Lateral System Analysis and Confirmation Design November 15, 2004

Transcription

1 Jonathan Hill Structural AE Faculty Consultant Dr. Hanagan Lynde and Harry Bradley School of Technology & Trade Milwaukee, Wisconsin Lateral System Analysis and Confirmation Design November 15, 2004 Executive Summary The following report is an extensive analysis of the existing lateral system used in Bradley Tech High School. The high school is located in Milwaukee, Wisconsin and contains spaces used for a variety of activities. The five story concrete building has a flat joist roof as well as a barrel vault roof which extends over half of the structure. The gravity system consists of cast-in-place pan and joists supported by concrete columns on a CMU block foundation or cast-in-place footings. The lateral system includes the main supporting members of the pan and joists. Due to the monolithic construction each concrete column and beam takes part in the lateral support. Because of the large number of frames in this building typical interior and exterior frames were analyzed and conclusions drawn based on those results. The method of analysis is as follows: Load and Load Cases: Floor, wall, snow and lateral loads were calculated based on the design code used today and compared to the results found using the original Wisconsin Building Code. Load cases are discussed and the worst case scenarios depicted. Lateral Distribution: The lateral loads are distributed through the building based on the stiffness of each frame, but more importantly based on the tributary area that each frame carries. In each direction the loads were placed on frames according to their orientation and location in the building. Lateral Analysis: Once the load distribution was complete typical interior and exterior lateral frames were analyzed. From the analysis results, story and building drift were able to be calculated and compared with the acceptable values. Building torsion was looked at and seen that due to the small lateral loads actually seen by each individual frame and their ability to support the building as a whole, torsion was not deemed as a problem. Likewise, overturning moment due to the lateral uplift was counteracted by the existing gravity system. As a result no significant effect on column locations or foundations was found. Member Checks: Member checks have been diagrammed and results are withstanding. Acceptable results have been found based on the completed analysis. 1

2 Table of Contents Introduction Building Description Page 3 Gravity System Page 3 Lateral System Page 4 Load and Load Cases Floor Loads Page 6 Wall Loads Page 7 Snow Loads Page 7 Wind Loads Page 8 Seismic Loads Page 9 Load Cases Page 9 Lateral Distribution Method of Distribution Page 10 Lateral Frames and Loads Page 11 Lateral Analysis Frame Analysis Page 12 Story Drift Page 13 Building Drift Page 14 Building Torsion Page 15 Overturning Moment Page 16 Member Checks Frame Checks Page 16 Foundation Checks Page 16 Column Checks Page 17 Conclusion Page 18 2

3 Introduction Building Description The Lynde and Harry Bradley School of Technology & Trade is a high school owned by the Milwaukee Public School District. The high school rests on the near south side of Milwaukee and is bounded by West National Avenue on the south, South Third Street on the east, South Fourth Street on the west and West Virginia Street on the north. The existing Milwaukee Tech High School was demolished and the new building along with an athletic practice field, asphalt playing courts, and playground for an adjacent elementary school now fills the space. The 280,000 square foot building contains five stories, one occurring below grade, the others above grade. The interior space is dividing according use of area. Laboratories, classrooms, offices and administration areas make up the buildings interior as well as an open gym. Gravity System The gravity framing layout consists of a typical cast-in-place pan and joist system. Steel joists are used to in the simple flat roof as well as the complicated barrel vault roof that spans half the building. The steel joists are supported by steel tubes which carry the loads to the concrete columns that make up the system found on the lower floors. A typical 30-0 by 32-0 bay is found throughout the building and helps to make the framing system simple and repetitive. The variation of floor loads found in the changing areas of the building is solved by altering the depths and widths of the pans and joists. A typical floor layout is shown below in Figure 1: Figure 1: Typical Pan & Joist Layout 3

4 Lateral System As mentioned before, the main supporting system of this building is a cast-inplace concrete frame. This being so, nearly all columns and intersecting beams take part in the lateral system and the simply laid out concrete frames carry the loads. However, when analyzing the barrel vault roof, the lateral system becomes a bit more complicated. Steel roof members transfer the lateral loads directly to the concrete beams using a bent plate which is embedded in the beams using expansion bolts. At the other end of the vault roof the steel joists transfer their lateral load into a steel tube column, again using a bent plate, which then distributes the load to its supporting concrete beam. The concrete frames cantilever up to the steel roof joists eliminating any need for moment frames or cross bracing within the steel members; therefore, all steel connections are kept simple and transfer only minimal lateral forces. Once the lateral loads are absorbed by the concrete framing system they are transferred to the CMU bearing walls and into the foundations. Figure 2: 3-D Frames 4

