Aguirre Carlos
Department of Civil Engineering, Universidad Santa María, Chile. [email protected]
ABSTRACT
Shear Lugs are frequently used in seismic areas where large lateral forces have to be transferred to the foundations. It is normally assumed that there are two controlling limits states for a shear lug: the bearing strength of concrete and the flexural yielding strength of the steel. Tests results performed during the last three years at Santa Maria University’s Laboratory show that the steel failure normally occur in shear yielding and this failure mode is more ductile than concrete bearing failure. In this paper, some typical steel building subjected to selected ground motion records was studied. It was found that ductile shear lugs have a slight isolation effect but it has no influence in the global performance of the buildings.
1. INTRODUCTION
Shear lugs are frequently used when large lateral forces occur, especially in structures built in seismic areas. Several types of steel shapes can be used as shear lugs; Fig. 1 illustrates a Cross type shear lug, it has to provide strength in any direction of the horizontal loads. Present codes design is based on methodologies coming from the engineering experience and some basic theoretical principles. There are only a few studies related to shear lugs design. This research work is a continuation of a research program developed at Santa Maria University. The first part of this program included the experimental testing of different type of shear lugs cross sections (Aguirre C and Palma I, 2009). The geometry of tested specimens is shown in Table 1, some of them were selected to produce failure in the steel and some others to produce the concrete failure. Fig.1 shows a detail of the cross type shear lug.
Figure 1. Cross Type Shear Lug
The first group of specimens (N° 1 up to N° 12) are cross steel shapes, the second group (N°13 up to N°20) are W steel shapes with the load applied on the strong axis, the third group (N°21 up to N°26) are W shapes too but the load is applied on the weak axis and finally Specimens N°10, 11 and 12 were extra samples, made with higher grout thicknesses, to evaluate the influence of the grout thicknesses on the results. The failure of a shear lug can happen either in the steel lug or in the surrounding concrete. Tests results demonstrate that the steel failure is shear yielding type and concrete failure is bearing type, Fig. 2 shows one of the samples tested. In a difference with the current design practice based on AISC N° 1 Design Guide (2010), the testing program demonstrated that the steel failure is normally a shear yielding type. The flexural yielding steel failure never occurs
Figure 2. Cross type shear lug Table 1. Specimens Geometry
1.- Cross type shear lug
Test W H t G Nº (mm) (mm) (mm) (mm) 1 100 100 5 8 2 100 75 5 8 3 100 50 5 8 4 100 100 8 11 5 100 75 8 11 6 100 100 12 15 7 100 75 12 15 8 100 50 12 15 9 100 100 19 20 10 140 140 5 40 11 140 140 8 40 12 140 140 12 40
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 251 252 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
2.- W type shear lug-Strong Axis
Test W H S t G Nº (mm) (mm) (mm) (mm) (mm) 13 100 100 90 5 15 14 100 50 90 5 15 15 100 75 225 3 15 16 100 75 75 3 15 17 100 75 75 19 15 18 100 75 225 19 15 19 150 130 130 3 15 20 150 130 130 6 15 21 100 100 90 5 15 22 100 50 90 5 15 23 100 75 75 3 15 24 100 75 150 19 15
3.- W type shear lug-Weak Axis
Test W H S t G
Nº (mm) (mm) (mm) (mm) (mm)
25 100 75 75 19 15 26 100 100 90 19 15
4.- O type shear lug
Test D H t G
Nº (mm) (mm) (mm) (mm)
29 114.3 100 6.02 15 30 114.3 75 6.02 15
The dotted red line on the picture emphasizes the shape of a typical shear deflection, which normally happens in short members. It suggests that shear lug strength can be obtained by using the shear capacity of the steel shape, expressed by equation (1).
