Calculation Report

UCLA LOS ANGELES, CA CEE 141

Westwood Nanoelectronics Laboratory

Structural Calculation Report 12/09/2023 Kevin Ho, 405535877 Connor Achziger, 105919674 Colby Martin Brown, 005613235 Jake Mumford, 805486785

Table of Contents Page 1. Loading Criteria

2

2. Column Load Tabulations

4

2.1. Loading

4

2.2. Tributary Area

4

2.3. Live Load Reductions

7

2.4. LRFD Load Combinations

7

3. Column Design

9

3.1. Splice Locations

9

3.2. Effective Lengths

10

3.3. Column Selection

10

4. Beam and Girder Design

12

4.1. Beam Layout Study

12

4.2. Roof Framing

17

4.3. Typical Floor Beams and Girders

31

4.4. Floor 2 Beams and Girders

43

5. Connection Design

60

5.1. Typical Beam to Girder Connection at Roof Level

60

5.2. Typical Girder to Column Connection at Office Level

61

6. Secondary Steel – Wind Girt Design

62

6.1. Layout

62

6.2. Loading

63

6.3. Final HSS Design

63

6.4. D-3 Column Check

66

7. Steel Member take-off and cost estimate

69

7.1. Columns

69

7.2 Beams

70

7.3 Girders

71

7.4 Wind Girt

71

7.5 Total Cost

71

1. Loading Criteria Table 1.1. Typical Floor Dead and Live Load Tabulations Typical Floor and Floor 2 Dead Load

Load (psf)

3 ¼” LWC over 3" Deck (18-GA)

49.7

MEP

10

Ceiling/Lights

4

Flooring/Misc.

5

Slab Total

68.7

Gravity Beam

4

Beam Total

72.7

Gravity Girder

4

Girder Total

76.7

Gravity Column

2

Column Total

78.7

Typical Floor Live Loads

Load (psf)

Office Occupancy (reducible)

50

Partitions

15

Floor 2 Live Loads

Load (psf)

Light Manufacturing (reducible, max 80%)

125

Partitions (Not required when the minimum specified load is greater than 80 psf)

0

2

Table 1.2. Roof Dead and Live Load Tabulations Roof Dead Load

Load (psf)

Bare Metal Deck (20-GA; N-24)

3

MEP

10

Ceiling/Lights

4

Flooring/Misc.

5

Roofing

10

Slab Total

32

Gravity Beam

4

Beam Total

36

Gravity Girder

4

Girder Total

40

Gravity Column

2

Column Total

42

Typical Floor Live Loads

Load (psf)

Flat Roof (reducible)

20

Partitions (none on the roof)

0

3

2. Column Load Tabulation 2.1. Loading Table 2.1.1. Dead and Unreduced Live Loading (excluding partitions) by Floor Dead Load (psf)

Live Load (psf)

Roof

42

20

Floor 6

78.7

50

Floor 5

78.7

50

Floor 4

78.7

50

Floor 3

78.7

50

Floor 2

78.7

125

2.2. Tributary Area 2.2.1. Floor Tributary Area The floor tributary area for a column is calculated by finding the area of the slab that the column takes load. Using the tributary width and length, we can easily multiply to get the tributary area of a column. Some conditions to consider are the slab overhang and the differing tributary dimensions.

Typical E-W Edge = 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ ∗ (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ + 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) 36'

= 24' ∗ ( 2 + 1') 2

= 456 𝑓𝑡

Typical N-S Edge = 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ ∗ (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ/2 + 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) 24'

= 36' ∗ ( 2 + 1') 2

= 468 𝑓𝑡

4

Typical Corner = (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ/2 + 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) ∗ (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ/2 + 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) 36'

24'

= ( 2 + 1') ∗ ( 2 + 1') 2

= 247 𝑓𝑡

Typical Interior = 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ ∗ 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ = 36' ∗ 24' 2

= 864 𝑓𝑡

Typical Interior = 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ ∗ 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ = 36' ∗ 24' 2

= 864 𝑓𝑡 Floor 2 C-2, C-4

= 𝑇𝑦𝑝𝑖𝑐𝑎𝑙 𝐼𝑛𝑡𝑒𝑟𝑖𝑜𝑟 − (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ/2 − 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) ∗ (𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ/2 − 𝑂𝑣𝑒𝑟ℎ𝑎𝑛𝑔) 2

24'

36'

= 864 𝑓𝑡 − ( 2 − 1) ∗ ( 2 + 1') 2

= 655 𝑓𝑡

Floor 2 C-3 (see Typical E-W Edge) 2

= 456 𝑓𝑡

Floor 2 D-2, D-4 (see Typical Corner) 2

= 247 𝑓𝑡 Floor 2 D-3 2

= 0 𝑓𝑡

2.2.2. Exterior Wall Tributary Area Roof Tributary Height = 𝑃𝑎𝑟𝑎𝑝𝑒𝑡 + 𝑊𝑎𝑙𝑙 𝐻𝑒𝑖𝑔ℎ𝑡 𝑓𝑟𝑜𝑚 𝑅𝑜𝑜𝑓 𝑡𝑜 𝐹𝑙𝑜𝑜𝑟 6 / 2 = 5' +

13' 2

= 11. 5'

5

Floor Tributary Height Example (Floor 6) = 𝑊𝑎𝑙𝑙 𝐻𝑒𝑖𝑔ℎ𝑡 𝑓𝑟𝑜𝑚 𝑅𝑜𝑜𝑓 𝑡𝑜 𝐹𝑙𝑜𝑜𝑟 6 / 2 + 𝑊𝑎𝑙𝑙 𝐻𝑒𝑖𝑔ℎ𝑡 𝑓𝑟𝑜𝑚 𝐹𝑙𝑜𝑜𝑟 5 𝑡𝑜 𝐹𝑙𝑜𝑜𝑟 6 / 2

=

13' 2

+

13' 2

= 13' Exterior Wall Tributary Area Example (Floor 6 on N-S Wall) = 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝑊𝑖𝑑𝑡ℎ ∗ 𝑇𝑟𝑖𝑏𝑢𝑡𝑎𝑟𝑦 𝐿𝑒𝑛𝑔𝑡ℎ = 24' ∗ 13' 2

= 312 𝑓𝑡 *The N-S wall uses a tributary width of 24’ and the E-W wall uses a tributary width of 36’ Table 2.2.2.1. N-S Exterior Wall Tributary Area Tabulation (Tributary Width = 24’) N-S Wall

Tributary Height (feet)

Tributary Area (ft^2)

Roof

11.5

276

Level 6

13

312

Level 5

13

312

Level 4

13

312

Level 3

16.5

396

Level 2

19

456

Table 2.2.2.2. E-W Exterior Wall Tributary Area Tabulation (Tributary Width = 36’) E-W Wall

Tributary Height (feet)

Tributary Area (ft^2)

Roof

11.5

414

Level 6

13

468

Level 5

13

468

Level 4

13

468

Level 3

16.5

594

Level 2

19

684

6

2.3. Live Load Reductions For floor live load reduction, we used ACSE-7 Eq. 3.7-1. The reduction is limited to 40% of the original value for floors supporting more than one floor and 50% for floors supporting one floor.

The tributary area used includes the tributary area of the above floors excluding the roof. For roof live load reduction, we used ACSE-7 Eq. 4.8-1. The minimum reduced roof live load is 12 psf.

Roof Live Load Reduction Example (A-3) = 𝐿0𝑅1𝑅2 = 𝐿0 ∗ (1. 2 − 0. 001(𝐴𝑇)) ∗ 1 = 50 ∗ (1. 2 − 0. 001(456)) ∗ 1 = 50 ∗ 0. 744 ∗ 1 = 14. 88 𝑝𝑠𝑓 Floor 4 Live Load Reduction Example (A-3) =𝐿 (0. 25 + 0

=50(0. 25 +

15 𝐾𝐿𝐿𝐴𝑇

)

15 4∗1368

)

=50(0. 45) =22. 6 𝑝𝑠𝑓 The second floor has a special condition according to ASCE-7 4.7.3 that limits the maximum live load reduction factor to be 80%.

2.4. LRFD Load Combinations Now that we have the tributary wall area and, the tributary floor area, dead loads, and reduced live loads, we can use the LRFD Load Combinations 1.4D and 1.2D+1.6L to calculate the load transferred from each floor to the column.

Roof LRFD Example (A-3) 2

2

2

2

1.4D = 1. 4(42𝑝𝑠𝑓 ∗ 456𝑓𝑡 + 15𝑝𝑠𝑓 ∗ 276𝑓𝑡 )/1000 = 32. 6 𝑘𝑖𝑝𝑠 2

1. 2𝐷 + 1. 6𝐿 = [1. 2(42𝑝𝑠𝑓 ∗ 456𝑓𝑡 + 15𝑝𝑠𝑓 ∗ 276𝑓𝑡 ) + 1. 6(14. 9𝑝𝑠𝑓 * 456𝑓𝑡 )]/1000 = 38. 8 𝑘𝑖𝑝𝑠

7

Table 2.4. Sum of Factored Loads At Each Floor Columns

Roof (Kips)

Floor 6 (Kips)

Floor 5 (Kips)

Floor 4 (Kips)

Floor 3 (Kips)

Floor 2 (Kips)

A-2/A-3/A-4 (North Edge)

38.8

120.4

198.2

274.3

351.0

475.2

B-1/B-5/C-1/C-5 (East/West Edge)

42.0

128.2

210.6

291.3

373.3

504.7

A-1/A-5/D-1/D-5 (Corners)

26.2

80.7

131.4

180.3

230.1

303.2

B-2/B-3/B-4 (Typ. Interior)

60.1

136.9

264.1

389.9

519.9

1272.0

D-2/D-4

38.8

120.4

198.2

274.3

351.0

422.0

D-3

38.8

120.4

198.2

274.3

351.0

359.2

C-2/C-4

33.8

109.8

182.0

252.5

322.0

409.0

C-3

33.8

109.8

182.0

252.5

322.0

380.0

8

3. Column Design 3.1. Splice Locations Maximum column length is 43', so column splices were introduced in each column. Column splices were placed 4 to 5 feet above the floor heights to avoid points of maximum moment and for ease of construction.

3.2. Effective Lengths Effective length was calculated between each floor with each floor having a K factor. The roof and base sections were idealized to pin to fixed connections and the other sections were idealized to fixed to fixed connections. The recommended value was used rather than the theoretical value for the K factor.

Table 3.2.1. Typical Effective Length Tabulation Height Section

K factor

Length (ft)

Effective Length (ft)

6-R

1

13

13

5-6

1

13

13

4-5

1

13

13

3-4

1

13

13

2-3

1

20

20

1-2

1

18

18

3.3. Column Selection With the effective lengths and load transfer from each floor to the column, we can use AISC Table 4-1 to design the columns. All columns that are spliced together are selected to have the same depth.