5 Sections taken of the monolithic cast-in-place system can be analyzed as rigid frames. Each gridline is a frame that continues from one end of the building to the other. Figure 2 (below) shows the complete system of concrete lateral frames spanning each direction. Figure 3: Typical Interior Frame Figure 4: Typical Exterior Frame 5

6 Loads and Load Cases Floor Loads The following is a summary of the floor loads acting on the structure. The building is divided into many areas each with a different purpose and therefore different loading conditions. The Wisconsin Administrative Code was referenced and used as the guideline for many of the live load calculations. Dead loads were calculated using material selfweight and company standards used by Hammel, Green & Abrahamson, Inc. Detailed calculations, load combinations, and live load reductions have been analyzed and are available in Appendix A. First Floor Laboratory Live Load: Dead Load Typical Laboratory Floor Live Load Dead Load Typical Classroom Floor Live Load Dead Load Administration Floor Live Loads Dead Load 150 PSF (floor load) 50 PSF (mech below) 200 PSF 140 PSF (30 pan & joist) 125 PSF (floor load) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 150 PSF 105 PSF (53 pan & joist) 80 PSF (floor load) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 105 PSF 105 PSF (53 pan & joist) 80 PSF (floor load) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 105 PSF 150 PSF (library) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 175 PSF 170 PSF (bookstore/vault) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 195 PSF 125 PSF (main corridor) 20 PSF (misc partition) 5 PSF (ceiling/misc/mech) 150 PSF 105 PSF (53 pan & joist) 6

7 Bar Joist w/ Flat Roof Live Load Dead Load 30 PSF with applicable drift 4 PSF (bar joists) 6 PSF (4 rigid insulation) 3 PSF (metal roof deck) 12 PSF (roofing & ballast) 5 PSF (ceiling/misc/mech) 30 PSF Curved Roof over Laboratories Live Load 30 PSF with applicable drift Dead Load 8 PSF (beams & girders) 3 PSF (metal roof deck) 8 PSF (roofing & insulation) 6 PSF (ceiling/misc/mech) 25 PSF Wall Loads All wall loads are taken as industry and company standards and are reflect the selfweight of the material and or systems. Interior Partitions 20 PSF (min) Snow Loads Exterior CMU w/ Brick Veneer 4 Brick 50 PSF 8 CMU 50 PSF 100 PSF Curtainwall / Metal Panel System 20 PSF Based on ASCE 7-02 snow loads were calculated and compared to company standards. Several areas of drift will occur along the building mainly on canopies, roof projections and along the two story section of the building where it meets the four story section. The snow drift along the two different roof heights has been calculated in detail and summarized below. Figure 4: Drift Diagram 7

8 Wind Loads The wind loads on this building were calculated using ASCE 7-02 methods. A 90mph worst case wind was applied to the building with an exposure factor of B. Since the building is below 60 feet in height a low-rise approach could have been taken. However, due to the minimal effect on the wind pressures, the standard analysis was done. The original design did not use the now accepted ASCE analysis methods; therefore a check of whether the building meets the new codes is in order. Shear calculations for windward and leeward sides of the building have been calculated from the known pressures and heights. Diagrams summarizing the shear forces acting on the building for each direction of wind appear below. Detailed calculations are available, please see the appendix. Figure 5: East / West Wind Shear Forces Figure 6: North / South Wind Shear Forces 8

9 Seismic Loads In the original design no seismic loads were accounted for. The analysis took place before any standards or codes were issued that dealt with seismic forces in areas where seismic activity is unlikely. To adhere to modern code, the seismic shear forces have been calculated and shown below. For calculations, please refer to the appendix Figure 7: Seismic Shear in Both Directions Load Cases Load combinations taken from ASCE 7-02 were used in the analysis of the lateral system of Bradley Tech. There are multiple combinations mentioned in the code, however only the standards cases as well as critical cases were analyzed. In the case of the acting lateral forces, the wind shear and seismic shear were compared to find the worst case scenario. In both directions shear forces due to seismic loads controlled. The following load combinations were considered: Dead Dead Live Snow Dead Live Snow Dead Live Snow Wind Wind Wind Wind Combinations 1 3 were used for simple analysis and comparison. Load combination 4 proves to be the critical combination when analyzing the existing structure. The final 2 combinations are used for building torsion and total building drift. 9

