Appendix J Structural Analysis

Transcription

1 Appendix J Structural Analysis Page J-1

2 Appendix J Structural Analysis Table of Contents J.1. Project Overview... J-3 J.2. Structural Frame Layout... J-3 J.2.1. Plan Views... J-4 J.2.2. Frame Line Elevations... J-5 J.3. Loading Cases and Serviceability... J-6 J.3.1. Live Load... J-7 J.3.2. Snow Load... J-7 J.3.3. Wind Loads... J-9 J.3.4. Seismic Loading... J-14 J.3.5. Structural Analysis Deflection Limit States... J-14 J.3.6. Summary of Loadings and Deflection Limits... J-14 J.4. Structural Analysis Methods... J-16 J.4.1. MASTAN analysis Method... J-16 J.4.1. Verified Hand Calculations... J-18 J.5. Structural Floor Joists and Slab Design... J-20 J.6. Conclusions... J-26 J.7. References... J-26 Page J-2

3 J.1. Project Overview Pastor Timothy Van Winkle and his wife Melanie Van Winkle have been looking for land to build Solomon s Training Institute in the heart of Terre Haute, Indiana. Pastor Van Winkle was given a vision of a place for his community and congregation to receive a practical education for the whole family. Pastor Van Winkle wants this training institute to be within walking distance of his church as well as within certain residential boundaries in hopes that this facility will better serve his community. The Pastor and his wife need a large plot of land for this size of a building and parking lot, but due to the development of the area, the only suitable and undeveloped parcel in their neighborhood was previously owned by Wabash Valley Habitat for Humanity Inc. During the design process Pastor Van Winkle was able to obtain the property rights for this property. Based on Appendix G: Assessment of Structural Material Options, N.Spire determined that structural steel should be used for the internal support structure of Solomon s Training Institute. In order to be able to size the steel beam and column members in Appendix K: Structural Member Selection, the internal forces for each member must be known. Axial, shear, and moment forces in each member must be calculated. N.Spire used the structural analysis software MASTAN to perform computer-based structural analysis of the system and then verified these results with hand calculations. This appendix presents the results from MASTAN and the hand verifications. J.2. Structural Frame Layout The room layout from Appendix H: Basic Architectural Layout dictated the position of the columns. N.Spire placed every column along the wall lines of rooms. The first floor has a footprint of 70 feet by 106 feet, but this changed to 68 feet by 104 feet to allow for one foot of exterior wall space on all sides. The second floor also reduces for the same reason from 70 feet by 62 feet to 68 feet by 60 feet. Page J-3

4 Additionally, the columns of the first floor align directly with the columns of the second floor. Solomon s Training Institute will have 16 columns varying in height from 12 feet to 30 feet. The plan and elevation views of Solomon s Training Institute provide indicators for the differing structural members. J.2.1. Plan Views Figure J.1 shows the plan view of the steel beams in the first floor, supporting the second floor slab. The plan view of Solomon s Training Institute shows the center lines of the steel beams in green. The dotted gray lines are the open-web trusses that support the second floor slab. The first and second floor slab designs can be found in the Appendix M: Foundation Design. The layouts of the steel members can be found in Appendix N: Plans. Each member can be indicated by a combination of letters and numbers. For instance in Figure J.1, the column in the lower left corner is A1 and the member running north-south from A1 is AB on frame line 1. The member running east-west from column A1 is 12 on frame line A. For each member indication, N.Spire calculated the design moment, shear, and axial forces. A summary of forces for each frame line is presented later in this Appendix. Page J-4

5 Figure J.1: First Floor Structural Layout J.2.2. Frame Line Elevations The elevations show the members in both the east-west and north-south direction. Figure J.2 shows frame line D in the east-west direction. Frame lines A and D lie in the east-west direction. These two frames were designed as pin connected braced frames utilizing chevron braces. These are shown in Figure J.2 as the angled members between frame lines 1 and 2. Frame lines 1 through 4 lie in the north-south direction, and frame line 4 only contains members in the first floor since the second floor is the roof top garden. Figure J.3 shows the structural frames 1 through 3. The frames in the northsouth direction are rigid frames with moment resisting connections. Page J-5

6 Figure J.2: Frame Line D Structural Layout Figure J.3: Frame Lines 1 through 3 Structural Layout Moment frames have the advantage of only having vertical columns impeding the interior spaces, unlike the braced frames with the obstructions caused by the chevrons. Braced frames are, however, better at resisting lateral deflections. For a moment frame to resist as much lateral deflection as a braced frame, the steel members must be much greater in size. This increase in size raises the costs, but the rigid frames are worth the expense for the benefit of unobstructed space in this case. J.3. Loading Cases and Serviceability For the structural analysis of Solomon s Training Institute, N.Spire considered the live loads on the slabs, the dead loads of the members, the dead loads of the roof, the dead loads of ceiling, and the dead load of the walls for the structure. These loads were Page J-6