Table 3.3.1. Column Selection and Capacities for all Columns

9

Columns

Top Section

KL Capacity (ft) (Kips)

Middle Section

KL (ft)

Capacity (Kips)

Bottom Section

KL Capacity (ft) (Kips)

A-2/A-3/A-4 (North Edge)

W8x31

13

266

W12x53

20

354

W12x65

18

591

B-1/B-5/C-1/C-5 (East/West Edge)

W8x31

13

266

W10x54

20

374

W12x65

18

591

A-1/A-5/D-1/D-5 (Corners)

W8x31

13

266

W8x48

20

239

W10x49

18

382

B-2/B-3/B-4 (Typ. Interior)

W8x31

13

266

W12x65

20

542

W14x132

18

1370

D-2/D-4

W8x31

13

266

W12x53

20

354

W12x58

18

445

D-3*

W8x31*

13

266

W12x53*

20

403

W12x53*

38

403

C-2/C-4

W8x31

13

266

W10x49

20

337

W10x54

18

422

C-3

W8x31

13

266

W10x49

20

337

W10x49

18

382

* D-3 Subject to change after wind girt calculation

4. Beam and Girder Design 4.1. Beam Layout Study 4.1.1. Loading Using the loading criteria calculated in Table 1.1., we can calculate the reduced live load for the typical interior bay. The reduced live load will be different from the reduced live load for the columns because the beams and girders will have a different KLL factor. In our case, the KLL for all the beams and girders will be 2.

Table 4.1.1.1. Typical Beam Dead and Live Load Tabulations

Long Length (36’) Floor

10

Dead Load (psf)

71.7

Live Load, Unreduced (psf)

50

Live Load, Reduced + Partition (psf)

58.75

Short Length (24’) Floor Dead Load (psf)

71.7

Live Load, Unreduced (psf)

50

Live Load, Reduced + Partition (psf)

63.6

4.1.2. Typical Interior Bay 4.1.2.1. Typical Interior Beam Calculations for the design of the typical interior beam members. The maximum moment and shear are calculated using the loading in Table 4.1.1.1. as distributed loads and a beam size is selected per Table 3-2. Deflection is calculated using the selected beam and is reiterated if needed.

4.1.2.2. Typical Interior Girder The beams apply point loads on the girders which are calculated using the loading in Table 4.1.1.1 and the girder’s tributary width. Then the same procedure as the typical interior beam occurs, where the maximum moment and shear are calculated, beam size is selected, and deflection is checked.

4.1.3. Final Interior Bay Design

11

The final interior bay design selected was that of the long length (36’). The long length design provided the necessary support from the typical interior beams and girders while maintaining the least amount of self-weight.

4.2. Roof Framing 4.2.1. Loading Using the loading criteria calculated in Increment 1, we are able to calculate the reduced live load for the roof.

Table 4.2.1.1. Dead and Live Loads on the Roof Frame Roof Dead Load (psf)

42

Live Load, Unreduced (psf)

20

Live Load, Reduced (psf)

18.24

4.2.2. Roof Members 4.2.2.1. Typical Interior Roof Beam The maximum moment and shear are calculated using the loading in Table 4.2.1.1 as distributed loads and a beam size is selected per AISC Table 3-2a. Deflection is calculated using the selected beam and is reiterated if needed.

4.2.2.2. Typical Interior Roof Girder The beams apply point loads on the girders which are calculated using the loading in Table 4.2.1.1 and the girder’s tributary width. Then the same procedure as the roof beam occurs, where the maximum moment and shear are calculated, beam size is selected, and deflection is checked.

4.2.2.3. Exterior Beam The exterior beam is calculated in the same way as the typical interior roof beam, but now there is an exterior wall on the beam and the beam has a smaller tributary width.

4.2.2.4. Exterior Girder

12

The exterior girder is calculated in the same way as the typical interior roof girder, but now there is an exterior wall on the girder and the girder has fewer beams connecting to the girder, which can also be seen as the girder has a smaller tributary width.

4.2.3. Final Roof Frame Design Table 4.2.3.1. Final Roof Frame Design WF Size Typical Interior Beam

W16x31

Typical Interior Girder

W18x35

Exterior Beam

W16x31

Exterior Girder

W18x35

4.2.3.1 Roof Framing Calculations Beam

𝑊𝑤 = 1. 2𝐷𝐿 + 1. 6𝐿𝐿 2

𝐴𝑇 = 8 𝑓𝑡 * 36 𝑓𝑡 = 288 𝑓𝑡

13

2

𝑅1 = 1. 2 − 0. 001𝐴𝑇 = 1. 2 − 0. 001(288𝑓𝑡 ) = 0. 912 𝑅2 = 1 𝐿𝑟 = 𝐿0𝑅1𝑅2 = 20 𝑃𝑆𝐹 * 0. 912 * 1 = 18. 24 𝑃𝑆𝐹 𝐷𝐿 = 42 𝑃𝑆𝐹 𝑊𝑤 = 1. 2(42 𝑃𝑆𝐹 * 8 𝑓𝑡) + 1. 6(18. 24 𝑃𝑆𝐹 * 8𝑓𝑡) = 636. 67 𝑃𝐿𝐹 2

𝑀𝑚𝑎𝑥 =

𝑊𝑤𝐿 8

2

=

(636.67 𝑃𝐿𝐹)(36 𝑓𝑡) 8

= 103. 14 𝐾𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select W16x31

ϕ𝑏𝑀𝑝𝑥 = 203 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥

OK

Shear

ϕ𝑣𝑉𝑛𝑥 = 131 𝐾𝑖𝑝𝑠 𝑉𝑚𝑎𝑥 = 𝑊𝑤𝐿/2 = (636. 67 𝑃𝐿𝐹)(36 𝑓𝑡)/2 = 11. 46 𝐾𝑖𝑝 ϕ𝑣𝑉𝑛𝑥 ≥ 𝑉𝑚𝑎𝑥

OK

Deflection LL only: 4

5𝑤𝐿 384𝐸𝐼

𝑤 =

𝐿

≤ 360

18.24 𝑃𝑆𝐹 *8 𝑓𝑡*1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

= 0. 01216 𝐾𝑖𝑝/𝑖𝑛 4

5(0.01216 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡)

≤

4

384(29000 𝐾𝑆𝐼)(375 𝑖𝑛 )

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 360

0. 507" ≤ 1. 2" OK LL + DL: 4

5𝑤𝐿 384𝐸𝐼

𝑤 =

𝐿

≤ 240

(18.24+42 𝑃𝑆𝐹) *8 𝑓𝑡*1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

14

= 0. 04016 𝐾𝑖𝑝/𝑖𝑛

4

5(0.04016 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

≤

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 240

1. 675" ≤ 1. 8" OK Girder

𝑃𝑢 =

636.67 𝑃𝐿𝐹*36 𝑓𝑡 1000

= 22. 92 𝐾𝑖𝑝𝑠

𝑀𝑚𝑎𝑥 = 𝑃𝑎 = 22. 92 𝐾𝑖𝑝𝑠 * 8 𝑓𝑡 = 183. 36 𝐾𝑖𝑝 · 𝑓𝑡 𝐿𝑏 = 8𝑓𝑡 𝐶𝑏 = 1. 00 AISC Table 3-10 Select W18x35 AISC Table 3-2

ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 0)[249 𝐾𝑖𝑝𝑠 − 12. 3(8 𝑓𝑡 − 4. 31 𝑓𝑡)] ≤ 249 𝐾𝑖𝑝𝑠 203. 613 𝐾𝑖𝑝𝑠 ≤ 249 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 ≤ 203. 613 𝐾𝑖𝑝𝑠 OK Shear

ϕ𝑣𝑉𝑛𝑥 = 159 𝐾𝑖𝑝𝑠

15

𝑉𝑚𝑎𝑥 = 𝑃𝑢 = 22. 92 𝐾𝑖𝑝𝑠 ϕ𝑣𝑉𝑛𝑥 ≥ 𝑉𝑚𝑎𝑥

OK

Deflection LL only: 3

23𝑃𝑙 648𝐸𝐼

𝑃=

𝐿

≤ 360

18.24 𝑃𝑆𝐹 *8 𝑓𝑡*36𝑓𝑡 *1 𝐾𝑖𝑝 1000 𝑙𝑏

= 5. 25 𝐾𝑖𝑝𝑠

3

23(5.25 𝐾𝑖𝑝)(24𝑓𝑡* 12𝑖𝑛/𝑓𝑡)

≤

4

648(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

0. 30" ≤ 0. 8"

24𝑓𝑡* 12𝑖𝑛/𝑓𝑡 360

OK

LL+DL: 3

23𝑃𝑙 648𝐸𝐼

𝑃=

𝐿

≤ 240

(18.24+42 𝑃𝑆𝐹) *8 𝑓𝑡*36𝑓𝑡 *1 𝐾𝑖𝑝 1000 𝑙𝑏 3

23(17.35 𝐾𝑖𝑝)(24𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

648(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

1. 00" ≤ 1. 2"

≤

= 17. 35 𝐾𝑖𝑝𝑠 24𝑓𝑡* 12𝑖𝑛/𝑓𝑡 240

OK

Beam I

𝑊𝑤 = 1. 2𝐷𝐿 + 1. 6𝐿𝐿 𝐷𝐿 = 42 𝑃𝑆𝐹 + 𝐸𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑊𝑎𝑙𝑙𝑠 2

𝐴𝑇 = 36 𝑓𝑡 * 5 𝑓𝑡 = 180 𝑓𝑡 𝑅1 = 1 𝑅2 = 1

𝐿𝑟 = 𝐿0𝑅1𝑅2 = 20 𝑃𝑆𝐹 * 1 * 1 = 20 𝑃𝑆𝐹 𝐷𝐿 = (42 𝑃𝑆𝐹 * 5 𝐹𝑇) + (15 𝑃𝑆𝐹 * 11. 5 𝑓𝑡) = 382. 5 𝑃𝐿𝐹 16

𝐿𝐿 = 20 𝑃𝑆𝐹 * 5 𝑓𝑡 = 100 𝑃𝐿𝐹 𝑊𝑤 = 1. 2(382. 5 𝑃𝐿𝐹) + 1. 6(100 𝑃𝐿𝐹) = 619 𝑃𝐿𝐹 2

𝑀𝑚𝑎𝑥 =

𝑊𝑤𝐿 8

2

=

(619 𝑃𝐿𝐹)(36 𝑓𝑡) 8

= 100. 278 𝐾𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select W16x31

ϕ𝑏𝑀𝑝𝑥 = 203 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥

OK

Shear

ϕ𝑣𝑉𝑛𝑥 = 131 𝐾𝑖𝑝𝑠 𝑉𝑚𝑎𝑥 = 𝑊𝑤𝐿/2 = (619 𝑃𝐿𝐹)(36 𝑓𝑡)/2 = 11. 142 𝐾𝑖𝑝 ϕ𝑣𝑉𝑛𝑥 ≥ 𝑉𝑚𝑎𝑥

OK

Deflection LL only: 4

5𝑤𝐿 384𝐸𝐼

𝑤 =

≤ 3/8"