10 Lateral Distribution Method of Distribution Due to the monolithic design of the building all horizontal and vertical members (excluding the roof) are considered lateral system components. This assumption simplifies the distribution of the lateral forces, but complicates the response of the building as a whole. For simplicity of the initial analysis the stiffness of each frame is to be considered equivalent. This is true for frames in both directions. A more detailed computation of the individual frame stiffness and the percentage of lateral loads each carry is in progress. Due to the large number of frames carrying the load, a complete lateral system diagnostic could not be presented. Under the assumption of equal stiffness the lateral loads may be distributed to the individual frames using tributary area. Exterior frames are to take 1/2 the load that a full interior frame sees. Several unevenly spaced interior frames occur on the south side of the building. Each of these smaller interior spans is assumed to act similar to exterior frames, meaning they receive 3/4 the load on a standard interior frame. This assumption is displayed on Figure 8. Figure 8: Lateral Load Distribution using Tributary Widths Using the calculated shear forces for each level, the correct percentage is applied to the corresponding frame. The frame is then analyzed for drift using RISA. The specific frames and loads follow. 10

11 Lateral Frames and Loads The large number of frames in this building makes it difficult to describe their composition in a detailed manner. There are, however some similarities between the frames. More specifically, all frames consist of base columns rigidly connected to footings. The level at which this happens varies between frames, and varies within individual frames. Each consists of a concrete grid made up of the supporting concrete columns and connecting concrete beams or joists. The minimum height of one frame is two stories (the location of the first roof level). Others extend the full height of the building, ending where supports to the flat roof or barrel vault roof meet the concrete members. The loads calculated using the distribution method described above are summarized below in Table 1: (No.) Level North / South East / West Wind Seismic Wind Frame (k) (k) (k) Seismic (k) Int Int Ext Int Int Ext Int Int Ext Int Int Ext Int Int Ext Table 1: Force Distributions As seen from Table 1, the seismic forces control in the design of the lateral system. This makes sense seeing how wind loads in the area are not that great, and the building is very heavy which adds to the seismic forces on each level. 11

12 Upon calculating the individual loads for each frame, the computer software RISA was used to analyze the frames response. At this point only two frames have been analyzed: one exterior frame taking the east / west shear forces and one interior frame taking the north / south shear forces. The remaining frames are being modeled and the results will be added to this report soon. Figure 9: Exterior Frame Figure 10: Interior Frame 12

13 Lateral Analysis Frame Analysis Due to the complexity and size of the frames being analyzed, RISA was used to and then checked for reassurance. Each frame was entered into RISA in its entirety and each member specified. When using RISA, material properties must be defined. This does not present a problem when dealing with steel members. However, since all frames are reinforced concrete adjustments to the properties must be made. Below is a short summary of the concrete properties. Elastic Modulus (E): 57000(f c )^(1/2) - for normal weight concrete Shear Modulus (G): E / (2.2) f c = 4000psi E = 3605 ksi f c = 5000psi E = 4030 ksi f c = 4000psi G = 1640 ksi f c = 5000psi G = 1832 ksi Moment of Inertia (I): Columns I = I conc Beams I = 1/2 I conc I conc = I of all concrete shape (neglecting reinforcement) Once the properties and loads are entered RISA solves the system. Deflections, member forces, and reactions can be found. Story Drift Allowable drift is taken to be L/400 and is summarized in the Table 2 below: Level Height (ft) Allowable Drift (in) Table 2: Allowable Drift The maximum deflection is observed on LC 4: 1.2D + 0.5L + 0.5S+1.6W The results for the interior and exterior frame are presented on the following page. 13

14 Interior Frame: The maximum displacement occurs at the top of the frame (1.2 in), which is to be expected. This drift computes out to a drift index of L/620 which is much less than the code maximum L/400 and therefore acceptable. A summary of the story drifts is given below in Table 3. Level Height (ft) Allowable Drift (in) Calculated Drift (in) Table 3: Interior Frame Drifts Exterior Frame: This maximum drift in this frame (1.67 in) comes out to an index of L/430 which is much less than the code maximum L/400 and therefore acceptable. A summary of the story drifts is given below in Table 4. Level Height (ft) Allowable Drift (in) Calculated Drift (in) Table 4: Exterior Frame Drifts Building Drift Due to the repetitiveness of lateral frames the total building drift can be taken as no greater than the worst case frame. Under maximum load conditions the maximum building drift in the north / south direction can be taken as 1.67 inches and 1.74 inches in the east / west direction. A more complete description will be given once all frames have been analyzed and accounted for. 14

