## 13

tension tie 3-2 = 198,286 x — = 166,304 lb (699 kN)

Use the larger of the two values for choice of the closed tension tie stirrups. Try No. 3 closed ties, giving a tensile strength per tie = ffyAv = 0.90 x 60,000 x 2(0.11) = 11,880 lb r . . 188,054

required number of stirrup ties =-=15.8

H 11,880

For the tension tie a-b-c in Figure 8.5, use the force Pu = 166,304 lb to concentrate additional No. 4 vertical ties ahead of the anchorage devices. Start the first tie at a distance of 11 in. from the end rigid steel plate transferring the load from the anchorage devices to the concrete

166,304

Use eight No. 4 closed ties @ 11 in. (12.7 mm @ 32 mm) center to center with the first tie to start at 11 in. ahead of the anchorage devices.

Only 13 ties in lieu of the 15.0 calculated are needed since part of the zone is covered by the No. 4 ties. Use 13 No. 3 closed ties @ 2^ in. (9.5 mm @ 57 mm) center to center beyond the last No. 4 tie so that a total distance of 40 in. (104 cm) width of the rectangular anchor block is confined by the reinforcement closed ties. Adopt this design of the anchorage zone.

It should also be noted that the idealized paths of the compression struts for cases where there are several layers of prestressing strands should be such that at each layer level a stress path is assumed in the design.

8.6.6 Ultimate-Strength Flexural Design 8.6.6.1 Cracking-Load Moment

One of the fundamental differences between prestressed and reinforced concrete is the continuous shift in the prestressed beams of the compressive C-line away from the tensile cgs line as the load increases. In other words, the moment arm of the internal couple continues to increase with the load without any appreciable change in the stress fpe in the prestressing steel. As the flexural moment continues to increase when the full superimposed dead load and live load act, a loading stage is reached where the concrete compressive stress at the bottom-fibers reinforcement level of a simply supported beam becomes zero.

This stage of stress is called the limit state of decompression. Any additional external load or overload results in cracking at the bottom face, where the modulus of rupture of concrete fr is reached due to the cracking moment Mcr caused by the first cracking load. At this stage, a sudden increase in the steel stress takes place and the tension is dynamically transferred from the concrete to the steel. It is important to evaluate the first cracking load, since the section stiffness is reduced and hence an increase in deflection has to be considered. Also, the crack width has to be controlled in order to prevent reinforcement corrosion or leakage in liquid containers.

The concrete fiber stress at the tension face is fb = -£(1 + ") +f=f- <834)

where the modulus of rupture fr = 7.5yf and the cracking moment Mcr is the moment due to all loads at that load level (MD + MSD + ML). From Equation 8.34

8.6.6.2 ACI Load Factors Equations

The ACI 318 Building Code for concrete structures is an international code. As such, it has to conform to the International Building Codes, IBC 2000 and IBC 2003 [10] and be consistent with the ASCE-7 Standard on Minimum Design Loads for Buildings and Other Structures. The effect of one or more loads not acting simultaneously has to be investigated. Structures are seldom subjected to dead and live loads alone. The following equations present combinations of loads for situations in which wind, earthquake, or lateral pressures due to earthfill or fluids should be considered:

U = |
1.4(D + F ) |
(8.36a) |

U = |
1.2(D + F + T) + 1.6(L + H) + 0.5(1, or S or R) |
(8.36b) |

U = |
1.2D + 1.6(Lr or S or R) + (1.0L or 0.8 W) |
(8.36c) |

U = |
1.2D + 1.6W + 0.5L + 1.0(L, or S or R) |
(8.36d) |

U = |
1.2D + 1.0E + 1.0L + 0.2S |
(8.36e) |

U = |
0.9D + 1.6 W + 1.6H |
(8.36f ) |

U = |
0.9D + 1.0E + 1.6H |
(8.36g) |

where D is the dead load, E is the earthquake load, F is the lateral fluid pressure load and maximum height; H is the load due to the weight and lateral pressure of soil and water in soil; L is the live load, Lr is the roof load, R is the rain load, S is the snow load; T is the self-straining force such as creep, shrinkage, and temperature effects; and W is the wind load.