7 distributed to the beams based on the tributary areas of the floors and walls. Since frames A and D were so far apart, we assumed that the frames in the north-south direction will act as one-way slabs. In the one-way approximation, the floor slabs distribute the applied surface pressure to the nearest structural beam supporting the diaphragm. Once the floor load is modeled as a uniform load on the beams, MASTAN can be used to analyze the structure using the direct stiffness method. J.3.1. Live Load From ASCE 7-05 by the American Society of Civil Engineers, N.Spire determined that the maximum loading required for the room occupancy types requested by the client was 100 pounds per square foot (American Society of Civil Engineers, 2005). This maximum loading was for the weight rooms and conference rooms. Since the final layout of Solomon s Training Institute is not set, N.Spire conservatively designed both slabs to carry the 100 pounds per square foot maximum loading case. J.3.2. Snow Load Based on the procedure for snow loading in ASCE 7-05, N.Spire determined the base snow loading to be 25 psf. From the base loading, partial snow loading and drift loading can be calculated. Solomon s Training Institute will have drift loading on the three foot high masonry parapets existing around the roof top garden of the second floor of the structure. Partial loading is when snow has been blown away from part of the roof and has remained present on other parts of the roof. Partial loading of the roof structure can have higher force effects depending on the interaction of the loadings throughout the structural frame. Figure J.4 shows sample calculations for the snow loading pressure, partial loading, drift loading, and the drift width to consider. Page J-7

8 Figure J.4: Sample Calculations for Snow Loading Page J-8

9 Figure J.4: Sample Calculations for Snow Loading (Continued) J.3.3. Wind Loads Like snow loads, wind loads were calculated using the ASCE 7-05 procedure (American Society of Civil Engineers, 2005). To determine the wind pressure, a building s exposure category and building type are used. Solomon s Training Institute is a type II building in exposure category B. According to ASCE 7-05, exposure B shall apply where the ground surface roughness condition, as defined by Surface Roughness B, prevails in the upwind direction for a distance of at least 2,600 ft (792 m) or 20 times the height of the building, whichever is greater (ASCE, 2005). The surface roughness used in wind calculations for exposure B is defined as: urban and suburban areas, wooded areas, or other terrain with numerous closely spaced obstructions having the size of single-family dwellings or larger. The maximum design wind speed for Solomon s Training Institute is 90 mph. The exposure category defines coefficient multipliers to determine the wind velocity pressure. An example of the procedure used to determine wind pressure can be found in Figure J.5. Page J-9

10 Figure J.5: Wind Load Design Procedure to Find Wind Pressure Page J-10

11 Effects of wind loads are calculated based on the rigidity of the building, which is determined from the shear resistance of the structural elements. Sample calculations for the rigidity of the braced and rigid frames are found in Figure J.6. Wind loads are calculated based on lateral and torsional effects on a building. Figure J.7 provides sample calculations for wind loads occurring in Solomon s Training Institute. Page J-11

12 Figure J.6: Sample Calculations for Rigidity of the Braced and Rigid Frames Page J-12

13 Figure J.7: Sample Calculations for Wind Loading Forces Page J-13

14 J.3.4. Seismic Loading N.Spire did not consider seismic loading for Solomon s Training Institute. Seismic loading was not calculated in the interests of time for the structural analysis. However, seismic loading would not likely be the limiting state for the design. A building the size of Solomon s training Institute is likely to have combinations of wind and snow loading acting as the limiting cases for design. In other words, these limiting states will probably have the greatest force values that will be used for accurate member sizing. Regardless, we recommend this assumption be verified by a licensed engineer. J.3.5. Structural Analysis Deflection Limit States Based on ASCE 7-05 by the American Society of Civil Engineers, the material that is most susceptible to horizontal deflection problems is masonry (American Society of Civil Engineers, 2005). The code requires that the building deflection be less than the story height divided by 500. The limiting vertical deflection for Solomon s Training Institute, based on the same code, is the span length that is experiencing the live and dead loading combined divided by 300. These limits states must be checked to make sure the final structure does not have serviceability problems such as cracking finishes or vibrations that are unpleasant to the occupants of the building. J.3.6. Summary of Loadings and Deflection Limits Table J.1 summarizes the applied loads on the structure and the serviceability criteria for deflections defined by ASCE N.Spire conservatively used 100 pounds per square foot as the live load for the second floor slab and the roof and 150 pounds per square foot as the live load for the design of the slab connected to the spread footing foundations as calculated in Appendix M: Foundation Plan. Page J-14

