PARTE III. RESULTADOS Y DISCUSIÓN
CAPÍTULO 7. GUÍAS DE ONDA ÓPTICAS EN LiTaO 3
7.5. C APA AMORFA EN LiTaO 3 : IRRADIACIONES CON IONES DE BROMO
2. Equivalent frame model: Shear and flexure in the slab beyond the width of the column are 2
assumed to be transferred to the column through torsional elements perpendicular to the 3
slab span direction (Vanderbilt and Corley 1983). Flexibility of the torsional elements reduces 4
the elastic stiffness of the overall frame. Although it is possible to model them separately, 5
torsional elements are typically lumped with columns or the slab to produce a frame with 6
equivalent stiffness (Chapter 8 of ACI 318); and 7
3. Finite element model: The slab distortion is modeled explicitly using finite elements.
8
Each approach is considered acceptable for analytical modeling of slab–column frames.
9
Research has shown that the effective beam approach tends to overestimate lateral stiffness, 10
whereas the equivalent frame approach tends to underestimate lateral stiffness of slab–column 11
systems responding in the elastic range (Hwang and Moehle 2000). For either approach, the 12
elastic stiffness should be reduced further to account for cracking in slab–column systems 13
responding in the inelastic range (Luo et al. 1994, Hwang and Moehle 2000, and Dovich and Wight 14
2005).
15 16
4.4.2 Stiffness of Slab–Column Moment Frames 17
4.4.2.1 Linear Static and Dynamic Procedures―Slabs shall be modeled considering flexural, 18
shear, and torsional (in the slab adjacent to the column) stiffnesses. Columns shall be modeled 19
considering flexural, shear, and axial stiffnesses. Slab–column connections shall be modeled as 20
stiff or rigid components. Although effective component stiffnesses shall be determined according 21
to the general principles of Section 3.1.2, adjustments shall be permitted based on experimental 22
evidence.
1 2
C4.4.2.1 Linear Static and Dynamic Procedures―
3
1. Effective beam width model: Allen and Darvall (1977) provide tables of effective width 4
coefficients for different combinations of plate aspect ratios (l1/l2) and column width‐to‐slab 5
span ratios (c1/l1 or c2/l1). Research indicates that the effective width of exterior bays should 6
be less than the effective width of interior bays because of the higher flexibility of one‐sided 7
slab–column connections at the frame end. Hwang and Moehle (2000) provide equations for 8
effective width that show the relationship between exterior and interior bays is about 1/2.
9
Eq. (C2) can be used instead of tables from Allen and Darvall (1977).
10
For interior bays: beff 2c l1 1/ 3 (C2a) 11
For exterior bays: beff c l1 1/ 6 (C2b) 12
where beff is the effective slab width.
13
To account for cracking from temperature, shrinkage, or nonlinear response, slab stiffness 14
determined using gross section properties based on the above guidance should be reduced 15
by an effective stiffness factor
eff . There is general agreement that
eff 1/ 3 is 16appropriate for nonprestressed slabs (Vanderbilt and Corley 1983). Somewhat higher, yet 17
conservative, values can be obtained using Eq. (C3) from Hwang and Moehle (2000):
18
eff 4 /c l1 11/ 3 (C3) 19For prestressed post‐tensioned slabs, it is generally agreed that higher values of
eff are20
appropriate (
eff 1/ 2) because of reduced cracking caused by prestressing (Kang and 1Wallace 2005).
2
2. Equivalent frame model: Column, slab–beam, and torsional connection element properties 3
for the equivalent frame model are defined in Chapter 8 of ACI 318. To account for cracking 4
caused by temperature, shrinkage, or nonlinear response, the stiffness of the torsional 5
connection element based on gross section properties defined in ACI 318 should be 6
multiplied by a factor of 1/3.
7 8
4.4.2.2 Nonlinear Static Procedure―Nonlinear load-deformation relations shall comply with the 9
requirements of Section 3.1.2. Nonlinear modeling parameters for slab–column connections are 10
provided in Table 15.
11
Nonlinear static models shall be capable of representing inelastic response along the component 12
length, except where it is shown by equilibrium that yielding is restricted to the component ends.
13
Idealized load-deformation relations shall be modeled using the generalized relation shown in 14
Fig. 1. The overall load-deformation relation shall be established so that the maximum resistance 15
is consistent with the strength specifications of Sections 3.2 and 4.4.3. For columns, the 16
generalized deformation shown in Fig. 1 is flexural plastic hinge rotation with parameters as 17
defined in Table 8 and Table 9. For slabs and slab–column connections, the generalized 18
deformation shown in Fig. 1 is plastic rotation with parameters as defined in Table 15. Different 19
relations shall be permitted where verified by experimentally obtained cyclic response relations of 20
slab–column subassemblies.
21 22
C4.4.2.2 Nonlinear Static Procedure―The values provided in Table 15 are used to assess 1
punching failures at slab–column connections. Elwood et al. (2007) provide a comparison of the 2
modeling parameters in Table 15 and test data summarized by Kang and Wallace (2006). Lateral 3
drift ratio is typically reported for test data; therefore, plastic rotations were derived from the test 4
data assuming column deformations were negligible and yield rotations of 0.01 and 0.015 radians 5
for reinforced concrete and post‐tensioned slabs, respectively. The larger rotation value for post‐
6
tensioned connections reflects the larger span‐to‐slab thickness ratios common for this type of 7
construction. Continuity reinforcement for reinforced concrete connections is based on Joint ACI‐
8
ASCE Committee 352 recommendations (ACI 352R).
9
Plastic rotation values are approximately mean and mean minus one standard deviation values 10
for connections with and without continuity reinforcement, respectively. Mean minus one 11
standard deviation values give total (yield plus plastic) rotation values that are close to the 12
maximum drift values allowed by ACI 318 Section 18.14.5.1, without the use of slab shear 13
reinforcement. Few data exist for reinforced concrete connections subjected to gravity shear 14
ratios greater than 0.6 and for post‐tensioned connections subjected to reverse cyclic loading. The 15
residual strength capacity for post‐tensioned connections is based on test results reported by 16
Qaisrani (1993). Although relatively few tests have been reported for edge connections, the 17
limited data available suggest that the relationship between rotation and gravity shear ratio for 18
exterior connections is similar to the trend for interior connections.
19
Modeling of slab–column connections is commonly accomplished using beam elements to 20
represent the slab and a rigid‐plastic torsional member to represent moment and shear transfer 21
at the connection between slab and column (Fig. C2) (Elwood et al. 2007). If the punching capacity 22
of the slab–column connection is insufficient to develop the nominal capacity for the developed