It should be noted that the philosophy used for combining the various load components for earthquake loading is essentially similar to that used for wing loading.

8.6.6.2.1 Exceptions to the Values in These Expressions

1. The load factor on L in Equations 8.36c to 8.36e is allowed to be reduced to 0.5 except for garages, areas occupied as places of public assembly, and all areas where the live load L is greater than 100 lb/ft2.

2. Where wind load Whas not been reduced by a directionality factor, the code permits to use 1.3 W in place of 1.6Win Equations 8.36d and 8.36f.

3. Where earthquake load E is based on service-level seismic forces, 1.4E shall be used in place of 1.0E in Equations 8.36e and 8.36g.

4. The load factor on H is to be set equal to zero in Equations 8.36f and 8.36g if the structural action due to H counteracts that due to W or E. Where lateral earth pressure provides resistance to structural actions from other forces, it should not be included in H but shall be included in the design resistance.

Due regard has to be given to sign in determining U for combinations of loadings, as one type of loading may produce effects of opposite sense to that produced by another type. The load combinations with 0.9D are specifically included for the case where a higher dead load reduces the effects of other loads.

8.6.6.3 Design Strength versus Nominal Strength: Strength-Reduction Factor 0

The strength of a particular structural unit calculated using the current established procedures is termed nominal strength. For example, in the case of a beam, the resisting moment capacity of the section calculated using the equations of equilibrium and the properties of concrete and steel is called the nominal strength moment Mn of the section. This nominal strength is reduced using a strength reduction factor f to account for inaccuracies in construction, such as in the dimensions or position of reinforcement or variations in properties. The reduced strength of the member is defined as the design strength of the member.

For a beam, the design moment strength f Mn should be at least equal to, or slightly greater than the external factored moment Mu for the worst condition of factored load U. The factor f varies for the

PHOTO 8.4 Paramount Apartments, San Francisco, CA: completed in 2002, it is the first hybrid precast prestressed concrete moment-resistant 39 floor high-rise frame building in a high seismicity zone. Based on tests of large-scale prototype of the moment-resisting connections, it was determined that the performance of the system was superior to cast-in-place concrete, both in cracking behavior and ductility. Hence, as a system, this new development succeeds in enhancing the performance of high-rise buildings and bridges in high seismicity earthquake zones. Since completion of this structure, several other buildings in California have been completed using the same principles (courtesy Charles Pankow Ltd, Design/Build contractors. Structural Engineers: Robert Englekirk Inc.).

PHOTO 8.4 Paramount Apartments, San Francisco, CA: completed in 2002, it is the first hybrid precast prestressed concrete moment-resistant 39 floor high-rise frame building in a high seismicity zone. Based on tests of large-scale prototype of the moment-resisting connections, it was determined that the performance of the system was superior to cast-in-place concrete, both in cracking behavior and ductility. Hence, as a system, this new development succeeds in enhancing the performance of high-rise buildings and bridges in high seismicity earthquake zones. Since completion of this structure, several other buildings in California have been completed using the same principles (courtesy Charles Pankow Ltd, Design/Build contractors. Structural Engineers: Robert Englekirk Inc.).

different types of behavior and for the different types of structural elements. For beams in flexure, for instance, f is 0.9.

For tied columns that carry dominant compressive loads, the factor f equals 0.65. The smaller strength-reduction factor used for columns is due to the structural importance of the columns in supporting the total structure compared to other members, and to guard against progressive collapse and brittle failure with no advance warning of collapse. Beams, on the other hand, are designed to undergo excessive deflections before failure. Hence, the inherent capability of the beam for advanced warning of failure permits the use of a higher strength reduction factor or resistance factor. Table 8.10 summarizes the resistance factors f for various structural elements as given in the ACI code.

TABLE 8.10 Resistance or Strength Reduction Factor f Structural element

### Factor f

Beam or slab: bending or flexurea Columns with ties Columns with spirals Columns carrying very small axial loads (refer to Chapter 5 for more details) Beam: shear and torsionb

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