15 Table J.1: Summary of Applied Structural Loads and Serviceablity Criteria Loads Roof Self Weight 56 psf psi Roof Superimposed Dead 7 psf psi Roof Live Load 100 psf psi Roof Top Garden Live Load 67 psf psi Floor Self Weight 7 psf psi Floor Superimposed Dead 100 psf psi Floor Live Load Library 150 psf psi Masonry Infill (Walls): 468 plf Masonry Parapet 117 plf Snow See Section J.3.2 Wind Pressure See Section J.3.3 Wind on Roof See Section J.3.3 Serviceability Criteria Maximum Dead Load Defl. Maximum Live Load Defl. Maximum Overall Defl. Maximum Horizontal Defl. L/240 in L/360 in L/300 in H/500 in For the horizontal deflection limit, we used the building height divided by 500. The vertical deflection limit was the span length divided by 300. Then the live loads, dead loads, wind loads, and snow loads are used in defined load combinations to determine the worst possible loading cases. Table J.2 shows the loading combinations N.Spire used in design from ASCE D is for dead load, L is for live load, S is for snow load, and W is for wind load. Once MASTAN is used to analyze the structure, the largest force results from these loading combinations are used to accurately size the structural members. Table J.2: ASCE 7 Loading Combinations Load Combinations 1.4D 1.2D+1.6L+0.5S 1.2D+1.6S+L 1.2D+1.6S+0.8W 1.2D+1.6W+L+0.5S 1.2D+L+0.2S 0.9D+1.6W Page J-15

16 J.4. Structural Analysis Methods N.Spire used the computer analysis software MASTAN to perform calculations for Solomon s Training Institute. We verified these results with hand calculations. J.4.1. MASTAN Analysis Method MASTAN is a computer-based structural analysis program. It uses the Direct Stiffness Method for structural analysis computations. This method uses the nodal displacements of each element relative to the other structural members and their relative stiffness to other members in order to find the forces present in each structural element. Table J.1 and Table J.2 summarize the maximum moments, shears, and axial forces occurring in each structural member from the MASTAN computer computations. The table also presents the reactions and deflections for each frame in the structure. Page J-16

17 Page J-17 Columns Beams 1st Story 2nd Story 1st Story 2nd Story Grade Beams Reactions (kips) Deflection (in) Frame Line 1 Frame Line 2 Frame Line 3 Frame Line 4 Moment Shear Axial Moment Shear Axial Moment Shear Axial Moment Shear Axial (in-kip) (kip) (kip) (in-kip) (kip) (kip) (in-kip) (kip) (kip) (in-kip) (kip) (kip) A B C D A B C D AB BC CD AB BC CD AB BC CD Ay By Cy Dy Ax Bx Cx Dx Vertical Lateral Table J.3: Summary of MASTAN Computations for North-South Frames Solomon s Training Institute

18 Table J. 4: Summary of MASTAN Computations for East-West Frames Columns Beams Chevron Braces 1st Story 2nd Story 1st Story Frame Line A Frame Line D Moment Shear Axial Moment Shear Axial (in-kip) (kip) (kip) (in-kip) (kip) (kip) W E W E y y y y x x x x Vertical Lateral nd Story 1st Story 2nd Story Reactions (kips) Deflection (in) J.4.2. Verified Hand Calculations N.Spire used the Moment Distribution Method to verify the MASTAN computer results for the rigid frames 1-4. The Moment Distribution Method systematically moves from connection to connection of the structure, releasing unbalanced moment (U.M.) at a connection caused by initial fixed end moments (FEMS). The FEMs are due to loads between nodes or member deflections. Once each node has no more unbalanced moment, the support reactions can be solved for. Figure J.8 presents N.Spire s hand calculations using the moment distribution method and equilibrium for braced frames. The hand calculations include Page J-18