20 𝑃𝑆𝐹 *5𝑓𝑡*1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

= 0. 0083 𝐾𝑖𝑝/𝑖𝑛 4

5(0.0083 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(375 𝑖𝑛 )

≤

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 360

0. 347" ≤ 0. 375" OK LL + DL: 4

5𝑤𝐿 384𝐸𝐼

𝑤 =

𝐿

≤ 240

(382.5+100 𝑃𝐿𝐹) *1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

= 0. 0402 𝐾𝑖𝑝/𝑖𝑛

4

5(0.0402 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

≤

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 240

1. 676" ≤ 1. 8" OK 17

Beam II

𝑊𝑤 = 1. 2𝐷𝐿 + 1. 6𝐿𝐿 𝐷𝐿 = 42 𝑃𝑆𝐹 2

𝐴𝑇 = 36 𝑓𝑡 * 8 𝑓𝑡 = 288 𝑓𝑡

𝑅1 = 1. 2 − 0. 001𝐴𝑇 = 1. 2 − 0. 001(288) = 0. 912 𝑅2 = 1 𝐿𝑟 = 𝐿0𝑅1𝑅2 = 20 𝑃𝑆𝐹 * 0. 912 * 1 = 18. 24 𝑃𝑆𝐹 𝑊𝑤 = 1. 2(42 𝑃𝑆𝐹 * 8 𝑓𝑡) + 1. 6(18. 24 𝑃𝑆𝐹 * 8𝑓𝑡) = 636. 67 𝑃𝐿𝐹 2

𝑀𝑚𝑎𝑥 =

𝑊𝑤𝐿 8

2

=

(636.67 𝑃𝐿𝐹)(36 𝑓𝑡) 8

= 103. 14 𝐾𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select W16x31

ϕ𝑏𝑀𝑝𝑥 = 203 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥

OK

Shear

ϕ𝑣𝑉𝑛𝑥 = 131 𝐾𝑖𝑝𝑠 𝑉𝑚𝑎𝑥 = 𝑊𝑤𝐿/2 = (636. 67 𝑃𝐿𝐹)(36 𝑓𝑡)/2 = 11. 46 𝐾𝑖𝑝 ϕ𝑣𝑉𝑛𝑥 ≥ 𝑉𝑚𝑎𝑥

OK

Deflection LL only: 4

5𝑤𝐿 384𝐸𝐼

𝑤 =

𝐿

≤ 360

18.24 𝑃𝑆𝐹 *8 𝑓𝑡*1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

= 0. 01216 𝐾𝑖𝑝/𝑖𝑛 4

5(0.01216 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(375 𝑖𝑛 )

≤

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 360

0. 507" ≤ 1. 2" OK LL + DL:

18

4

5𝑤𝐿 384𝐸𝐼

𝑤 =

𝐿

≤ 240

(18.24+42 𝑃𝑆𝐹) *8 𝑓𝑡*1 𝐾𝑖𝑝 12 𝑖𝑛 *1000 𝑙𝑏

= 0. 04016 𝐾𝑖𝑝/𝑖𝑛

4

5(0.04016 𝐾𝑖𝑝/𝑖𝑛)(36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

≤

36 𝑓𝑡* 12𝑖𝑛/𝑓𝑡 240

1. 675" ≤ 1. 8" OK Perimeter Girder

𝑊𝑤 = 1. 4(15 𝑃𝑆𝐹 * 11. 5 𝑓𝑡) = 241. 5 𝑃𝐿𝐹 𝑃𝑢 =

636.67 𝑃𝐿𝐹*36 𝑓𝑡 1000

= 22. 92 𝐾𝑖𝑝𝑠

2

𝑀𝑚𝑎𝑥 = 𝑃𝑎 +

𝑤𝐿 8

2

= (22. 92 𝐾𝑖𝑝𝑠 * 8 𝑓𝑡) +

241.5 𝑃𝐿𝐹*24𝑓𝑡 8

= 200. 75 𝐾𝑖𝑝 · 𝑓𝑡

𝐿𝑏 = 8𝑓𝑡 𝐶𝑏 = 1. 00 AISC Table 3-10 AISC Table 3-2

Select W18x35

ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 0)[249 𝐾𝑖𝑝𝑠 − 12. 3(8 𝑓𝑡 − 4. 31 𝑓𝑡)] ≤ 249 𝐾𝑖𝑝𝑠 203. 613 𝐾𝑖𝑝𝑠 ≤ 249 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 ≤ 203. 613 𝐾𝑖𝑝𝑠 OK Shear

ϕ𝑣𝑉𝑛𝑥 = 159 𝐾𝑖𝑝𝑠 241.5 𝑃𝐿𝐹(24 𝑓𝑡) 𝐾𝑖𝑝𝑠 = 2000

𝑉𝑚𝑎𝑥 = 𝑃𝑢 + 𝑤𝐿/2 = 22. 92 𝐾𝑖𝑝𝑠 + ϕ𝑣𝑉𝑛𝑥 ≥ 𝑉𝑚𝑎𝑥

OK

Deflection LL only: 3

23𝑃𝑙 648𝐸𝐼

4

5𝑤𝐿

+ 384𝐸𝐼 ≤ 3/8" 19

25. 818 𝐾𝑖𝑝𝑠

𝑃 =

18.24 𝑃𝑆𝐹 *8 𝑓𝑡*36𝑓𝑡 *1 𝐾𝑖𝑝 1000 𝑙𝑏

= 5. 25 𝐾𝑖𝑝𝑠

3

23(5.25 𝐾𝑖𝑝)(24𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

648(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

+ 0≤

0. 30" ≤ 0. 375"

24𝑓𝑡* 12𝑖𝑛/𝑓𝑡 360

OK

LL+DL: 3

23𝑃𝑙 648𝐸𝐼

𝑃 =

4

+

5𝑤𝐿 384𝐸𝐼

𝐿

≤ 240

(18.24+42 𝑃𝑆𝐹) *8 𝑓𝑡*36𝑓𝑡 *1 𝐾𝑖𝑝 1000 𝑙𝑏

= 17. 35 𝐾𝑖𝑝𝑠

𝑤 = 241. 5 𝑃𝐿𝐹 * 1/1000 𝐾𝑖𝑝 * 1/12 𝑖𝑛 3

23(17.35 𝐾𝑖𝑝)(24𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

648(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

−1

= 0. 0201 𝐾𝑖𝑝/𝑖𝑛 4

+

5(0.0201 𝐾𝑖𝑝/𝑖𝑛)(24𝑓𝑡* 12𝑖𝑛/𝑓𝑡) 4

384(29000 𝐾𝑆𝐼)(510 𝑖𝑛 )

1. 00" + 0. 12" = 1. 12" ≤ 1. 2"

20

≤

OK

24𝑓𝑡* 12𝑖𝑛/𝑓𝑡 240

4.3. Typical Floor Beams and Girders Figure 4.3.1. Layout Table 4.3.1.1. Loading Criteria for Typical Floor Typical Floor

Loading (PSF)

Composite Beam and Slab Self Weight

53.7

Superimposed Dead Load

19

Exterior Wall

15

Construction Live Load

20

Post Composite Live Load

50

Reduced Post Composite Live Load (Interior Beam)

38

Reduced Post Composite Live Load (Exterior Beam)

45.9

Reduced Post Composite Live Load (Interior Girder)

38.02

Reduced Post Composite Live Load (Exterior Girder)

50

Partitions

15

Table 4.3.1.2. Final Beam and Girder Design WF Size

Studs

Interior Beam

W16x31 <1.5”>

40

Interior Girder

W16x40

36

Exterior Beam

W18x40

72

Exterior Girder

W16x31

24

4.3.3. Typical Floor Girder Calculations Girders

21

Interior 2

𝐴𝑇 = 12𝑓𝑡 * 36 𝑓𝑡 = 432 𝑓𝑡 Pre-composite

𝑞𝑠𝑤 = 𝑞𝑠𝑙𝑎𝑏 + 𝑞𝑑𝑒𝑐𝑘 + 𝑞𝑏𝑒𝑎𝑚 = 49. 7 𝑃𝑆𝐹 + 8 𝑃𝑆𝐹 = 57. 7 𝑃𝑆𝐹 𝑞𝐿𝐿, 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20 𝑃𝑆𝐹 Post Composite

𝑞𝐷𝐿 = 𝑞𝑠𝑤 + 𝑞𝑆𝐼𝐷𝐿 = 57. 7 𝑃𝑆𝐹 + 19 𝑃𝑆𝐹 = 76. 7 𝑃𝑆𝐹 𝑞𝐿𝐿 = 50 𝑃𝑆𝐹 * (0. 25 + 0

15 𝐾𝐿𝐿𝐴𝑇

) = 50 𝑃𝑆𝐹 * (0. 25 +

15

𝑞𝐿𝐿 = 38. 02 𝑃𝑆𝐹 + 15 𝑃𝑆𝐹 = 53. 02 𝑃𝑆𝐹 Pre-composite strength

𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚 𝑃𝑢 = (1. 2(57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(20 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 36 𝑓𝑡 𝑃𝑢 = 43736 𝑙𝑏𝑠 = 43. 7 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

=

43.7 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

2*432 𝑓𝑡

= 262. 41 𝐾𝑖𝑝 · 𝑓𝑡

𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 22

) = 38. 02 𝑃𝑆𝐹

AISC Table 3-2 Select W16x40

ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 67)[274 𝐾𝑖𝑝𝑠 − 10(12 𝑓𝑡 − 5. 55 𝑓𝑡)] ≤ 274 𝐾𝑖𝑝𝑠 349. 86 ≥ 274 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 = 274 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥 𝑃 = (57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) * 36 𝑓𝑡 = 24. 92 𝐾𝑖𝑝𝑠 3

∆𝑆𝑊 =

𝑃𝐿 48𝐸𝐼

3

24.92 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

=

4

48(29000 𝐾𝑆𝐼)(518 𝑖𝑛 )

= 0. 83"

Camber

0. 8(0. 83") = 0. 66" NO CAMBER Post Composite Strength

𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚 𝑃𝑢 = (1. 2(76. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(45. 54 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 36 𝑓𝑡 𝑃𝑢 = 71. 24 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

71.24 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

=

= 427. 43 𝐾𝑖𝑝 · 𝑓𝑡

1 stud/ft

Σ𝑄𝑛 = 24/2 * (17. 1 𝐾𝑖𝑝𝑠) = 205. 2 𝐾𝑖𝑝𝑠 𝐿

𝑏

𝑏𝑒𝑓𝑓 = 2 * 𝑚𝑖𝑛( 8 , 20 ) = 2 * 𝑚𝑖𝑛( 𝑎=

Σ𝑄𝑛 0.85𝑓𝑐'𝑏𝑒𝑓𝑓

=

205.2 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(72𝑖𝑛)

