LA LICITACIÓN PÚBLICA
IV.1 EL PROCEDIMIENTO DE LICTACIÓN PÚBLICA
The first step was to calculate the load-carrying capacity of the critically damaged AB-14A beam that provided support to heavy equipment in the fan room above (Figure 3.11). The structural assembly consists of a 7-in reinforced-concrete floor slab supported by beam AB-64, 18⫻30 in. spanning north–south. The entire structural system, in turn, rests on two beams of approximately 64 ft span: AB-14A on the north side and AB-16A on the south side. Of the two, AB-14A was the weakest even though it carried about the same load:
Concrete strength:ƒ⬘c ⫽ 4000 psi
Reinforcing steel: Grade 60, ƒy⫽ 60,000 psi We used ACI and UBC recommendations:
Tributary width for
3.5 CASE 1: REINFORCED-CONCRETE PARKING GARAGE 55
Figure 3.11 Cracks in AB-14A beam that supported the fan room and other electrical equipment on the floor above.
Housekeeping concrete pads to mount fans, 4 in.
high, acting on only half of the beam span at B
⫽ 0.56 k / ft 2(10 ⫻ 6)(0.33)(150)1000 冉 冊321
Converting the 0.56 k / ft into a uniformly distributed load over the span yields
0.56(32.0 ft)
wpad⫽ ⫽0.28 k / ft 64.0 ft
The factored dead load is
wD⫽1.4(2.61 ⫹ 0.28⫹ 0.05 (metal studs, lath, and plaster)
⫽4.116 k / ft say 4.12 k / ft
The shearing resistance of the beam at the support is determined as follows:
56 REINFORCED-CONCRETE STRUCTURES
#4 stirrups @ 6 in. OC for 6 ft, 0 in.
2兹4000(26)(42 ⫺5.4)
Vc⫽ ⫽ 120.37 k
1000 (0.4)(60)36.6
Vs ⫽ ⫽ 146.40 k
6
266.77 k The shearing resistance at the support (span 63.83 ft) is
0.85(266.77)⫽ 226.75 k
The equipment only occupies the west side of BM (from the centerline to B).
The weight of the equipment as obtained from the architect’s report is as follows:
Fans 5.3 k each
Duct work
350 lb⫹ 130 ⫹ 90 / 100⫽ 285 lb ⫽ 0.3 k each Factored loads 5.6 k each 1.7⫻ 5.6 ⫽ 9.52 k Electric transformer 4.0 k 1.7(4.0)⫽ 6.8 k⫽ 6.80 k Floor mounted 5-kV load interruptor
switch 1.35 k 1.7(1.35) ⫽ 2.3 k⫽ 2.30 k
Floor-mounted switchboard 1.20 k 1.7(1.20) ⫽ 2.00 k⫽ 2.0 k 2.3(38.83)⫹6.8(43.25)⫹ 2.0(43.83)⫹ 9.52(51.83⫹ 57.83) VBequip.⫽
63.83
⫽ 23.73 k 63.83
VBD⫹equip.⫽ 冉 冊2 (4.12)⫹23.73 ⫽155 k
Reaction of factored DL at B DL⫹ equipment⫹ 75 psf
LL (UBC Table 23-A, item 29, light) The factored live load is
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3.5 CASE 1: REINFORCED-CONCRETE PARKING GARAGE 57
wL⫽ 0.075 (28.84 / 2)(1.7)⫽ 1.84 k / ft The maximum shear at B due to wD⫹ wequip ⫹ wL is
VBmax ⫽(4.12 ⫹ 1.84) 63.83 / 2⫹ 23.73⫽ 214 k⬍ 226.75 Original shear resistance OK for static load.
The AB-14A beam that supported the fan room and equipment on the floor above had pulled away from the concrete pilaster support at B5. A wide crack approximately 85% of the entire height and the full width of the beam separated the beam from the pilaster. Only four #11 top reinforcement held the beam in shear friction (Figures 3.12 and 3.13). There was widespread moisture throughout the structure and rust-ing of rebars in the two major beams AB-14A and AB-16A. To deter-mine the shear friction resistance of AB-14A we assumed that 50% of the cross section was impaired by rust and 50% of the reinforcement area was still providing some resistance.
ƒ⬘ ⫽c 4000 psi, grade 60
Avƒ ⫽(0.50)(4)(1.56) ⫽3.12 in.2
From the shear friction equation UBC (11.26)
Vn⫽ A ƒvƒ y ⫽3.12(60)(1.0)⫽187.2 k ⬍ 214 k
⫽1.4, ⫽ 1.0 normal weight factored reaction of equipment⫹ DL ⫹ LL.
where
⫽ 1.4 ⫽ 1.4(I) for monolithically cast stone concrete.
