COUNTRY MUSIC HALL OF FAME & MUSEUM

Transcription

1 TECHNICAL ASSIGNMENT #2 Executive Summary Technical report #2 analyzes the viability of different structural materials in place of the structural steel that is used in the Country Music Hall of Fame & Museum. In keeping with the architectural intent, especially in the conservatory, the steel in the museum symbolizes the railroads and bridges that linked America over the past century, and in keeping with the architecture, timber seems to be an apposite replacement in that it has also built this country long before steel and iron were discovered. Another material considered, a more conservative and modern type, concrete, has also been given thought about it s practicality, however due to the broad variations of loads, including the three-hundred fifty pound-per-square-foot live load located in the archive library and the multiple cantilevered floors, concrete is left as a last option for the time being. So for this report glue laminated timber (known hereafter as glulam) will be analyzed in a number of the roof and floor areas of the museum listed below. Redesigning the following support areas to glue laminated timbers 1. Museum s 3rd Floor Cantilevered Walkway 2. Museum s Archive Library 3. Hall of Fame Stair-stepping Roof 4. Conservatory s Roof From the analysis performed in this report, glulam does appear to be a viable alternative to support the museum s floor and roof frame. However, only beams were analyzed in this report and a further analysis would need to be performed on the columns and the design connections. A cost comparison between steel and glulam would also need to be performed. My biggest concern would be the cost of glulam to structurally support the museum s frame.

2 Assumptions The structural plans indicate end reactions of each joist that frames into a girder. These reactions were used to calculate a uniform load on the joists and point loads on the girders. Once all of the point loads were known on the girder, the end reactions for the girders were determined by computer analysis, STAAD Pro. STAAD includes the beam s self weight in the analysis for the reactions and most noticeably the moments. To derive unbiased reactions and moments, members were reduced to W6x9s to neglect the self weight. The maximum moment in the beam was then used to calculate the LRFD section modulus (Zx=(Mmax/(0.9Fy)) and an appropriate size was then determined by the Zx tables in the steel manual. The analysis was recomputed using the appropriate size found in the steel manual and deflection was checked for that appropriate member. To calculate the wood properties, the maximum moment was used again to calculate the ASD section modulus (Sx=Mmax/F b) and the ASD area (A=1.5V/F v) by the maximum shear. To convert the moment of inertia of steel to wood, a relationship was set up with an arbitrary deflection equation. Both deflection equations (steel and wood) are the same ( =*/EI) and equal the same (l/360 ( =l/360=esis/ewiw)). The only differences are the 4 values of E and I. I, the moment of inertia for wood is the only unknown (Es=29,000, Ew=1,800, say Is=510 for a W18x35). Setting both deflection equations equal and solving reveals a factor of This makes clear sense when you think about steel having a strength of 50ksi and wood having a strength of about 2ksi, a factor of twenty-five. This method was used to redesigned the stiffness of the floors to wood. For the roofs, another approach was taken. Reaction loads were not given and based on the complexity of the roof structures, the moment capacity of the W-shapes was used to design the bending (fiber) of the wood members. This is a very conservative approach and the actual moments could be far less than the moment capacity. It is possible they were chosen simply because they were the lightest member in the group, but they will never be higher. And besides the conservatory girders are over designed from the beginning. For this assignment an approximate size is believed to be appropriate. A brief summary of calculations is included in the appendix of this report. 2

3 Museum s 3rd Floor Cantilevered Walkway Fig 1: 3rd Floor Museum Cantilevered Walkway Located on the museum s third floor is an exhibit walkway cantilevered by six W36x194 girders, twenty feet in length, equally spaced thirty feet, cantilevered from the rear wall columns that support the rear of the building and the floors above and below (See Fig 1). Framed on both sides of the cantilevered girder are W16x26 joists, three rows equally spaced, supporting the composite slab above. Each joist transfers seventeen kips into the cantilevered girder, six joists per girder, thus each girder carrying a total load of 102 kips and a moment of 1,360 ft-k (See Fig 2). Being a cantilever, deflection is obviously known to govern the design of these six girders. To maintain a minimum floor deflection limit of l/360, the required moment of inertia using 29,000 ksi steel is 14,744 in 4. This is a simple analysis and was performed by beam tables and superposition because max remains fixed at the free end and the maximum moment remains fixed at the fixed end. There is question about the W36x194 that is actually used with a moment Fig 2: FBD of typical girder supporting cantilevered walkway of inertia of 12,100 in 4 and why a difference. It is assumed the joist and slab stiffness accounts for that difference. Redesigning the cantilevered girders to glulam, the moment of inertia, calculated backwards by the deflection equation using =l/360, required to maintain the same l/360 floor deflection limit is an astonishing 203,611 in 4. The strongest member in the NDS specifications is a 30F-2.1E SP/SP 10-1/2 x 60-1/2 with a mo- 3