𝑎

𝑌2 = 𝑡 − 2 = 6. 25" −

1.12 𝑖𝑛 2

24 𝑓𝑡 , 8

36 𝑓𝑡 ) 2

= 72 𝑖𝑛

= 1. 12 𝑖𝑛 = 5. 69 𝑖𝑛 → 𝑌2 = 5. 5"

AISC Table 3-18 Use Σ𝑄 = 192 𝐾𝑖𝑝𝑠, 𝑌 = 5. 5" 𝑛

2

ϕ𝑏𝑀𝑛 = 423 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑛 ≤ 𝑀𝑚𝑎𝑥 Try 1.5 stud/ft Σ𝑄𝑛 = (24/2) * 1. 5 * (17. 1 𝐾𝑖𝑝𝑠) = 307. 8 𝐾𝑖𝑝𝑠 𝑎=

Σ𝑄𝑛 0.85𝑓𝑐'𝑏𝑒𝑓𝑓

=

𝑎

307.8 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(72𝑖𝑛)

𝑌2 = 𝑡 − 2 = 6. 25" −

1.68 𝑖𝑛 2

= 1. 68 𝑖𝑛 = 5. 41 𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-18

23

Use Σ𝑄 = 237 𝐾𝑖𝑝𝑠, 𝑌 = 5" 𝑛

2

ϕ𝑏𝑀𝑛 = 436 𝐾𝑖𝑝 · 𝑓𝑡 AISC Table 3-19 4

𝐼𝐿𝐵 = 1090 𝑖𝑛

Check Deflection LL only:

𝑃 = 45. 54 𝑃𝑆𝐹 * 12 𝑓𝑡 * 36 𝑓𝑡 = 19. 67 𝐾𝑖𝑝𝑠 3

∆𝐿𝐿 =

3

𝑃𝐿 48𝐸𝐼

=

19.67 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

= 0. 31" ≤

4

48(29000 𝐾𝑆𝐼)(1090 𝑖𝑛 )

24*12 𝑖𝑛 360

= 0. 8"

DL Post-Composite:

𝑃 = 19 𝑃𝑆𝐹 * 12𝑓𝑡 * 36 𝑓𝑡 = 8. 21 𝐾𝑖𝑝𝑠 3

∆𝐷𝐿, 𝑃𝐶 =

𝑃𝐿 48𝐸𝐼

3

=

8.21 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(1090 𝑖𝑛 )

= 0. 13 "

Total Deflection

∆𝐷𝐿, 𝑃𝐶 + ∆𝐿𝐿 + ∆𝑆𝑊 = 0. 13 " + 0. 31" + 0. 70" ∆𝑇𝑜𝑡𝑎𝑙 = 1. 14" ≤

12*24 𝑖𝑛 240

= 1. 2"

W16x40 w/ (36) studs Exterior

2

𝐴𝑇 = 12𝑓𝑡 * 36/2 𝑓𝑡 = 216 𝑓𝑡 Pre-composite

𝑞𝑠𝑤 = 𝑞𝑠𝑙𝑎𝑏 + 𝑞𝑑𝑒𝑐𝑘 + 𝑞𝑏𝑒𝑎𝑚 = 49. 7 𝑃𝑆𝐹 + 8 𝑃𝑆𝐹 = 57. 7 𝑃𝑆𝐹 𝑞𝐿𝐿, 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20 𝑃𝑆𝐹 24

Post Composite

𝑞𝐷𝐿 = 𝑞𝑠𝑤 + 𝑞𝑆𝐼𝐷𝐿 = 57. 7 𝑃𝑆𝐹 + 19 𝑃𝑆𝐹 = 76. 7 𝑃𝑆𝐹 𝑞𝐿𝐿 = 50 𝑃𝑆𝐹 * (0. 25 + 0

15

) = 50 𝑃𝑆𝐹 * (0. 25 +

𝐾𝐿𝐿𝐴𝑇

15 2

) = 63. 54 𝑃𝑆𝐹 ≥ 50

1*216 𝑓𝑡

𝑞𝐿𝐿 = 50 𝑃𝑆𝐹 0

𝑞𝐿𝐿 = 50 𝑃𝑆𝐹 + 15 𝑃𝑆𝐹 = 65 𝑃𝑆𝐹 𝑊𝑤 = 1. 2(15 𝑃𝑆𝐹 * 13 𝑓𝑡) = 234 𝑃𝐿𝐹 𝑊𝑡𝑜𝑡𝑎𝑙 = 234 𝑃𝐿𝐹 + 1. 2(76. 7 𝑃𝑆𝐹 * 1 𝑓𝑡) + 1. 6(50 𝑃𝑆𝐹 * 1 𝑓𝑡) = 406. 04 𝑃𝐿𝐹 Pre-composite strength

𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) *

𝐿𝑏𝑒𝑎𝑚 2

𝑃𝑢 = (1. 2(57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(20 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 21865 𝑙𝑏𝑠 = 21. 87 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

2

+

𝑤𝐿 8

=

21.87 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

+

406.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

= 131. 19 + 29. 23 𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 160. 42 𝐾𝑖𝑝 · 𝑓𝑡 𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 AISC Table 3-2 Select W16x31

ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 67)[203 𝐾𝑖𝑝𝑠 − 10. 3(12 𝑓𝑡 − 4. 13 𝑓𝑡)] ≤ 166 𝐾𝑖𝑝𝑠 203. 63813 ≥ 203 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 = 203𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥 𝑃 = 57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 12. 46 𝐾𝑖𝑝𝑠 3

∆𝑆𝑊 =

𝑃𝐿 48𝐸𝐼

3

=

12.46 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(375 𝑖𝑛 )

= 0. 20"

NO CAMBER Post Composite Strength

𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚/2 𝑃𝑢 = (1. 2(76. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(45. 54 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 35. 62 𝐾𝑖𝑝𝑠

25

𝑀𝑚𝑎𝑥 =

2

𝑃𝐿 4

+

𝑤𝐿 8

35.62 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

=

2

+

406.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

= 213. 72 + 29. 23 𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 242. 95 𝑘𝑖𝑝 · 𝑓𝑡 1 stud/ft

Σ𝑄𝑛 = 24/2 * (17. 1 𝐾𝑖𝑝𝑠) = 205. 2 𝐾𝑖𝑝𝑠 𝑏

𝐿

𝑏𝑒𝑓𝑓 = 12" + 𝑚𝑖𝑛( 8 , 20 ) = 12" + 𝑚𝑖𝑛( 𝑎=

Σ𝑄𝑛 0.85𝑓𝑐'𝑏𝑒𝑓𝑓

205.2 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(48𝑖𝑛)

=

𝑎

1.68 𝑖𝑛 2

𝑌2 = 𝑡 − 2 = 6. 25" −

24 𝑓𝑡 , 8

36 𝑓𝑡 ) 2

= 48 𝑖𝑛

= 1. 68 𝑖𝑛 = 5. 41𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-18 Use Σ𝑄 = 164 𝐾𝑖𝑝𝑠, 𝑌 = 5" 𝑛

2

ϕ𝑏𝑀𝑛 = 325 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑛 ≥ 𝑀𝑚𝑎𝑥 OK AISC Table 3-19 4

𝐼𝐿𝐵 = 780 𝑖𝑛

Check Deflection LL only:

𝑃 = 45. 54 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 9. 835 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐿 = 50 𝑃𝐿𝐹 * 12000 𝑖𝑛 = 0. 0041 𝐾𝑖𝑝/𝑖𝑛 4

5𝑤𝐿𝐿

3

∆𝐿𝐿 =

𝑃𝐿 48𝐸𝐼

3

+ 384𝐸𝐼 =

4

9.835 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

+

4

48(29000 𝐾𝑆𝐼)(780𝑖𝑛 )

5*0.0041 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛)

= 0. 23" ≤ 3/8"

4

384(29000 𝐾𝑆𝐼)(812 𝑖𝑛 )

DL Post-Composite:

𝑃 = 19 𝑃𝑆𝐹 * 12𝑓𝑡 * 18 𝑓𝑡 = 8. 21 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐷 = (15 𝑃𝑆𝐹 * 13 𝑓𝑡 + 76. 7𝑃𝐿𝐹) * 12000 𝑖𝑛 = 0. 023 𝐾𝑖𝑝/𝑖𝑛 4

3

∆𝐷𝐿, 𝑃𝐶 =

𝑃𝐿 48𝐸𝐼

+

5𝑤𝐷𝐿

384𝐸𝐼

3

=

8.21 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(812 𝑖𝑛 )

4

+

Total Deflection

∆𝐷𝐿, 𝑃𝐶 + ∆𝐿𝐿 + ∆𝑆𝑊 = 0. 30 " + 0. 23" + 0. 20" ∆𝑇𝑜𝑡𝑎𝑙 = 0. 73" ≤

12*24 𝑖𝑛 240

= 1. 2"

OK

W16x31 w/ (24) studs

26

5*0.023 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛) 4

384(29000 𝐾𝑆𝐼)(812 𝑖𝑛 )

= 0. 30"

4.4. Floor 2 Beams and Girders Table 4.4.1. Loading Floor 2

Loading (PSF)

Composite Beam and Slab Self Weight

53.7

Superimposed Dead Load

19

Exterior Wall

15

Construction Live Load

20

Post Composite Live Load

125

Table 4.4.2. Final Beam and Girder Design WF Size

Studs

Interior Beam

W21x73

72

Interior Girder

W24x84

48

Exterior Beam

W33x152 <2 ¼”>

100

Exterior Girder

W21x44

24

Special Beam

W16x31

24

Special Exterior Girder

W12x14

0

Special Girder

W21x44

24

4.4.3. Floor Members Using the loading criteria calculated in Increment 1, we are able to calculate the reduced live load for the floor. The reduced live load will be different from the reduced live load for the columns because the beams and girders will have a different KLL factor. In our case, the KLL for all the beams and girders will be 2.

4.4.4. Typical Interior Floor Beam

27

The maximum moment and shear are calculated using the loading in Table 4.4.1 as distributed loads, and a beam size is selected per AISC Table 3-2a. Deflection is calculated using the selected beam and is reiterated if needed.

4.4.5. Typical Interior Floor Girder The beams apply point loads on the girders which are calculated using the loading in Table 4.4.1 and the girder’s tributary width. Then the same procedure as the floor beam occurs, where the maximum moment and shear are calculated, beam size is selected, and deflection is checked.

4.4.6. Exterior Beam The exterior beam is calculated in the same way as the typical interior floor beam, but now there is an exterior wall on the beam and the beam has a smaller tributary width.

4.4.7. Exterior Girder The exterior girder is calculated in the same way as the typical interior floor girder, but now there is an exterior wall on the girder and the girder has fewer beams connecting to the girder, which can also be seen as the girder has a smaller tributary width.