steel y shear
V = 0.6 F ·A (1)
2. DESIGN APPROACH
Shear Lug Design use to be done by applying either AISC N° 1 Design Guide (2010) or ACI 349-01 Code (2001), both of them assume two possible controlling limit states:
• Bearing of Concrete
• Flexural Yielding of the Steel
AISC Steel Design Guide N°1, accepts both ASD and LRFD design methods. When ASD design method is used, it is assumed for the bearing stress of concrete a safe value of 0.35·f’c (unconfined concrete). For LRFD design method a 0.85·ϕc·f`c is
assumed as a nominal bearing stress. The dimensions of shear lugs must provide enough bearing area between the shear lug and concrete to fulfil the concrete limit state (without considering the grout), as it is shown on Table 1. The shear lug is assumed a steel plate behaving as a cantilever beam. The design is based on the maximum moment (Mlg) at the base. The shear lug thickness is obtained considering
the steel plate moment strength, according to Table 2 and figure 2. Table 1. Required bearing area
DESIGN METHOD
ASD LRFD
Table 2. Shear lug thickness. DESIGN METHOD
ASD LRFD
Figure 2 - Load and deflection of the Shear lug
ACI 349-01 Code states that design compression stress, either for concrete or grout, shall not exceed 1.3⋅φ⋅f’c (LRFD method), and φ reduction is 0.70. A comparison
of ACI and AISC nominal stress is shown in Table 3. It can be seen that ACI nominal stress is 78% larger than AISC nominal stress, that means ACI proposal for the concrete bearing pressure is less conservative than AISC-Guide N°1. In spite of this approach ACI produces safe designs of the lugs. It seems that there is no reason for a more conservative approach.
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 253 254 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
Table 3. ACI-349 and AISC-Guide N°1 comparison Nominal stress (LRFD)
ACI 349-01
Nominal stress (LRFD) Guide N°1, AISC σnom=1.3·φ·f’c=0.91·f’c σnom=0.85·ϕc·f’c=0.51·f’c
Both approaches are based on Rotz and Reifschneider (1989) research work, who studied the behavior of the plates under a combination of shear and axial load, in tension and compression. The results of their tests presented a prime and first failure type denominated “bearing mode”, related to concrete compression bearing capacity. The “bearing mode” is associated to the formation of shallow fracture plane on the top surface of the specimen, a fast increase of horizontal and vertical displacement, and a fast reduction of the shear load strength. From this study, expression (2) for the shear capacity was proposed.
concrete b c lg c y a
V =K f´ A + K (P - P ) (2)
The first term of the equation is the typical compression strength of concrete; the second term is the concrete confinement effect on the base plate produced by the anchor bolts, it increases the strength capacity. Kb and Kc are parameters empirically
obtained.
Figure 3. Rotz tests results
In order to understand the predominant failure mode of the steel, the chart on Figure 3 was prepared. It is a comparison of Rotz tests results and the calculated strengths of the shear lug. Vreal is the test result, Vbend was determined assuming
the lug behaves as a cantilever beam clamped at the base plate, who yield in bending. Vshear was obtained assuming a shear yielding failure (Equation 1). It can be seen
that the steel flexural yielding was the smallest strength in most of the cases (92%),
which means that the shear lugs should have been failed into this first mode. But the failure mode reported by the authors is the bearing of concrete, which according to Fig. 3 exhibit a larger strength than the flexural yielding mode in almost all of the tests. In other words concrete bearing was the typical failure mode in spite of its strength is larger than the flexural steel yielding strength. On the other hand, the shear steel yielding mode has the highest strength; such a result agrees well with Rotz’s tests failures in concrete bearing.
Fig. 4 is a comparison of concrete and steel failure modes obtained from tests results. It can be seen the higher ductility level of shear yielding of the steel compare to the concrete bearing failure mode. From the standpoint of the earthquake engineering larger ductilities are advantageous, but the difficulty to replace a shear lug after a severe earthquake, have to be considered in any design approach.
Fig. 4. Comparison of typical steel shear yielding failure and concrete bearing failure for cross section
3. NON LINEAR BUILDING ANALYSIS
In order to study the influence of the shear lug ductility in the seismic behaviour of buildings, a set of steel frame buildings was chosen and analyzed under the action of some selected ground motion records occurred during the last 30 years. The goal was to determine whether the shear lug ductility reduces or increases the structural damage of the buildings and to explore the possibility of using the lug properties to get safer and more economic structures.