19 vertical and horizontal deflection calculations. Also the hand calculations show reaction calculations for one location on the frame that could be repeated for other reactions in the frame. N.Spire showed sample calculations for frame line A and frame line 4. Additionally, Figure J.9 shows the hand calculations for the structural analysis of the rigid frame. Braced Frames Frame A Wind Lateral Loads Fw2 = lbs 1.6 x lbs Fw1 = lbs 1.2 x lbs 1x 2x 3x 4x Table of Properties Columns Beams Chevron Braces 1st Story 2nd Story 1st Story 2nd Story 1st Story 2nd Story 1y 2y 3y 4y From the AISC Steel Manual, 13 Edition Table 1 Size E (ksi) Wgt (plf) A (in 2 ) I (in 4 ) 1 W14X W12X W14X W14X W14X W12X W14X W10X W10X W10X W12X W12X W HSS 3 1/2 X 3 1/2 X 1/ E HSS 3 1/2 X 3 1/2 X 1/ W HSS 3 1/2 X 3 1/2 X 1/ E HSS 3 1/2 X 3 1/2 X 1/ Figure J.8: Hand Calculations for the Structural Analysis of the Braced Frame Page J-19

20 Story Drift - Horizontal Deflections Method for Predicting Horizontal Deflection of Braced Frames, Based on Mechanics of Materials Equations PL δ = AE For Structures = story VL story = 2 AEcos Θ V = Shear in Braces A = Area of Brace E = Modulus of Elasticity of Brace Θ = Angle of Brace with Horizontal Assumptions/Limitations of Method Shear Distributed Equally to Braces, None to Columns Diagonal Members are Symmetrically Braced at Point in Middle of Bay The Lateral Deflection is Relativily Small Neglects Shortening of the Beam Neglects Effect of Column Length Change Using the fact the fact that each Brace Shares Half the Shear Carried by the Story Abrace = 1.54 in 2 Ebrace = ksi If V2nd = lbs L2 = 12 ft Δ2 = in cos 2 Θ2 = rad V1st = lbs L1 = 12 ft Δ1 = in cos 2 Θ1 = rad Δ = in This is an under prediction due to the Assumptions and Limitations, column deflection will increase total deflection Vertical Deflections Method for Predicting Vertical Deflections, Based on Simply Supported Beam Spans From AISC Steel Manual, 13th Edition Table 3-22 max = 5wl EI w = loading on member L = Span Length E = Modulus of Elasticity of Brace I = Moment of Inertia Span 34 w = 133 plf (100plf LL) Δ = in L = 44 ft This is an under prediction because it is a simplifying E = ksi equation, the deflections change as Spans Interact I = 36.6 Figure J.8: Hand Calculations for the Structural Analysis of the Braced Frame(Continued) Page J-20

21 Reactions Since the Shear in the Brace is The Axial in the Brace is From Pythagorean V2nd = lbs N = Axial N2nd cosθ2 = rad V V1st = lbs N = cos N1st Θ cosθ1 = rad To Check MASTANS outputs we evaluated the Governing Loading Combination 1.2D + 1.6W Continue Static Equilibrium Process for all Reactions Summary Process is continued for all Reactions and The Maximum Vertical Deflection from all the Beam Spans Determines the Frames Vertical Deflection. This Process is the Same for Frame D as well. Results are similar to MASTAN Results Reactions (kips) Deflection (in) Hand Calcs MASTAN Results 1y y y y x x x x Vertical Lateral Figure J.8: Hand Calculations for the Structural Analysis of the Braced Frame (Continued) Page J-21

22 Rigid Frames Frame 4 Fw1 = 1500 lbs Ax 2x 3x 4x 1y 2y 3y 4y Table of Properties Columns Beams 1st Story 1st Story Grade Beams From the AISC Steel Manual, 13 Edition Table 1 and the American Concrete Institute Building Code Requirements for Structural Concrete Size E (ksi) Wgt (plf) A (in 2 ) I (in 4 ) A W14X B W14X C W14X D W14X AB W14X BC W14X CD W14X AB 12"X12" conc BC 12"X12" conc CD 12"X12" conc Stiff Beam - Horizontal Deflections Method for Predicting Horizontal Deflection of Rigid Frames, Based on the Portal Method of Structural Analysis V story j = 3 Vh = 12EI Where I j I c c V V = Shear in column h = height of column E = Modulus of Elasticity of column Ic = Moment of Inertia Figure J.9: Hand Calculations for the Structural Analysis of the Rigid Frames Page J-22