4.4.8. Floor 2 Beam Calculations Lvl 2: Interior Beam (Longways Beam Orientation) 𝑙 = 36𝑓𝑡 2

𝐴𝑇 = 12𝑓𝑡 × 36𝑓𝑡 = 432𝑓𝑡

Pre-Composite Loads & Deflections (DL & Construction LL) 𝐷𝐿 = 𝑤 = 𝑤𝑠𝑙𝑎𝑏 + 𝑤𝑑𝑒𝑐𝑘 + 𝑤𝑏𝑒𝑎𝑚 = 53. 7𝑝𝑠𝑓 𝑝

𝐿𝐿 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20. 0 𝑝𝑠𝑓 Pre-Composite Strength 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 12𝑓𝑡 = 1157. 28 𝑝𝑙𝑓 2

𝑀𝑚𝑎𝑥 =

𝑤𝑙 8

2

=

1157.28 𝑝𝑙𝑓 × 36𝑓𝑡 8

= 187. 47 𝑘𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select: W16x31 ϕ𝑏𝑀𝑛 = 203 𝑘𝑖𝑝 · 𝑓𝑡 ≥ 𝑀𝑚𝑎𝑥 = 187. 47 𝑘𝑖𝑝 · 𝑓𝑡 4

5𝑤𝑙

∆𝑚𝑎𝑥 = 384𝐸𝐼 =

4

5× 1.157𝑘𝑙𝑓 ×(36×12)

4

384×(29000𝑘𝑠𝑖)(375𝑖𝑛 )

= 2. 24𝑖𝑛

Specify Camber

28

Camber: (0. 8) × 2. 24 = 1. 79 1.5” CAMBER Post-Composite Loads & Deflections 𝐷𝐿 = 72. 7 𝑝𝑠𝑓 (Table 1.1) 𝐿𝐿 = 125 Post-Composite Strength 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 12𝑓𝑡 = 3. 45 𝑘𝑙𝑓 2

2

𝑤𝑙 8

𝑀𝑚𝑎𝑥 =

3.45 𝑘𝑙𝑓 *(36𝑓𝑡) 8

=

= 558. 39 𝑘𝑖𝑝 · 𝑓𝑡

Determine Σ𝑄𝑛 (Assuming 1 stud per foot) Σ𝑄𝑛 = 18 × 17. 1𝑘 = 307. 8𝑘 𝐿

𝑏

72

24

Determine 𝑏𝑒𝑓𝑓 = 𝑚𝑖𝑛( 8 , 20 ) = 𝑚𝑖𝑛( 8 , 2 ) = 9' Σ𝑄

307.8𝑘

𝑎 = 0.85𝑓'𝑛𝑏

= 0.85 × 3𝑘𝑠𝑖 × (9𝑓𝑡 𝑥 12𝑖𝑛) = 1. 12𝑖𝑛

𝑐 𝑒𝑓𝑓

𝑎

1.12 2

Determine 𝑌2 = 𝑇 − 2 = 6. 25 −

= 5. 69𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-19 Select: W18x46 Composite ϕ𝑏𝑀𝑝 ≈ 565 𝑘𝑖𝑝 · 𝑓𝑡 > 𝑀𝑚𝑎𝑥 = 558. 39 𝑘𝑖𝑝 · 𝑓𝑡 OK Post-Composite Deflection 4

𝐼𝐿𝐵 ≈ 1550𝑖𝑛

Add Studs as Required Σ𝑄𝑛 = 307. 8𝑘 4

4

5𝑤𝑙

∆𝐿𝐿 = 384𝐸𝐼 =

5(125𝑝𝑠𝑓*12𝑓𝑡)(36×12)

𝐿

= 1. 26 ≥ 720 = 0. 6

4

384(29000 𝑘𝑠𝑖) 9510𝑖𝑛

4

4

5𝑤𝑙

𝐼𝑟𝑒𝑞 = 384𝐸∆

=

5(125𝑝𝑠𝑓*12𝑓𝑡)(36×12)

𝐿𝐿

4

384(29000 𝑘𝑠𝑖)0.6𝑖𝑛

= 3257. 87

Upsize to W21x62 788𝑘

(94) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

=

(2.6) 𝑠𝑡𝑢𝑑 1 𝑓𝑡

>

(2)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

NO

717𝑘

(84) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

=

(2.3) 𝑠𝑡𝑢𝑑 1 𝑓𝑡

>

(2)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

NO

614𝑘

(72) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

=

(2) 𝑠𝑡𝑢𝑑 1 𝑓𝑡

Σ𝑄'𝑛 = 788𝑘, 𝑁 = 17.1𝑘 = 47 𝑠𝑡𝑢𝑑𝑠, Upsize to W21x68 Σ𝑄'𝑛 = 717𝑘, 𝑁 = 17.1𝑘 = 42 𝑠𝑡𝑢𝑑𝑠, Upsize to W21x73 Σ𝑄'𝑛 = 614𝑘, 𝑁 = 17.1𝑘 = 36 𝑠𝑡𝑢𝑑𝑠, Use W21x73 w/ (72) Studs

29

=

(2)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

OK

Exterior Beam 2

𝐴𝑇 = 7𝑓𝑡 × 36𝑓𝑡 = 252𝑓𝑡

Pre-Composite Loads & Deflections (DL & Construction LL) 𝐷𝐿 = 𝑤 = 𝑤𝑠𝑙𝑎𝑏 + 𝑤𝑑𝑒𝑐𝑘 + 𝑤𝑏𝑒𝑎𝑚 + 𝑤𝑤𝑎𝑙𝑙 = 68. 7𝑝𝑠𝑓 𝑝

𝐿𝐿 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20. 0 𝑝𝑠𝑓 Pre-Composite Strength (Laterally Supported) 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 7𝑓𝑡 = 0. 801 𝑘𝑙𝑓 2

𝑤𝑙 8

𝑀𝑚𝑎𝑥 =

2

=

0.686𝑘𝑙𝑓 × 36𝑓𝑡 8

= 129. 77𝑘𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select: W12x26 ϕ𝑏𝑀𝑛 = 140𝑘𝑖𝑝 · 𝑓𝑡 ≥ 𝑀𝑚𝑎𝑥 = 129. 77 𝑘𝑖𝑝 · 𝑓𝑡 4

4

5𝑤𝑙

∆𝑚𝑎𝑥 = 384𝐸𝐼 =

5×0. 801𝑘𝑙𝑓 ×(36×12)

4

384×(29000𝑘𝑠𝑖)(204𝑖𝑛 )

= 2. 95𝑖𝑛

Specify Camber Camber: (0. 8) × 2. 95 = 2. 36, 2.25” CAMBER Post-Composite Loads & Deflections 𝐷𝐿 = 72. 7 𝑝𝑠𝑓 + 19 𝑝𝑠𝑓 = 87. 7 (Table 1.1) 𝐿𝐿 = 125𝑝𝑠𝑓 Post-Composite Strength 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 7𝑓𝑡 = 2. 17 𝑘𝑙𝑓 2

𝑤𝑙 8

𝑀𝑚𝑎𝑥 =

2

=

2.17 𝑘𝑙𝑓 *(36𝑓𝑡) 8

= 351. 58 𝑘𝑖𝑝 · 𝑓𝑡

Determine Σ𝑄𝑛 (Assuming 1 stud per foot) Σ𝑄𝑛 = 36 × 17. 1𝑘 = 615. 6𝑘 𝐿

𝑏

72

24

Determine 𝑏𝑒𝑓𝑓 = 𝑚𝑖𝑛( 8 , 20 ) = 𝑚𝑖𝑛( 8 , 2 ) = 9𝑓𝑡 = 108𝑖𝑛 Σ𝑄

𝑎 = 0.85𝑓'𝑛𝑏

𝑐 𝑒𝑓𝑓

615.6𝑘

= 0.85 × 3𝑘𝑠𝑖 × 108 = 2. 235𝑖𝑛 𝑎

Determine 𝑌2 = 𝑡 − 2 = 6. 25" −

2.23" 2

= 5. 135𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-19 Select: W14x26 Composite

30

Σ𝑄𝑛 = 385𝑘 ϕ𝑏𝑀𝑝 ≈ 359𝑘𝑖𝑝 · 𝑓𝑡 > 𝑀𝑚𝑎𝑥 = 351. 58 𝑘𝑖𝑝 · 𝑓𝑡 OK Post-Composite Deflection 4

𝐼𝐿𝐵 ≈ 794𝑖𝑛

Add Studs as Required 4

4

5𝑤𝑙

∆𝐿𝐿 = 384𝐸𝐼 =

5(2.17𝑘𝑙𝑓)(36×12)

3

= 3. 561 ≥ 8

4

384(29000 𝑘𝑠𝑖)794𝑖𝑛

4

4

5𝑤𝑙

𝐼𝑟𝑒𝑞 = 384𝐸∆

=

𝐿𝐿

4

5(125𝑝𝑠𝑓*36𝑓𝑡)(36×12)

= 7540. 9 𝑖𝑛

4

384(29000 𝑘𝑠𝑖) 0.375𝑖𝑛

AISC Table 3-20 Select: W27x94 Composite 1190𝑘

Σ𝑄'𝑛 = 1190𝑘, 𝑁 = 17.1𝑘 = 70 𝑠𝑡𝑢𝑑𝑠 𝑥 2,

(140) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

>

(3)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

NOT OK

Upsize to W30x90 Composite 839𝑘

Σ𝑄'𝑛 = 839𝑘, 𝑁 = 17.1𝑘 = 50 𝑠𝑡𝑢𝑑𝑠 𝑥 2,

(100) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

<

(3)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

Use W33x152 Composite w/ (100) studs

Special Case (Adjacent to Artium) 2

𝐴𝑇 = 6. 5𝑓𝑡 × 36𝑓𝑡 = 234𝑓𝑡

Pre-Composite Loads & Deflections (DL & Construction LL) 𝐷𝐿 = 𝑤 = 𝑤𝑠𝑙𝑎𝑏 + 𝑤𝑑𝑒𝑐𝑘 + 𝑤𝑏𝑒𝑎𝑚 = 53. 7𝑝𝑠𝑓 𝑝

𝐿𝐿 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20. 0 𝑝𝑠𝑓 Pre-Composite Strength (Laterally Supported) 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 6. 5𝑓𝑡 = 0. 6268 𝑘𝑙𝑓 2

𝑀𝑚𝑎𝑥 =

𝑤𝑙 8

2

=

0.686𝑘𝑙𝑓 × 36𝑓𝑡 8

= 101. 55 𝑘𝑖𝑝 · 𝑓𝑡

AISC Table 3-4 Select: W10x49 ϕ𝑏𝑀𝑛 = 106 𝑘𝑖𝑝 · 𝑓𝑡 ≥ 𝑀𝑚𝑎𝑥 = 101. 55 𝑘𝑖𝑝 · 𝑓𝑡 4

5𝑤𝑙

∆𝑚𝑎𝑥 = 384𝐸𝐼 =

4

5 × 0.6268 𝑘𝑙𝑓× (36𝑓𝑡×12) 4

384(29000 𝑘𝑠𝑖)272𝑖𝑛

= 0. 5 𝑖𝑛

Specify Camber NO CAMBER Post-Composite Loads & Deflections 𝐷𝐿 = 72. 7 𝑝𝑠𝑓 (Table 1.1)