4 ment of inertia of 193,800 in 4, the required moment of inertia far exceeds this and is deemed realistic only if the deflection limit is reduced to l/340, but yet the cost. An alternative is to support the free end Fig 3: FBD of proposed cantilevered walkway with tension rod of the cantilever with an axial tension rod using the intended thirty-foot girder spacing and a proposed reduced fifteen-foot girder spacing (See Fig 3). Using the tension rods, the required moment of inertia, section modulus, and area for the 30 and 15 span are (12,325 in 4, 1,145in 3, 314in 2 ) and (4,760in 4, 575in 3, 157in 2 ), respectively. Under NDS specifications, suitable sizes for both are 24F-1.8E, SP 8-1/2 x 37-1/8 and 8-1/2 x 20-5/8, respectively. Shear controls the 30 span and bending for the 15 span. Further analysis would be needed to determine where to connect the other end of the tension rod. Since the fourth floor doesn t span over this rear area, the roof would have to carry the 57k of each girder. As for the steel design, tensions rods would reduce the girders to W18x35s for the 30 spacing and W14x22s for the 15 spacing. Museum s Archive Library Also located on the third floor is part of the museum s musical archive and library. This area is distinctive in that it requires a three-hundred fifty Fig 4: Floor bay for the Archive Library pound-per-square-foot live load. A typical bay in this area was analyzed to determine the feasibility of glulam (See Fig 4). The joists span thirty feet and are spaced every three feet and support the composite slab. The girders span twenty-two feet with a five-foot overhang. The columns near the overhang that support the girders are not continuous (the two circled). The girders actually rest on the columns below and two new columns begin above to support the upper floor. The bay analyzed is supported by 2 girders that are simple beams overhanging Fig 5: FBD of typical girder supporting archive library one support with the multiple point loads (See Fig 5). The 4

5 joists are treated as a simple beam with a uniformly distributed load derived by the end reactions and the girders are analyzed using all of the end reactions as loads. Redesigning the bay using glulam, the W16x26 joists can be redesigned using 24F-1.8E, SP 8-1/2 x 24-3/4 glulams and the W21x50 girders by 24F-1.8E, SP 10-1/2x35-3/4 glulams. All of the glulam members are controlled by bending. Hall of Fame Roof Table 1: Correlalative sizes between steel and wood for HOF Roof HOF Roof Fbx psi Fvx 2, Sx=Mn/Fbx From NDS Steel Steel Glulam 24F-1.8E Size Mn (in-lb) Sx Based on Sx Area W21x62 5,978,400 2, x42-5/ W14x22 1,413, x24-3/ W10x22 1,170, x24-3/ W10x12 567, x24-3/ W6x9 280, x16-1/ Fig 6: HOF Stair-stepping Roofs The Hall of Fame has three stair-stepping roofs, each roof framed as an octagon with the roof purlins converging from the center of the drum (See Fig 6). The roof is comprised of W21x62, W14x22, 5

6 W10x22, & W10x12 rafters and W6x9 purlins. The snow loads by ASCE 97-8 are less than the roof live loads there the roof is calculated for the roof live load of twenty pound-per-square-foot. Because of the minimum loadings, bending moment is assumed to be more of a concern than deflection. To determine the matching glulams a simplified approach was taken. The glulam sizes are based on the moment capacity of each W-flange shape listed. This is a very conservative approach but it gives the approximate sizes needed. The correlations are listed in the Table 1 on the previous page. Conservatory Roof Girders The 11,000-square-foot Conservatory architecturally anchors the museum's entrance and is a simple steel structure with W10x22 columns, W36x135 roof girders, and W18x35 purlins filled inbetween with glass (See Fig 7). The W36x135 roof girders are what I redesigned to glulam. There are a lot of questions about the design of these girders, as mentioned earlier, they re symbolic and were intentionally oversized for grandness. Using the same approach with the Hall of Fame roof, the section modulus required for glulam is 9,109 in 3, again beyond the NDS specifications. The next approach was to find the tributary area for each girder to find the moment and shear of each girder. The roof live load is twenty pound-per-square-foot and a dead load of fifteen pound-per-square-foot per inch of structural glass (Steel Manual Table 17-13). With the glass assumed to be a half inch think, a flat roof, a tributary width of 13-3, and a deflection limit of l/360 (for fragility of the glass) the uniform load on the longest girder is 550 pounds per foot. Treating the girder as a beam fixed at one end and supported at the other, reveals a maximum moment of 413 ft-k and a steel section modulus of 2,491in 4 and a wood section modulus of 40,133 in 4. With a section modulus of 40,133 in 4, the girders can be redesigned to 24F-1.8E, 10-1/2 x 37-1/8 glulams. 6 Fig 7: Conservatory Roof Structure