23 Assumptions/Limitations of Method Assumes beams are infinitely more stiff than columns Assumes fixed at base Neglects the axial length change in columns Always under predicts due to assumming no beam length change by being infinitely stiff Column h (ft) E (ksi) Ic (in 4 ) V (lbs) Δ (in) A B C D Δtot = Vertical Deflections Method for Predicting Vertical Deflections, Based on Simply Supported Beam Spans From AISC Steel Manual, 13th Edition Table 3-22 max = 5wl EI This is an under prediction due to the Assumptions and Limitations, beam shortening will increase the total deflection w = loading on member L = Span Length E = Modulus of Elasticity of Brace I = Moment of Inertia Span CD w = 0.5 klf Δ = in L = 25 ft This is an under prediction because it is a E = ksi simplifying equation, the deflections change I = 881 in 4 Reactions To Check MASTANS outputs we evaluated the Governing Loading Combination 1.2D + 1.6L + 0.5S Note: Variable Letters for for Purpose of Calculation and Do not correspond to any structural element I J K L DL = LL = S = ω = R 1723 plf 2265 plf 566 plf 4554 plf 12 ft E F G H 21 ft 22ft 25ft Figure J.9: Hand Calculations for the Structural Analysis of the Rigid Frame (Continued) Page J-23

24 Moment Distribution Uses a Method of Releasing Fixed End Moments Caused by the Uniform Loading Until all Nodes have no Unbalanced Moment Solve for R Continue Static Equilibrium Process for all Reactions Summary Process is continued for all Reactions and The Maximum Vertical Deflection from all the Beam Spans Determines the Frames Vertical Deflection. This Process is the Same for Frames 1-3 as well. Results are similar to MASTAN Results Reactions (kips) Deflection (in) Hand Calcs MASTAN Results Ay By Cy Dy Ax Bx Cx Dx Vertical Lateral Figure J.9: Hand Calculations for the Structural Analysis of the Rigid Frame (Continued) J.5. Structural Floor Joists and Slab Design N.Spire used the Vulcraft, a division of Nucor Corporation, composite floor joists manual to choose the open web joists used to support the floor slabs for Solomon s Training Institute. Vulcraft provides a table of open-web composite joists based on the slab loading, thickness, and joist spacing. (See Table J.5 and Table J.6). In the table, Js stands for joist spacing, tc combined with hr is the slab thickness, Wtj is the weight of the joist, W360 is the applied load on the joist, and N-ds is the number of shear studs with its diameter (Vulcraft, 1999). For Solomon s Training Institute, the joists under the slab carry 62.5 pounds per square foot for the 5 inch thick concrete slab (150 pounds per cubic foot) and 100 pounds per square foot of live loading. By multiplying the pounds per square foot by the possible span spacing, we get a value for the applied load. Page J-24

25 For the joists between column line 1 and 2 we used 8 foot joist spacing, Js, meaning the applied load is 1300 plf. Then when you examine the 26 foot span in the Vulcraft table you find that an 18 inch in depth open web joist W360 has a capacity of 1343 plf. This is larger than the applied load and makes the web sufficient. This process was used to size the 34 ft and 44 ft span joists. Open web joists are far less expensive than steel members and have the advantage of openings in the members to allow for mechanical equipment to be run through them. This allows Solomon s Training Institute to have three mechanical roof corridors to run between frame lines 1 through 4 in the north-south direction. A drop down ceiling is placed under the joists to conceal the mechanical equipment in the room spaces. Figure J.10 shows a schematic of the cross section of the structural floor joists. Table J.5: Vulcraft Open Web Joist Look Up Tables (Vulcraft, 1999) Page J-25

26 Joists Between Frame Line Span Lengt h (ft) Table J.6: Vulcraft Composite Joist Calculations Linear Applied Load (plf) Joist Spacin g (ft) Joist Depth (in) Joist Load Capacity (plf) Weight of Joist (plf) Number of Shear Studs - Diameter of Shear Stud (in) / / /8 Figure J.10: Structural Floor Joists and Floor Slab J.6. Conclusions The moments, shears and axial forces calculated by direct stiffness method from MASTAN can be used to size the steel members and grade beams in Appendix K: Structural Member Selection. MASTAN uses the direct stiffness method to determine these forces. Appendix N: Plans, shows the final structural layouts for the members of Solomon s Training Institute. J.7. References American Concrete Institute. (2008). Building Code Requirements for Structural Concrete. Committee 318. American Institute of Steel Construction. (2006). Steel Construction Manual, 13th Edition. American Institute of Steel Construction. American Society of Civil Engineers. (2005). Minimum Design Loads for Buildings and Other Structures. In ASCE American Society of Civil Engineers International Code Council.(2006) International Building Code. Delmar Cengage Learning. Page J-26

27 Vigo County Administrative Code. (2008). County Code Retrieved October 25, 2008, from Unified Zoning Ordinance: pages/6%20-%20uzo%20-%20index.htm/ Vulcraft. (1999). Composite and Noncomposite Floor Joists. Vulcraft: A Division of Nucor Corporation Retrieved April 1, 2009, from catalogs/composite/comnoncomcat.pdf Page J-27