31

OK

𝐿𝐿 = 125 Post-Composite Strength 𝑤 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) × 6. 5𝑓𝑡 = 1. 867 𝑘𝑙𝑓 2

𝑤𝑙 8

𝑀𝑚𝑎𝑥 =

2

1.867 𝑘𝑙𝑓 *(36𝑓𝑡) 8

=

= 302. 46 𝑘𝑖𝑝 · 𝑓𝑡

AISC Table 3-2 Select: W14x398 Determine Σ𝑄𝑛 (Assuming 1 stud per foot) Σ𝑄𝑛 = 36 × 17. 1𝑘 = 615. 6𝑘 𝐿

𝑏

72

13

Determine 𝑏𝑒𝑓𝑓 = 𝑚𝑖𝑛( 8 , 20 ) = 𝑚𝑖𝑛( 8 , 2 ) = 7. 5𝑓𝑡 = 90𝑖𝑛 Σ𝑄

615.6𝑘

𝑎 = 0.85𝑓'𝑛𝑏

𝑐 𝑒𝑓𝑓

= 0.85 × 3𝑘𝑠𝑖 × 90 = 2. 684𝑖𝑛 𝑎

Determine 𝑌2 = 𝑡 − 2 = 6. 25" −

2.684" 2

= 5. 9𝑖𝑛 → 𝑌2 = 6. 0"

AISC Table 3-19 Select: W12x26 Composite Σ𝑄𝑛 = 321𝑘 ϕ𝑏𝑀𝑝 ≈ 319 𝑘𝑖𝑝 · 𝑓𝑡 > 𝑀𝑚𝑎𝑥 = 302. 46 𝑘𝑖𝑝 · 𝑓𝑡 OK Post-Composite Deflection 4

𝐼𝐿𝐵 ≈ 715𝑖𝑛

Add Studs as Required Σ𝑄𝑛 = 321𝑘 4

4

5𝑤𝑙

5(1.867𝑘𝑙𝑓)(36×12)

∆𝐿𝐿 = 384𝐸𝐼 =

𝐿

= 3. 40 ≥ 720 = 0. 6" Not OK

4

384(29000 𝑘𝑠𝑖) 715𝑖𝑛

AISC Table 3-19 Select: W16x31 Composite 4

4

5𝑤𝑙

𝐼𝑟𝑒𝑞 = 384𝐸∆

=

𝐿𝐿

5(1.867𝑘𝑙𝑓)*(36×12) 384(29000 𝑘𝑠𝑖)0.6 164𝑘

= 337. 914 𝑖𝑛

Σ𝑄'𝑛 = 164, 𝑁 = 17.1𝑘 = 10 𝑠𝑡𝑢𝑑𝑠,

(20) 𝑠𝑡𝑢𝑑𝑠 36 𝑓𝑡

=

4 (1) 𝑠𝑡𝑢𝑑 8.30 𝑖𝑛.

<

(2)𝑠𝑡𝑢𝑑𝑠 1 𝑓𝑡

Use W16 x 31 w/ (20) Studs 4.4.9. Floor 2 Girder Calculations Girder Interior 2

𝐴𝑇 = 24𝑓𝑡 * 36 𝑓𝑡 = 864 𝑓𝑡

Pre-Composite Loading 𝑞𝑠𝑤 = 𝑞𝑠𝑙𝑎𝑏 + 𝑞𝑑𝑒𝑐𝑘 + 𝑞𝑔𝑖𝑟𝑑𝑒𝑟 = 49. 7 𝑃𝑆𝐹 + 8 𝑃𝑆𝐹 = 57. 7 𝑃𝑆𝐹

32

OK

𝑞𝐿𝐿, 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20 𝑃𝑆𝐹 Post-Composite Loading 𝐷𝐿 = 𝑞𝑠𝑤 + 𝑞𝑆𝐼𝐷𝐿 = 57. 7 𝑃𝑆𝐹 + 19 𝑃𝑆𝐹 = 76. 7 𝑃𝑆𝐹 𝐿𝐿 = 125 × (0. 25 +

15

) = 125 × (0. 25 +

𝐾𝐿𝐿𝐴𝑇

15 2*864

) = 76. 36𝑝𝑠𝑓 < 0. 8 × 150

𝐿𝐿 = 125 × 0. 8 = 100 𝑃𝑆𝐹 Pre-composite strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚 𝑃𝑢 = (1. 2(57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(20 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 36 𝑓𝑡 𝑃𝑢 = 43736 𝑙𝑏𝑠 = 43. 7 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

43.7 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

=

= 262. 41 𝐾𝑖𝑝 · 𝑓𝑡

𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 AISC Table 3-2 Select W16x40 ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 67)[274 𝐾𝑖𝑝𝑠 − 10(12 𝑓𝑡 − 5. 55 𝑓𝑡)] ≤ 274 𝐾𝑖𝑝𝑠 349. 86 ≥ 274 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 = 274 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥 𝑃 = (57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) * 36 𝑓𝑡 = 24. 92 𝐾𝑖𝑝𝑠 3

∆𝑆𝑊 =

3

𝑃𝐿 48𝐸𝐼

=

24.92 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(518 𝑖𝑛 )

= 0. 83"

0. 8(0. 83") = 0. 66" NO CAMBER Post Composite Strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚 𝑃𝑢 = (1. 2(76. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(100 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 36 𝑓𝑡 𝑃𝑢 = 108. 88 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

=

108.88 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

= 653. 28 𝐾𝑖𝑝 · 𝑓𝑡

1 stud/ft Σ𝑄𝑛 = 24/2 * (17. 1 𝐾𝑖𝑝𝑠) = 205. 2 𝐾𝑖𝑝𝑠 𝐿

𝑏

𝑏𝑒𝑓𝑓 = 𝑚𝑖𝑛( 8 , 20 ) = 𝑚𝑖𝑛(

24 𝑓𝑡 , 8

36 𝑓𝑡 ) 2

= 36 𝑖𝑛

33

𝑎=

Σ𝑄𝑛

=

0.85𝑓𝑐'𝑏𝑒𝑓𝑓

205.2 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(36𝑖𝑛)

𝑎

𝑌2 = 𝑡 − 2 = 6. 25" −

= 2. 235 𝑖𝑛

2.235 𝑖𝑛 2

= 5. 13 𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-18 Use Σ𝑄𝑛 = 192 𝐾𝑖𝑝𝑠, 𝑌2 = 5" ϕ𝑏𝑀𝑝 = 416 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑝 ≤ 𝑀𝑚𝑎𝑥 Upsize Beam to W21x44 and Increase to 2 studs/ft Σ𝑄𝑛 = 24 * (17. 1 𝐾𝑖𝑝𝑠) = 410. 4 𝐾𝑖𝑝𝑠 𝑎=

Σ𝑄𝑛

=

0.85𝑓𝑐'𝑏𝑒𝑓𝑓

410.4 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(36𝑖𝑛)

𝑎

𝑌2 = 𝑡 − 2 = 6. 25" −

= 4. 47 𝑖𝑛

4.47 𝑖𝑛 2

= 4 𝑖𝑛

AISC Table 3-18; Use Σ𝑄𝑛 = 358 𝐾𝑖𝑝𝑠, 𝑌2 = 4" ϕ𝑏𝑀𝑝 = 607 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑝 ≤ 𝑀𝑚𝑎𝑥 Upsize Beam to W21x48 and Increase to 3 studs/ft Σ𝑄𝑛 = 𝑎=

3(24) 2

* (17. 1 𝐾𝑖𝑝𝑠) = 615. 6 𝐾𝑖𝑝𝑠

Σ𝑄𝑛

=

0.85𝑓𝑐'𝑏𝑒𝑓𝑓 𝑎

615.6 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(36𝑖𝑛)

= 6. 7 𝑖𝑛

6.7 𝑖𝑛 2

= 2. 9 𝑖𝑛

𝑌2 = 𝑡 − 2 = 6. 25" −

AISC Table 3-18; Use Σ𝑄𝑛 = 530, 𝑌2 = 2. 5", 𝑌2 = 3" 𝑌2 = 2. 5": 643 𝐾 · 𝑓𝑡 , 𝑌2 = 3": 662 𝐾 · 𝑓𝑡 662−643 (2. 9 − 2. 5) + 643 = 658. 2 𝐾 · 𝑓𝑡 3−2.5

𝑌2 = 2. 9":

ϕ𝑏𝑀𝑝 = 658. 2 𝐾𝑖𝑝 · 𝑓𝑡 ≥ 𝑀𝑚𝑎𝑥 = 653. 28 𝐾𝑖𝑝 · 𝑓𝑡 Camber 3

∆𝑆𝑊 =

3

𝑃𝐿 48𝐸𝐼

=

24.92 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(959 𝑖𝑛 )

= 0. 45"

0. 8(0. 45") = 0. 36" NO CAMBER AISC Table 3-19; Use Σ𝑄𝑛 = 530, 𝑌2 = 2. 5" 4

𝐼𝐿𝐵 = 1950 𝑖𝑛

Deflection LL only: 𝑃 = 100 𝑃𝑆𝐹 * 24 𝑓𝑡 * 36 𝑓𝑡 = 86. 4 𝐾𝑖𝑝𝑠 3

∆𝐿𝐿 =

𝑃𝐿 48𝐸𝐼

3

=

86.4 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(1950 𝑖𝑛 )

= 0. 76" ≤ 34

24*12 𝑖𝑛 720

= 0. 4"

3

𝐼𝐿𝐵,𝑟𝑒𝑞 =

𝑃𝐿 48𝐸𝐼

3

=

4

86.4 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛) 48(29000 𝐾𝑆𝐼)(0.4")

= 3706. 74 𝑖𝑛

Upsize Beam to W24x84 and 2 studs/ft AISC Table 3-19; Use Σ𝑄𝑛 = 308, Σ𝑄𝑛 = 425, 𝑌2 = 4" 𝐼𝐿𝐵 =

4 4 4000−3640 (410. 4 − 308) + 3640 = 3955 𝑖𝑛 ≥ 3706. 74 𝑖𝑛 425−308 3

∆𝐿𝐿 =

3

𝑃𝐿 48𝐸𝐼

=

86.4 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

= 0. 375" ≤

4

48(29000 𝐾𝑆𝐼)(3955 𝑖𝑛 )

24*12 𝑖𝑛 720

= 0. 4"

12*24 𝑖𝑛 240

= 1. 2"