7 Full Scale Drawings A r e a s A n a l y z e d H i g h l i g h t e d i n Y e l l o w 7

8 Conservatory Roof Plan

9 3rd Floor Museum Cantilevered Walkway and Archive Library C D E F G H J 9

10 Roof Plan 10

11 Hall of Fame Elevation Plan 11

12 Calculations 12

13 Calculations 12

14 Members Being Analyzed Conservatory Rafters Size Ix Zx Sx ФbMpx ФbMrx ФbMn Cb ry Lb Lp Lr BF ФvVn W36x135 7, , , , Hall of Fame Rafters/Purlins Size Ix Zx Sx ФbMpx ФbMrx ФbMn Cb ry Lb Lp Lr BF ФvVn W6x W21x62 1, W14x W10x W10x Museum Interior Cantilevered Walkway & an Archive Room Bay Size Ix Zx Sx ФbMpx ФbMrx ФbMn Cb ry Lb Lp Lr BF ФvVn W16x W21x W36x194 12, , , ,

15 E (ksi) F'b (psi) F'v (psi) Steel 29, Glulam 1,800 2, Tension Zone in Tension 24F-1.8E 1, Comp Zone in Tension 2,100 3, Tension Zone in Tension 30F-2.1E2 3,000 Comp Zone in Tension =l/ Museum Cantilevered Walkway Girder (1 of 6) Calucated by superposition, see report for FBD 30' Span Load 1 Load 2 Load 3 Total Length ' a ' b ' P k Vmax k Mmax 'k ,360 l/ I Steel 8,104 5,302 1,338 14,744 Z Steel 363 A Steel 2.27 I Wood 111,909 73,224 18, ,611 S Wood 5,440 A Wood 567 Sizes Steel W36x194 Wood No Size (30F-2.1E2) STRONGEST Note: Compression Zone in Tension, F'b=1950 Cantilevered Walkway w/ Tension Free End Calucated by STADD Pro see report for FBD Properties Calculations Trail Design Actual Trail Design Actual 30' Span W6x9 W18x35 W36x135 15' Span W6x9 W14x22 None R rod R rod R Fixed End R Fixed End Mmax 'k Mmax 'k max max l/ l/ I Steel 510 I Steel 197 Z Steel Z Steel A Steel A Steel 1 1 I Wood 12,325 I Wood 4,761 S Wood 1,158 1,145 1,106 S Wood A Wood A Wood Sizes Steel W18x35 Sizes Steel W14x22 Wood 8-1/2 x 37-1/8 24F-1.8E Wood 8-1/2 x 20-5/8 24F-1.8E

16 Archive Room - Joist Design Calucated by beam tables see report for FBD Archive Room - Girder Design Calucated by STADD Pro see report for FBD 30' Span Load 30' Span W6x9 W18x55 W21x50 Length ' 30 Vmax w klf 1.46 Mmax V1 22 l/ V Mmax 164 I Steel 1,140 l/ Z Steel I Steel 367 A Steel Z Steel 43.8 I Wood 27,550 A Steel 0.49 S Wood 2,132 2,080 2,080 I Wood 5913 A Wood 991 1,389 1,394 S Wood A Wood Sizes Steel W16x26 Sizes Steel W18x55 Wood 8-1/2 x 24-3/4 24F-1.8E Wood 10-1/2 x 35-3/4 24F-1.8E HOF Roof Correlations Steel Steel Glulam Size Mn (in-lb) Sx W36x135 21,861,600 9,109 W21x62 5,978,400 2,491 W14x22 1,413, W10x22 1,170, W10x12 567, W6x9 280, F-1.8E Based on Sx 8.5x42-5/8 5.5x24-3/4 5.5x24-3/4 5x24-3/4 3x16-1/2 Conservatory Roof Calucated by beam tables 30' Span Load Length ' 78 Roof LL 20 psf Dead Load 7.5 psf wu klf 0.54 Vmax k 26 Mmax ftk 413 l/ I Steel 2491 Z Steel A Steel 0.59 I Wood S Wood A Wood Sizes Steel W18x130 Wood 10-1/2 x 37-1/8 24F-1.8E