Figure 5 shows a sketch of a typical building, the number of stories selected was 4, 8, 12 and 16; the plan is the same for all of them. The ground motions records selected are presented in Table 4. The building analyses were performed under two assumptions: (1) the columns are fixed to the base and (2) the columns are connected to the base through a non linear shear lug. The non linear properties were obtained from the experimental tests results (Palma, I., 2008).
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 255 256 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 4. 5 7.32 7.32 7.32 7.32 3 3 3 (a) Elevation 7.32 7.32 7.32 7.32 7.32 7.32 7.32 D C B A 1 2 3 4 5 (b) Plan
Figure 5. Plan and Elevation of the selected buildings
Shear lug design was performed according two approaches: (1) AISC Design Guide N° 1 (AISC, 2010) assuming that the limit state that for the lug design is the yielding in flexure and (2) according to Palma, I (2008) proposal, assuming that the limit state is shear yielding. In order to avoid the concrete bearing failure, a larger concrete strength was provided. Table 5 shows the Design Base Shear for all the buildings and the geometric properties of the shear lugs according to both design approaches. It can be seen that the first approach produces stronger shear lugs.
Time history analyses of the buildings were performed by using the elasto- plastic hysteresis model included in Ruaumoko program. Shear lugs were modelled by considering elasto-plastic shear elements at the base of the columns, the properties were obtained from the experimental results Palma, I (2008). Fig. 6 shows some characteristic curves of cross type shear lugs.
Table 4. Ground Motion Records
Earthquake Record Duration
(s) Richter Magnitude Amax (g) Chile [03-03-1985] Viña 60 7,8 0,36 Chile [03-03-1985] Llolleo 60 7,8 0,71 México [19-09-1985] SCT 60 8,1 0,17 U.S.A [17-01-1994] Northridge 60 6,8 0,84 Japan [17-01-1995] Kobe 60 6,9 0,84 Chile [27-02-2010] Concepcion 60 8,8 0,48
Table 5. Design Parameters
LIMIT STATE CRITERIA FOR SHEAR LUG DESIGN Building
Height
Base
Shear Flexural Yielding Shear Yielding
Stories Q [kN] W [cm] H [cm] t [cm] W [cm] H [cm] t [cm] 4 1804 15 9 2 20 17 0,5 8 1557 15 8 2 18 16 0,5 12 2199 15 10 2 24 20 0,5 16 2950 15 12 2 22 21 0,8 4. RESULTS
In order to understand the influence of the shear lug ductility in the building behavior, the amount of plastic hinges formed under both kind of the column base conditions was selected as a measure of the building damage. The comparison is shown on Table 6, it can be seen some reduction of the number of hinges when ductile shear lugs are used, with the exception of Kobe and Mexico earthquakes. Table 7 shows the maximum demanded member ductility in every building. In some cases can be observed a slight isolating effect and sometimes a sort of a slight increase in the member ductility demands, but this is a minor effect and in some cases there is no effect.
Figure 6. Shear Lug Curves
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 257 258 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012
Table 6. Amount of Plastic hinges formed depending on the base type
Stories Base Support Kobe 1995 Llolleo 1985 México 1985 North. 1994 Viña 1985 Conc. 2010 Fixed 37 29 0 37 23 27 4 Ductile 37 21 0 31 5 6 Fixed 69 53 0 69 48 61 8 Ductile 69 37 0 69 34 59 Fixed 93 84 60 77 46 69 12 Ductile 93 73 52 77 41 68 Fixed 123 105 106 113 15 87 16 Ductile 123 105 106 113 14 86
Table 7. Ductility demand at the most demanded member in each building
Stories Base Support Kobe 1995 Llolleo 1985 México 1985 North. 1994 Viña 1985 Conc. 2010 Fixed 10 3,6 1 5 3,1 3 4 Ductile 9,4 2,6 1 4,6 2,4 2,4 Fixed 5,4 1,7 1 7 1,5 3,7 8 Ductile 4,5 1,7 1 7 1,4 3,4 Fixed 4,3 2,8 4,2 7,7 1,7 2 12 Ductile 4,7 2,8 4,8 8,2 1,6 2,6 Fixed 6,5 3,3 9,7 9,5 1,2 2,7 16 Ductile 7,6 3,8 9,6 9,4 1,2 3,2
Table 8 shows the ductility demands to the shear lugs. When the shear lug remains in the elastic zone the demanded ductility is 1 and when the ductility demand exceeds 14 it was considered a shear lug failure.
