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