Lateral System Analysis and Confirmation Design (S-3)

Transcription

1 November 13, 2002 Lateral System Analysis and Confirmation Design (S-3) Executive Summary: This report summarizes the analysis of the lateral systems used in the 250 West Street building in Columbus, Ohio. The loads used in this report were determined as part of the Structural Concepts / Structural Existing Conditions, S-1. The loads were then distributed to each frame using the stiffness method. Once it was determined how much of the total load each frame must resist, a lateral analysis was preformed to determine the forces in each member and the total drift of each frame. After the analysis was complete, every frame in the current building was found to be inadequate in both strength and stiffness. The drift at the top of the frames is almost twice the industry standard of h/400. However, there is a logical reason for this: the load calculations determined in the Structural Concepts / Structural Existing Conditions (S-1) used a seismic response modification factor of 3 while the original design used a factor of 5. Also, at the time the loads were calculated, it was assumed that the building was on a site class of D since the soil report was not available at the time. Since then, the soil report has been viewed, and the actual site class was determined as B. The combination of these two things has greatly overestimated the seismic load that the building will ever experience. Before any more lateral analysis is preformed on the building the seismic loads should be recalculated to reflect the actual site of the building and the implications of increasing the seismic response modification factor and specifically designing the structure of seismic loads. Also, as a result of the overestimated seismic loads, the spread foundations were not checked for possible uplifting. It should be noted that no analysis outputs or member designs are included in this report because of the length of the material. However, all the material may be viewed if requested. Introduction: This report will look at the lateral system used in 250 West Street and its responses when lateral loads are applied. The lateral system consists of four braced frames with 2 in each direction of the building. The loads applied to each frame were computed according to ASCE 7-98 and are identical to the ones used in the Structural Concepts / Structural Existing Conditions Report, S-1. For the analysis of the braced frames, STAAD was used in order to determine the forces in each member, nodal displacement and the reactions at the base of each frame. These forces were then used to determine the adequacy of selected members by hand using the LRFD 3 rd Edition of the

2 Manual of Steel Construction. The results of this analysis will then be compared to the existing design to determine the existing structure s is adequacy in carrying the loads. Lateral Load Resisting System: The lateral loads are resisted by 4 braced frames. On page 10 an illustration can be seen depicting 2 frames and is similar to the other 2. The frames have the following locations. Column line D from Column line C from Column line 4.4 from D C Column line 7.4 from D C A floor plan on page 11 shows the locations of the braced frames. Each frame uses steel tubes to take the lateral loads that range in shape from HSS 8x8x1/4 to HSS 8x8x5/8. Each brace is field welded in place to a gusset plate located at the beam column connection location or a gusset Figure 1 - Typical Bracing Connection plate welded to the beam depending on where it connects. Figure 1 shows a typical connection. Lateral Loadings: Wind loads are one of the loads the braced frames must withstand. The basic wind speed for Columbus, Ohio was determined from figure 6-1 in ASCE 7-98 to be 90 2

3 mph. According to the code, the building is exposure type B because of its urban location. The site is also relatively flat with no hills or depressions in the surrounding topography, resulting in a topographic factor of 1.0. The importance factor is also 1.0 because of the building s function. The frequency of the building was determined to be 1.47 seconds, qualifying it as a rigid structure and simplifying the gust factor calculations to a conservative.85. The external pressure coefficient, C p, varies around the building depending on whether the windward or leeward side of the building is under consideration. Table 3 summarizes the coefficients. Table 1 - External Pressure Coefficients Location C p Windward.8 Leeward (North South) -.35 Leeward (East West) -.5 Side -.7 The wind load calculations can be found in technical assignment S-1 and are summarized in Figure 2. 3

4 Figure 2 - Wind Load Distribution (psf) The final lateral loads the building must withstand are seismic loads. The structure is a category II building with a seismic use group of I. The site class was assumed to be D because of the uncertainty in the site conditions, and it is also conservative according to the code when the original load calculations were performed. A response modification factor of 3 was used because the building will not specifically be designed for seismic resistance at this point in time. The base shear for the building was determined to be kips. The distribution of the base shear can be seen in Figure 3. The calculations for the seismic loads can also be found in technical assignment S-1. 4

5 Figure 3 - Vertical Distribution of Seismic Forces (in Kips) Lateral Load Distribution: The lateral load for each floor is distributed to each braced frame according to the stiffness of the frame. This was done because of how the loads reach each frame. The wind load will be distributed to each floor through the buildings façade. After that, the load will be transmitted to the braced frames through the rigid concrete floor. Since the floor system is rigid, the load will be distributed to each frame proportional to its stiffness. To determine the stiffness of each frame, the current framing system was modeled in STAAD and loaded with a unit force at the top of each frame. The output of STADD gives the defection of each frame. The stiffness is then determined by dividing the load by the displacement it produces. The distribution of the direct shear taken by each frame 5

