horizontal leg) will simply increase the
demands on the remainder of the assembly.
Precast Concrete Design -58
Using ACI 318 Section 21.4.3, the tension force for the remainder of this connection
and the balance of the wall design are based upon a probable strength equal to
150 percent of the yield strength.
Precast Concrete Design -59
The Provisions Section 21.4.4 (ACI 318 21.4.3) requires that connections that are
designed to yield be capable of maintaining 80 percent of their design strength at
the deformation induced by the design displacement. For yielding of a flat bar
(angle leg), this can be checked by calculating the ductility capacity of the bar and
comparing it to Cd. Note that the element ductility demand (to be calculated below
for the yielding angle) and the system ductility, Cd, are only equal if the balance of
the system is rigid. This is a reasonable assumption for the intermediate precast
structural wall system described in this example.
The idealized yield deformation of the angle is calculated as shown in the slide.
Precast Concrete Design -60
Weld design calculations are also based on providing the overstrength required.
Precast Concrete Design -61
Weld design calculations, continued. The displacement from plastic hinge rotation
is compared to yield deflection to determine the ductility of the connection
compared to the design displacement amplification factor.
Precast Concrete Design -62
Base connection detail from the design calculations. The figure shows anchorage of
the plate embedded in the double tee to include bars that project into the stem for
development.
Although the design examples continues with overstrength design of the precast
panel, the requirements for overstrength design of the provisions are limited to the
non-yielding elements of connections.
Precast Concrete Design -63
Introduction to review of special moment frames constructed using precast concrete
construction. This method is considered emulation of monolithic cast-in-place
concrete.
Precast Concrete Design -64
Description of requirements for ductile connections form the text is provided.
Precast Concrete Design -65
Figure showing offset of Type 2 splice from face of column for ductile connection
design. The figure shows a space between the end of the precast beam and the
face of the precast column that permits the offset of the splice to meet the distance
of h/2 from the face of the support. This space would be filled with cast-in-place
concrete to complete the joint.
Precast Concrete Design -66
Description and figure for strong connections with ductile region offset from face of
column. The figure shows splice couplers at the face of the column, but the
reinforcing must be proportioned to ensure sufficient strength in the region of the
splice so that yielding occurs in the beam beyond the ends.
Precast Concrete Design -67
Calculation of moment strength of beam in frame example
Precast Concrete Design -68
Calculation of the probable moment strength of beam joint in frame example is
shown in the slide.
Precast Concrete Design -69
Calculation of moment strength for strong connection of beam in frame example is
shown.
If column-to-column connections are required, ACI 318 Section 21.8.3(d) requires a
1.4 amplification factor, in addition to loads associated with the development of the
plastic hinge in the beam. Locating the column splice near the point of inflection,
while difficult for construction, can help to make these forces manageable.
Precast Concrete Design -70
This is a slide provided as a summary of the examples covered in the presentation.
Precast Concrete Design -71
A summary slide on the general considerations for the seismic design of precast
concrete structural systems.
Precast Concrete Design -72
A slide to recognize that precast systems based on jointed behavior rather than
emulation of monolithic cast-in-place concrete can also be used, but these are
beyond the scope of the provision.
Precast Concrete Design -73
This slide is a placeholder for opening the floor up to questions
Precast Concrete Design -74