DL Post-Composite: 𝑃 = 19 𝑃𝑆𝐹 * 24𝑓𝑡 * 36 𝑓𝑡 = 16. 42 𝐾𝑖𝑝𝑠 3

𝑃𝐿

∆𝐷𝐿, 𝑃𝐶 = 48𝐸𝐼 =

3

16.42 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(3955 𝑖𝑛 )

= 0. 07"

∆𝑇𝑜𝑡𝑎𝑙 = 0. 45" + 0. 07" + 0. 375" = 0. 895" ≤ W24x84 w/ (48) studs Exterior Girder

𝐴𝑇 = 12𝑓𝑡 * 36/2 𝑓𝑡 = 216 𝑓𝑡

2

Pre-composite 𝑞𝑠𝑤 = 𝑞𝑠𝑙𝑎𝑏 + 𝑞𝑑𝑒𝑐𝑘 + 𝑞𝑏𝑒𝑎𝑚 = 49. 7 𝑃𝑆𝐹 + 8 𝑃𝑆𝐹 = 57. 7 𝑃𝑆𝐹 𝑞𝐿𝐿, 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20 𝑃𝑆𝐹 Post Composite 𝑞𝐷𝐿 = 𝑞𝑠𝑤 + 𝑞𝑆𝐼𝐷𝐿 = 57. 7 𝑃𝑆𝐹 + 19 𝑃𝑆𝐹 = 76. 7 𝑃𝑆𝐹 𝑞𝐿𝐿 = 125 𝑃𝑆𝐹

35

𝑊𝑤 = 1. 2(15 𝑃𝑆𝐹 * 13 𝑓𝑡) = 234 𝑃𝐿𝐹 𝑊𝑡𝑜𝑡𝑎𝑙 = 234 𝑃𝐿𝐹 + 1. 2(76. 7 𝑃𝑆𝐹 * 1 𝑓𝑡) + 1. 6(125 𝑃𝑆𝐹 * 1 𝑓𝑡) = 526. 04 𝑃𝐿𝐹 Pre-composite strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) *

𝐿𝑏𝑒𝑎𝑚 2

𝑃𝑢 = (1. 2(57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(20 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 21865 𝑙𝑏𝑠 = 21. 87 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

2

+

𝑤𝐿 8

=

21.87 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

+

526.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

= 131. 19 + 37. 87𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 169. 06 𝐾𝑖𝑝 · 𝑓𝑡 𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 AISC Table 3-2 Select W21x44 ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 67)[358 𝐾𝑖𝑝𝑠 − 16. 8(12 𝑓𝑡 − 4. 45 𝑓𝑡)] ≤ 358 𝐾𝑖𝑝𝑠 386. 03 𝐾𝑖𝑝𝑠 ≥ 358 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 = 358 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥 𝑃 = 57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 12. 46 𝐾𝑖𝑝𝑠 3

∆𝑆𝑊 =

𝑃𝐿 48𝐸𝐼

3

=

12.46 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(843 𝑖𝑛 )

= 0. 25"

NO CAMBER Post Composite Strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚/2 𝑃𝑢 = (1. 2(76. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(125 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 63. 08 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

2

+

𝑤𝐿 8

=

63.08 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

+

526.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 416. 35 𝐾𝑖𝑝 · 𝑓𝑡 1 stud/ft Σ𝑄𝑛 = 24/2 * (17. 1 𝐾𝑖𝑝𝑠) = 205. 2 𝐾𝑖𝑝𝑠 𝐿

𝑏

𝑏𝑒𝑓𝑓 = 12" + 𝑚𝑖𝑛( 8 , 20 ) = 12" + 𝑚𝑖𝑛( 𝑎=

Σ𝑄𝑛 0.85𝑓𝑐'𝑏𝑒𝑓𝑓 𝑎

=

205.2 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(48𝑖𝑛)

𝑌2 = 𝑡 − 2 = 6. 25" −

1.67 𝑖𝑛 2

24 𝑓𝑡 , 8

36 𝑓𝑡 ) 2

= 1. 67 𝑖𝑛 = 5. 41 𝑖𝑛 → 𝑌2 = 5" 36

= 48 𝑖𝑛

AISC Table 3-18 Use Σ𝑄𝑛 = 163 𝐾𝑖𝑝𝑠, 𝑌2 = 5" ϕ𝑏𝑀𝑝 = 518 𝐾𝑖𝑝 · 𝑓𝑡 AISC Table 3-19 𝐼𝐿𝐵 = 1460 𝑖𝑛

4

Check Deflection LL only: 𝑃 = 125 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 27 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐿 = 125 𝑃𝐿𝐹 * 12000 𝑖𝑛 = 0. 010 𝐾𝑖𝑝/𝑖𝑛 4

5𝑤𝐿𝐿

3

𝑃𝐿 48𝐸𝐼

∆𝐿𝐿 =

3

+ 384𝐸𝐼 =

4

27 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

+

4

48(29000 𝐾𝑆𝐼)(1460𝑖𝑛 )

5*0.010 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛)

4

384(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

= 0. 32" ≤ 3/8"

DL Post-Composite: 𝑃 = 19 𝑃𝑆𝐹 * 12𝑓𝑡 * 18 𝑓𝑡 = 8. 21 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐷 = (15 𝑃𝑆𝐹 * 13 𝑓𝑡 + 76. 7𝑃𝐿𝐹) * 12000 𝑖𝑛 = 0. 023 𝐾𝑖𝑝/𝑖𝑛 4

5𝑤𝐷𝐿

3

∆𝐷𝐿, 𝑃𝐶 =

𝑃𝐿 48𝐸𝐼

+

3

= 384𝐸𝐼

8.21 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

4

+

Total Deflection ∆𝐷𝐿, 𝑃𝐶 + ∆𝐿𝐿 + ∆𝑆𝑊 = 0. 36" + 0. 32" + 0. 25" ∆𝑇𝑜𝑡𝑎𝑙 = 0. 93" ≤

12*24 𝑖𝑛 240

OK

= 1. 2"

W21x44 w/ (24) studs Special Exterior Girder 𝐴𝑇 = 0 𝑓𝑡

2

Loading Exterior Wall = 15 𝑃𝑆𝐹 * 19 𝐹𝑇 = 285 𝑃𝐿𝐹 Deflection (there is no live loading) 4

5𝑤𝐿 384𝐸𝐼

∆𝑚𝑎𝑥 =

𝐿

≤ 240 = 4

285

𝐼𝑟𝑒𝑞 =

24*12 240

5( 12*1000 )(24*12) 384(29000)(1.2)

= 1. 2" 4

= 61. 14 𝑖𝑛

4

AISC Table 3-3 Select W12x14;𝐼𝑥 = 88. 6 𝑖𝑛 ϕ𝑏𝑀𝑝𝑥 = 65. 3 𝐾𝑖𝑝 · 𝑓𝑡; Strength 2

𝑀𝑚𝑎𝑥 =

𝑤𝐿 8

2

=

285 𝑃𝐿𝐹 *( 24 𝑓𝑡) 8(1000)

= 20. 52 𝐾𝑖𝑝 · 𝑓𝑡

37

5*0.023 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛)

4

384(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

= 0. 36"

𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 ϕ𝑏𝑀𝑛 = 18. 6 𝐾𝑖𝑝 · 𝑓𝑡 × 1. 67 = 31. 06 𝐾𝑖𝑝 · 𝑓𝑡 ≤ ϕ𝑏𝑀𝑝𝑥 = 65. 3 𝐾𝑖𝑝 · 𝑓𝑡 ϕ𝑏𝑀𝑛 = 31. 06 𝐾𝑖𝑝 · 𝑓𝑡 ≥ 20. 52 𝐾𝑖𝑝 · 𝑓𝑡 W12x14 Lvl 2, Special Case: Girder

𝐴𝑇 = 12𝑓𝑡 * 36/2 𝑓𝑡 = 216 𝑓𝑡

2

Pre-composite 𝑞𝑠𝑤 = 𝑞𝑠𝑙𝑎𝑏 + 𝑞𝑑𝑒𝑐𝑘 + 𝑞𝑏𝑒𝑎𝑚 = 49. 7 𝑃𝑆𝐹 + 8 𝑃𝑆𝐹 = 57. 7 𝑃𝑆𝐹 𝑞𝐿𝐿, 𝐶𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛 = 20 𝑃𝑆𝐹 Post Composite 𝑞𝐷𝐿 = 𝑞𝑠𝑤 + 𝑞𝑆𝐼𝐷𝐿 = 57. 7 𝑃𝑆𝐹 + 19 𝑃𝑆𝐹 = 76. 7 𝑃𝑆𝐹 𝑞𝐿𝐿 = 125 𝑃𝑆𝐹 𝑊𝑡𝑜𝑡𝑎𝑙 = 1. 2(76. 7 𝑃𝑆𝐹 * 1 𝑓𝑡) + 1. 6(125 𝑃𝑆𝐹 * 1 𝑓𝑡) = 292. 04 𝑃𝐿𝐹 Pre-composite strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) *

𝐿𝑏𝑒𝑎𝑚 2

38

𝑃𝑢 = (1. 2(57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(20 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 21865 𝑙𝑏𝑠 = 21. 87 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

2

+

𝑤𝐿 8

=

21.87 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

+

292.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

= 131. 19 + 21. 03 𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 152. 22 𝐾𝑖𝑝 · 𝑓𝑡 𝐿𝑏 = 12𝑓𝑡 𝐶𝑏 = 1. 67 AISC Table 3-2 Select W21x44 ϕ𝑏𝑀𝑛 = 𝐶𝑏[ϕ𝑏𝑀𝑝𝑥 − ϕ𝑏𝐵𝐹(𝐿𝑏 − 𝐿𝑝)] ≤ ϕ𝑏𝑀𝑝𝑥 (1. 67)[358 𝐾𝑖𝑝𝑠 − 16. 8(12 𝑓𝑡 − 4. 45 𝑓𝑡)] ≤ 358 𝐾𝑖𝑝𝑠 386. 03 𝐾𝑖𝑝𝑠 ≥ 358 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 = 358 𝐾𝑖𝑝𝑠 ϕ𝑏𝑀𝑝𝑥 ≥ 𝑀𝑚𝑎𝑥 𝑃 = 57. 7 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 12. 46 𝐾𝑖𝑝𝑠 3

∆𝑆𝑊 =

𝑃𝐿 48𝐸𝐼

3

=

12.46 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(843 𝑖𝑛 )

= 0. 25"

NO CAMBER Post Composite Strength 𝑃𝑢 = (1. 2𝐷𝐿 + 1. 6𝐿𝐿) * 𝐿𝑏𝑒𝑎𝑚/2 𝑃𝑢 = (1. 2(76. 7 𝑃𝑆𝐹 * 12 𝑓𝑡) + 1. 6(125 𝑃𝑆𝐹 * 12 𝑓𝑡)) * 18 𝑓𝑡 𝑃𝑢 = 63. 08 𝐾𝑖𝑝𝑠 𝑀𝑚𝑎𝑥 =