15 Building Torsion According to the ASCE code building torsion should be analyzed using the following loading diagram. Figure 11: Torsion Loading Diagram Since only typical frames were analyzed, the center of rigidity is assumed to be the center of mass. Once further analysis of all frames in the building is complete the relative stiffness of each frame and its relation to the building will be used to calculate the exact location of the center of rigidity. This calculation is underway and is expected to be reported soon. Based on the above loading scenario, shear forces were placed on the lateral frames and the building was analyzed. The results show that very little torsion acts upon the building. This is due to the great number of frames present and how they evenly distribute the imposed lateral load. A more complete summary of results will be available once the center of rigidity is confirmed. Figure 12: 3-D Loaded Frames 15

16 Overturning Moment A check of the overturning moment due to the lateral loads was completed. Upon analysis it was determined that uplift forced caused by the lateral loads is not great enough to counteract the loads due to gravity at the columns. A more detailed calculation of the overturning moment and its comparison to the acting dead load is available in the appendix. Typical Exterior Column (Grid Line L) Cumulative Dead Load (k) Uplift Reaction (k) Overturning Moment Issue (k) (k) No Typical Exterior Column (Grid Line 20) Cumulative Dead Load Uplift Reaction Overturning Moment Issue (k) (k) No Table 5: Summary of Overturning Moment Member Checks Frame Checks Due to the large number of frames used in the lateral system of this building, the loads are distributed quite evenly to the members. The horizontal members receive minimal stress due to the lateral forces acting on them. The gravity loads are the controlling conditions when looking at the horizontal members of the frames. Foundation Checks With the applied wind and seismic loads unable to create a positive uplift force on the columns, due to the counteracting gravity force, the foundations do not experience any additional stress. The design of the foundations based on gravity loads is enough to compensate any additional worst case lateral loads on the frames of the building. 16

17 Column Checks All columns used in the lateral frames are slender columns. Load rundowns have been done for typical columns in frames spanning in both directions. Typical Exterior Column (Grid Line L) Level Size Area Dead Load Live Load Self Wt DL DL LL LL Red Adj LL LL No. Ht. in x in SF PSF PSF k k k k k k x x x x Roof x Typical Exterior Column (Grid Line L) Level Size Area Dead Load Live Load Self Wt DL DL LL LL Red Adj LL LL No. Ht. in x in SF PSF PSF k k k k k k x x Roof 16 20x Table 6: Column Rundowns Story 1.2D + 1.6L Design Design DL LL Design Load Roof Story 1.2D + 1.6L Design Design DL LL Design Load Roof Table 7: Factored Column Loads Strength comparisons are in the process of being completed and will be posted. 17

18 Conclusions After a significant investigation of the lateral system used in Bradley Tech, once can conclude that the lateral system originally designed using the Wisconsin Building Code is effective when new standards of ASCE are placed on the building. Several aspects of the lateral system were analyzed to understand the design of the system. Load and Load Cases Floor loads and wall loads were tabulated based on areas of building. Snow loads were calculated based on design standards for the area; this included a typical snow drift run-through. Wind loads were changed from the previously calculated WBC standards to the now accepted ASCE 7-02 principles. Seismic loads were not included in the initial design done by HGA; however for the purpose of testing the lateral system under today s design standards, seismic forces were considered and ended up controlling some of the design. Lateral Distribution The method that was used to distribute the lateral forces through the building was discussed and diagramed. Examples of typical interior and exterior lateral frames were given. Based on the stiffness and impact area of the frames, loads were distributed to individual frames. Lateral Analysis After the lateral loads were calculated and distributed to the frames an analysis was able to be done. For this the analysis tool RISA was used. Typical frames were entered into the computer software with their respective loads and analyzed for drift and strength concerns. Once some frame analysis was complete conclusions concerning the total building drift could be drawn from the results of the frame analysis. Building torsion was looked at using loading patterns described in ASCE 7 and the resulting torque was assumed to not control the design of any members. Finally, the overturning moment due to the worst case lateral shears was checked against the gravity loads. The results concluded that the gravity forces were more than able to counteract any lateral uplift forces. Member Checks To complete analysis of the lateral system member checks of frame members were included. It was determined that gravity controlled for horizontal members and therefore lateral loads would not impact the design of such members. Column loads have been calculated and checks concerning the slender concrete columns are underway and will be added to this report once finished. As a result of this investigation the conclusion can be made that the lateral system that was initially designed for earlier loading standards was able to pass the updated code and no changes need to be made. 18