6 is then determined by dividing its individual stiffness by the total stiffness in the direction of the building being looked upon. Another force each frame must endure is the force that results from torsion on the building. To determine this force, the center of force and center of rigidity is determined for each direction in the building. The difference between the center of force and center of rigidity is then multiplied by a unit force in order to determine the moment created by the force not being applied at the center of rigidity. The force on each frame resulting from the torsion is then determined from the following equation: F i i = M 2 kidi k d F Force M Moment d i Difference between center of rigidity and frame location k i Frame stiffness The total force resisted by each frame is then determined by adding the direct shear to the force produced by the torsion. The maximum force each frame will experience is determined by adding the direct shear to the absolute value of the torsional force since the lateral forces will come from both directions. Table 2 summarizes the results of the analysis in Appendix 1. The force distribution at each level can be also be found in Appendix 1. Table 2 - Force Distribution to Frames (%) North South Direction East West Direction Frame C D Load

7 Frame Analysis: Once the load resisted by each frame was determined, an analysis was performed on each frame in order to determine the forces in each member. Once again, STAAD was used to analyze each frame. Both the wind and seismic loads were modeled in STAAD with the appropriate load factor. The results of the analysis determined the forces in each member and showed that the seismic load controlled the design of all the braces with the exception of the braces between the 7 th floor, roof, upper roof and penthouse roof, which are governed by the wind load. The overturning moment was also calculated by hand. This was achieved by taking moments around the foundation of each level s forces. This resulted in an overturning moment of 41,345 foot-kips. Member Strengths and Drift: The results of the STAAD output were used to determine the adequacy of several braces in each frame. In each brace, some of the members shown in the original design are inadequate to carry the loads. This is consistent with the results in the Structural Concepts / Structural Existing Conditions Report, S-1, when the forces were assumed to be distributed by tributary area for the ease of an initial analysis. The drift of each frame was also found as a result of the STAAD analysis. The maximum drift at the top of all the frames was 7.04 inches, which is nearly twice the h allowable industry standard of 400 or 3.6 inches. As a result of these findings and the fact that several members failed in strength, the individual floor drift was not calculated. 7

8 Comparison to Existing Structure: As a result of my findings, the current lateral system is inadequate for the loads applied to the braced frame. However, there is a logical reason for this. In the calculations of the seismic loads, the structure was assumed to not be specifically designed for seismic and resulted in a seismic response modification factor of 3 being used. The original design used a seismic response modification of 5. Since the response modification factor is used in the denominator in calculating the seismic forces, the original structure was designed for smaller seismic loads. Also, a conservative site class of D was used in the calculations of the seismic loads. After reviewing the soil report, using site class D is extremely conservative since the actual soil conditions indicate a site class of B. This again will reduce the seismic loads. It is quite possible that the combination of changing the site class and response modification factor will cause the wind load case to control. Conclusion: The results of the analysis show that the existing lateral system fails in both strength and stiffness for the loads checked in this report. The design of most of the braces in each frame are controlled by the seismic loads and cause the frames to drift almost twice the industry standard for limitations. From the findings of this report, the seismic design load is going to have to be reduced, the strength and stiffness of the braced frames increased or a combination of both. The seismic loads need to be recalculated to reflect the actual site class in which the building is built. Some research will also have to be done in order to determine the implications of increasing the seismic 8

9 response modification factor. Once the seismic load is recalculated, another analysis will have to be performed to determine the adequacy of the existing structure. 9

10 Figure 4 - Braced Frames 10

11 11 Figure 5 - Third Floor Framing Plan (Floors 2-7 Similar)

12 Appendix 1

13 Forces East - West Direction Forces North - South Direction Frame d k Direct Shear Frame d k Direct Shear C D Sum Sum Torsion Torsion moment moment d Rigidity d Rigidity d Load d Load Frame k d kd kd 2 F Frame k d kd kd 2 F C D Sum Sum Frame % Load Frame % Load C D 0.578

14 East - West Direction Unfactored Seismic Loads North - South Direction C D Level Total Load Level Total Load C D P.H. Roof P.H. Roof Upper Roof Upper Roof Roof Roof

15 East - West Direction Unfactored Wind Loads North - South Direction Distribution Distribution C D Load Load C D Level Windward Leeward Windward Leeward Windward Leeward Level Windward Leeward Windward Leeward Windward Leeward P.H. Roof P.H. Roof Upper Roof Upper Roof Roof Roof /Ground /Ground