𝑃𝐿 4

2

+

𝑤𝐿 8

=

63.08 𝐾𝑖𝑝𝑠 * 24 𝑓𝑡 4

2

+

292.04 𝑃𝐿𝐹*(24𝑓𝑡) 8000

𝐾𝑖𝑝 · 𝑓𝑡

𝑀𝑚𝑎𝑥 = 399. 51 𝐾𝑖𝑝 · 𝑓𝑡 1 stud/ft Σ𝑄𝑛 = 24/2 * (17. 1 𝐾𝑖𝑝𝑠) = 205. 2 𝐾𝑖𝑝𝑠 𝐿

𝑏

𝑏𝑒𝑓𝑓 = 12" + 𝑚𝑖𝑛( 8 , 20 ) = 12" + 𝑚𝑖𝑛( 𝑎=

Σ𝑄𝑛 0.85𝑓𝑐'𝑏𝑒𝑓𝑓

=

205.2 𝐾𝑖𝑝𝑠 0.85(3𝐾𝑆𝐼)(48𝑖𝑛)

𝑎

𝑌2 = 𝑡 − 2 = 6. 25" −

1.67 𝑖𝑛 2

24 𝑓𝑡 , 8

36 𝑓𝑡 ) 2

= 1. 67 𝑖𝑛 = 5. 41 𝑖𝑛 → 𝑌2 = 5"

AISC Table 3-18 Use Σ𝑄𝑛 = 163 𝐾𝑖𝑝𝑠, 𝑌2 = 5" ϕ𝑏𝑀𝑝 = 518 𝐾𝑖𝑝 · 𝑓𝑡 AISC Table 3-19

39

= 48 𝑖𝑛

𝐼𝐿𝐵 = 1460 𝑖𝑛

4

Check Deflection LL only: 𝑃 = 125 𝑃𝑆𝐹 * 12 𝑓𝑡 * 18 𝑓𝑡 = 27 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐿 = 125 𝑃𝐿𝐹 * 12000 𝑖𝑛 = 0. 010 𝐾𝑖𝑝/𝑖𝑛 4

5𝑤 𝐿

3

∆𝐿𝐿 =

𝑃𝐿 48𝐸𝐼

𝐿 + 384𝐸𝐼 =

3

4

27 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

+

4

48(29000 𝐾𝑆𝐼)(1460𝑖𝑛 )

5*0.010 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛)

4

384(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

= 0. 32" ≤ 3/8"

DL Post-Composite: 𝑃 = 19 𝑃𝑆𝐹 * 12𝑓𝑡 * 18 𝑓𝑡 = 8. 21 𝐾𝑖𝑝𝑠 1 𝐾𝑖𝑝

𝑤𝐷 = 76. 7𝑃𝐿𝐹 * 12000 𝑖𝑛 = 0. 0064 𝐾𝑖𝑝/𝑖𝑛 4

3

∆𝐷𝐿, 𝑃𝐶 =

𝑃𝐿 48𝐸𝐼

+

5𝑤𝐷𝐿

= 384𝐸𝐼

3

8.21 𝐾𝑖𝑝𝑠*(24*12 𝑖𝑛)

4

48(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

4

+

5*0.0064 𝐾𝑖𝑝/𝑖𝑛(24*12 𝑖𝑛)

Total Deflection ∆𝐷𝐿, 𝑃𝐶 + ∆𝐿𝐿 + ∆𝑆𝑊 = 0. 33" + 0. 32" + 0. 25" ∆𝑇𝑜𝑡𝑎𝑙 = 0. 91" ≤

12*24 𝑖𝑛 240

= 1. 2"

OK

W21x44 w/ (24) studs

5. Connection Design 5.1. Typical Beam to Girder Connection at Roof level

𝐿 = 15. 9" − 2(2") = 11. 9" → 11. 5" AISC Table 10-10a 𝑙 = 11. 5" , 𝑛 = 4 𝑉𝑢 = 11. 46 𝐾𝑖𝑝𝑠 (𝑖𝑛𝑐. 2) USE ¼” Plate w/ ¾” bolts & 3/16” weld

40

4

384(29000 𝐾𝑆𝐼)(1460 𝑖𝑛 )

= 0. 33"

Check beam web for block shear

𝑙𝑒ℎ = 1. 5" 2

𝐴𝑛𝑡 = (𝑙𝑒ℎ − Ø/2)𝑡𝑤 = (1. 5" − (3/4" + 1/16")/2)(0. 275") = 0. 30 𝑖𝑛 2

𝐴𝑔𝑣 = 𝑙𝑡𝑤 = 11. 25" * 0. 275" = 3. 09 𝑖𝑛 𝐴𝑛𝑣 = (𝑙 − (𝑛 − 0. 5)(Ø/2))𝑡𝑤

𝐴𝑛𝑣 = (11. 25" − (3. 5")( (3/4" + 1/16")/2)))(0. 275")) = 2. 70 𝑖𝑛

2

2

0. 6𝐹𝑦𝐴𝑔𝑣 = 0. 6(50 𝐾𝑆𝐼)(3. 09 𝑖𝑛 ) = 92. 7 𝑘𝑖𝑝𝑠 2

0. 6𝐹𝑢𝐴𝑛𝑣 = 0. 6(65 𝐾𝑆𝐼)(2. 70 𝑖𝑛 ) = 105. 3 𝑘𝑖𝑝𝑠 ϕ𝑅𝑛 = 0. 75(0. 6𝐹𝑦𝐴𝑔𝑣 + 𝑈𝑏𝑠𝐹𝑢𝐴𝑛𝑡) = 0. 75(92. 7 𝑘𝑖𝑝𝑠 + (1)19. 5 𝐾𝑖𝑝𝑠)) ϕ𝑅𝑛 = 84. 15 𝑘𝑖𝑝𝑠 ϕ𝑅𝑛 ≥ 𝑉𝑢

OK

5.2. Typical Girder to Column Connection at Office Level

3" 1

12"

41

Single Plate Connection using: ⅞” Diameter A325-N BOLTS 𝐹𝑦 = 36 𝑘𝑠𝑖 7

Girder: W18x35 ; 𝑡𝑓 = 16 " Shear Demand: 𝑉𝑢 = 35. 62 𝑘𝑖𝑝𝑠 (Typical Girder Calcs) 3

7

1

𝐿 = 17 4 " − 2( 16 ") = 16. 875" → 14 2 " AISC Table 10-10a 1

𝐿 = 16. 875" → 14 2 " N=5 1

Plate Thickness = 4 " USE ¼” Plate w/ ¾” bolts & 3/16” weld

6. Secondary Steel – Wind Girt Design 6.2. Loading Load Type

Loading (PLF)

Exterior Wall

71.3

Out of Plane Wind (Ultimate)

570

6.3. Final HSS Design HSS Size Wind Girt

HSS16x4x3/16

42

6.4. D-3 Column Check 6.4.1. Loading Load Type

Loading

Live Axial Load

79.3 Kips

Dead Axial Load

193.7 Kips

Out of plane Wind Load

13.68 Kips

6.4.2. Final D-3 Column Design D-3 Column Initial Column

W12x53

Final Column

W12x65

7. Steel Member Take-Off 7.1. Columns Column

Top Section

Length (ft)

Weight (lbs)

Middle Section

Length Weight (ft) (lbs)

Bottom Section

Length (ft)

Weight (lbs)

A-1

W8x31

39

1209

W8x48

33

1584

W10x49

23

1127

A-2

W8x31

39

1209

W12x53

33

1749

W12x65

23

1495

A-3

W8x31

39

1209

W12x53

33

1749

W12x65

23

1495

A-4

W8x31

39

1209

W12x53

33

1749

W12x65

23

1495

A-5

W8x31

39

1209

W8x48

33

1584

W10x49

23

1127

B-1

W8x31

39

1209

W10x54

33

1782

W12x65

23

1495

B-2

W8x31

39

1209

W12x65

33

2145

W14x132

23

3036

B-3

W8x31

39

1209

W12x65

33

2145

W14x132

23

3036

43

Column

Top Section

Length (ft)

Weight (lbs)

Middle Section

Length Weight (ft) (lbs)

Bottom Section

Length (ft)

Weight (lbs)

B-4

W8x31

39

1209

W12x65

33

2145

W14x132

23

3036

B-5

W8x31

39

1209

W10x54

33

1782

W12x65

23

1495

C-1

W8x31

39

1209

W10x54

33

1782

W12x65

23

1495

C-2

W8x31

39

1209

W10x49

33

1617

W10x54

23

1242

C-3

W8x31

39

1209

W10x49

33

1617

W10x49

23

1127

C-4

W8x31

39

1209

W10x49

33

1617

W10x54

23

1242

C-5

W8x31

39

1209

W10x54

33

1782

W12x65

23

1495

D-1

W8x31

39

1209

W8x48

33

1584

W10x49

23

1127

D-2

W8x31

39

1209

W12x53

33

1749

W12x58

23

1334

D-3

W8x31

39

1209

W12x65

33

2145

W12x65

23

1495

D-4

W8x31

39

1209

W12x53

33

1749

W12x58

23

1334

D-5

W8x31

39

1209

W8x48

33

1584

W10x49

23

1127

Total Weight (lbs)

Weight (Tons)

Cost/Ton

Cost of Steel

Number of Splices

Cost/Splice

Cost of Splices

Total Cost

90548

45.274

$6000

$271644

60

$2000

$120000

$391644

Length (ft)

Weight (lbs)

7.2. Beams

Beam Size

Location

Quantity

Total Weight (lbs)

39

43524

Roof W16x31

Interior/Exterior

36

1116

Typical Floor

44

W16x31

Interior

36

1116

21

23436

W18x40

Exterior

36

1440

6

8640

Floor 2 W16x31

Atruim

36

1116

2

2232

W21x73

Interior

36

2628

16

42048

W33x152

Exterior

36

5472

6

32832

Total Weight (lbs)

Weight (Tons)

Cost/Ton

Cost of Steel

152712

76.36

$6000

$458160

45

7.3. Girders

Beam Size

Location

Length (ft)

Weight (lbs)

Quantity

Total Weight (lbs)

16

13440

Roof W18x35

Interior/Exterior

24

840

Typical Floor W16x31

Exterior

24

744

8

5952

W16x40

Interior

24

960

8

7680

Floor 2 W12x14

Atrium Exterior

24

336

2

672

W21x44

Exterior/Interior Atrium

24

1056

8

8448

W24x84

Interior

24

2016

6

12096

Total Weight (lbs)

Weight (Tons)

Cost/Ton

Cost of Steel

48288

24.14

$6000

$144864

Member

Member Size

Nominal Weight (lb/ft)

Cost

Wind Girt

HSS16x4x3/16

24.73

$3,561.12

7.4. Wind Girt

7.5. Total Cost Colum cost

Beam Cost

Girder Cost

Wind Grit Cost

Total Cost

$391,644

$458,160

$144,864

$3,561.12

$998,229.12

46