Table 8. Demanded ductilities at shear lugs Stories Kobe 1995 Llolleo 1985 México 1985 North. 1994 Viña 1985 Conc. 2010
4 Failure Failure 1 Failure Failure Failure
8 Failure Failure Failure Failure Failure Failure
12 Failure Failure Failure Failure 9,6 Failure
16 Failure 9,8 Failure Failure 3,8 8,5
It can be seen that ductile shear lugs often fail and even though it does not mean a building collapse it’s necessary to replace the shear lug, which is expensive and difficult. The shear lug designed according to AISC Design Guide N° 1 does not require ductility capacity, however those shear lugs has no strength capacity considerations in their design and they could fail in a brittle fashion.
5. CONCLUDING REMARKS
1. Shear lugs should be designed to fail after the failure of the structure in order to avoid the necessity to be replaced because the replacing is difficult and expensive. 2. In the event of a shear lug failure, it is better to have the steel failure first than the
concrete failure, which is normally a brittle failure mode.
3. In order to guarantee a ductile steel failure, shear lug design should include capacity considerations to avoid a premature steel failure. In that sense the provided concrete strength should be larger than steel strength.
4. The steel failure mode is a typical shear yielding failure. Tests show that flexural yielding mode did not happen. As a consequence, shear steel yielding should be the controlling limit state for the steel lug design.
5. The more flexible the shear lug the higher is the isolation effect, however flexible shear lugs fails and the replacement is difficult and expensive.
6. The influence of shear lug ductility in the building behavior depends of the ground motion characteristics, the building and shear lugs structural properties. It produces a reduction of the earthquake forces but, in practice, it does not change substantially the damage of the structure.
REFERENCES
[1] ACI Committee 349 (2001): “Code Requirements for Nuclear Safety Related Concrete Structures”, American Concrete Institute, USA.
[2] Aguirre C, Palma I. (2009): “Shear Lugs for Column Bases”, Steel Structures in Seismic Areas (STESSA), Philadelphia, USA.
[3] AISC-a (2010): “Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL, USA.
[4] AISC-b (2010): “Seismic Provisions for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL, USA.
[5] AISC-c (2010): “Design Guide 1: Base Plate and Anchor Rod Design”, 2nd Edition, American Institute of Steel Construction, Chicago, IL, USA.
[6] Carr, A. (2004): “Ruaumoko: Theory and User Guide to Associate Programs”. University of Canterbury, New Zealand, 2004.
[7] Grauvilardell, J.E., Lee D., Hajjar, J.F., Dexter, R.J. (2005): “Synthesis of Design, Testing and Analysis Research on Steel Column Base Plate Connections in High Seismic Zones, Structural Engineering Report N° ST-04-02, Department of Civil Engineering, University of Minnesota, Minneapolis, Minnesota.
[8] INN 2002. NCh2369-2002 - Diseño Sísmico de Estructuras e Instalaciones Industriales, Instituto Nacional de Normalización Santiago, Chile.
[9] Palma, I. (2008): “Estudio experimental de llaves de corte en cruz”. Tesis para obtener el grado de Magíster en Ciencias de la Ingeniería Civil. Valparaíso. UTFSM, Departamento de Obras Civiles, 2008.
[10] Rotz, J.V. & Reifschneider, M. (1989): “Combined Axial and Shear Capacity of Embedments in Concrete”, 10th International Conference: Structural Mechanics in Reactor Technology, Anaheim, CA.
[11] Rotz, J.V. & Reifschneider, M. (1991): “Combined Axial and Shear Load Capacity of Steel Embedments in Concrete”, Report by Bechtel Power Corporation.
Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012 259 260 Connections in Steel Structures VII / Timisoara, Romania / May 30 - June 2, 2012