Therefore there is not enough resistance based on the embedment along the top of the beam.
Actual Bond Provided for Hook of #11 Bars into B4 Required:
1200db
L ⫽ ⫽26.75 in.
58 REINFORCED-CONCRETE STRUCTURES
Figure 3.12 Close-up of earthquake-caused cracks in RC beams. One of the beams separated from the concrete pilaster support and was held in friction by four #11 reinforcement.
Provided: 17 in. (per original engineering drawings, March 1968).
17 in. ⬍ 26.75 in. This is not enough.
The resistance of the hook end of the bars is
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3.5 CASE 1: REINFORCED-CONCRETE PARKING GARAGE 59
Figure 3.13 AB-14A beam and pilaster configuration.
17 / 26.75 (187.2)⫽ 119.0 k GOVERNS
just slightly over the unfactored maximum support shear of its own weight and equipment load (110.7 k).
There is not enough safety in shear.
Precast Lightweight Concrete Beam, 63.83-ft Span
We first determined the maximum factored shear and the shearing ca-pacity of the beam at supports:
ƒ⬘ ⫽c 4000 psi Beams 19.0 ft apart ƒy⫽ 60,000 psi
Two bottom bars are available for shear friction. Pretensioned tendons would not help in shear friction since they do not extend to provide support and do not build up adequate bond and compressive strength near the end.
The factored DL⫹ LL on the beam is as follows:
19-ft-wide, 7-in.-thick lightweight concrete slab
(7 / 12)0.11(19.0)⫽ 1.22 k / ft Weight of 12 in. ⫻ 2.5 ft lightweight
concrete beam
(1.0)2.5(0.11)⫽ 0.275 k / ft 1.495 k / ft wD⫽1.495 ⫻1.4 ⫽2.10 k / ft
The live load using UBC is determined as follows:
60 REINFORCED-CONCRETE STRUCTURES
Figure 3.14
D 1.495
R⫽23.1 1冉 冊 冉⫹ L ⫽ 23.1 1⫹ 19(0.05)冊⫽ 59.45% GOVERNS or
R⫽ r (A⫺ 150)⫽ 冋冉 冊 册63.8319.0 ⫺ 150 ⫻ 0.08⫽ 85%
Reduction formulas 0.5945(50)⫻ 19.0
wL⫽ ⫽ 0.5648 k / ft
1000
wL,ult⫽ 0.96 k / ft Factored live load wDu⫹ wLu⫽ 2.10⫹ 0.96⫽ 3.06 k / ft
The maximum factored shear at B (Figure 3.14) is
3.06(63.83 / 2 ⫺2.7) ⫽ 90.0 k applied static shear
We then apply UBC shear friction formula (11-27) assuming a 20%
failure plane with the vertical.
Contribution of the two #7 horizontal reinforcements:
Vn⫽ A ƒ [(1.4vƒ y sin␣1) ⫹cos ␣1]
⫽ 2(0.6)60[1.4(0.85)⫹0.34] ⫽ 33.12 k Contribution of #4 at 9-in.-OC vertical stirrups:
Vn,stirrups⫽ 3(2)(0.2)(60)(1.19⫻0.34 ⫹0.94) ⫽ 96.8 k
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3.5 CASE 1: REINFORCED-CONCRETE PARKING GARAGE 61
Combined shear resistance:
Vu ⫽ Vn⫽ 0.85(33.12⫹96.8) ⫽ 110.4 k⬎ 90.0 k or 13% over OK
Corbel Supporting T-1 Precast Beam
Now we calculate the shearing resistance of the corbel. The available Avƒ for bars crossing the potential crack at the face of the support is
Avƒ⫽ 3(0.6)⫽ 1.81 in.2
Vu⫽ A ƒvƒ y ⫽ 0.85(1.8)(60)1.4⫽ 128.5 k ⬎102.35 k However, a minimum of 0.2Vu tensile force due to shrinkage must be applied (ACI 11.9.34), resulting in a loss in steel area:
0.2(128.5) 2
An ⫽ ⫽0.428 in.
60
The effective reinforcement available for shear friction is determined as 1.8⫺ 0.43⫽ 1.37 in.2
Vu,corrected (ACI)⫽ 0.85(1.37)(60)(1.4)⫽ 98.0 k ⬇102.35 k applied No significant extra safety in corbel. OK for static load.
The fact that some of the corbels cracked leads to the conclusion that the dynamic impact of the earthquake produced much larger reactions than estimated by purely static analysis.