B08_Att_8_Combined_Design_Calcs_FOSU_318708-322870.pdf

REPLACE AND REHABILITATE DOCKS AT

FORT SUMTER, FORT MOULTRIE AND

LIBERTY SQUARE

FORT SUMTER AND FORT MOULTRIE

NATIONAL HISTORICAL PARK

FOSU PMIS NO. 318708 / 322870

DESIGN CALCULATIONS

File No. 2983-22.02

Sheet 1 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

PROBLEM STATEMENT & OBJECTIVE

EXECUTIVE SUMMARY

CODES AND REFERENCES

1. Contract Documents

2. Latest South Carolina Building Code

3. IBC International Building Code, 2021

4. Ft. Sumter and Ft. Moultrie Geotechnical Report, 6/23/2023

5. ACI 318 Building Code Requirements for Structural Concrete, Latest Edition

6. AISC Steel Construction Manual, Latest Edition

7. PCI Design Manual, Latest Edition

8. ASCE 7-16 Minimum Design Loads and Associated Criteria for Buildings and Other Structures

9. AISC 61-14 Seismic Design of Piers and Wharves

10. AISC Manual of Steel Construction, Latest Edition

11. AITC American Institute of Timber construction 6th with NDS 2018

12. UFC 4-152-01 Unified Facilities Criteria Design: Piers and Wharves

13. FHWA Project Development and Design Manual

14. PIANC 2002 and Shibata Design Manuals (for berthing force design)

CONSIDERATIONS

3. Per Reference 4, during a seismic event, the effects of pile lateral spreading due to soil liquifaction will be fully mitigated by supporting the piers and fenders on deep foundations into the local Cooper Marl layer. In addition, per Reference 4, as long as Section

11.4.8 of ASCE 7-16 (Reference 8), exceptions 1 and 3 are satisfied, a site specific ground motion hazard analysis is not required.

Specifically, Exception 3 requires that the "Equivalent static force procedure" must be used. Therefore, this calculation uses a static force procedure for sesimic loading of the pier structure.

4. The seismic design procedures pertaining to piers open to the general public are directed to ASCE 7-16 (Ref. 8). The seismic coefficients (R values) presented do not specifically address the unique condition of battered pile supports on a pier type structure.

ASCE 61-14 (Ref. 9) contains design procedures that directly relate to pier structures, but only to pier structures that are not open to the public. UFC 4-152-01 (Reference 12) requires that piers be designed to ASCE 61-14 procedures (noting that military facilities are not "open" to the general public). Faced with this situation, this design will follow the procedures for seismic design based on ASCE 61- 14, as they are more appropriate to pier structures supported by battered piles. Using a "forced based design", the pier structure design will consider a "Design Earthquake" (DE) level to ensure life safety and prevent collapse of the structure. At this level, the structural design factor of safety is reduced to 1, and will include detailing that allows the structure to resist the anticipated sesimic loading. In addition, the pile bearing factor of safety in compression and tension will be reduced from 2.5 for service loads to typically 1.5 for seismic loading, and to 1.3 for the most highly loaded piles during a seismic event.

This calculation provides the design of a new proposed pier for Ft. Sumter, including the precast concrete deck, cast in place deck sections, cast in place concrete pile caps, steel fender piles, and pre stressed concrete piles.

The new proposed pier design utilizes straight and battered 16" square pre stressed concrete piles attached to cast in place concrete pile caps to support 9" thick pre cast concrete deck planks with a 2" thick concrete topping. Three sections of the deck will be fabricated with and 11 " cast in place concrete. The pier consists of a 12 foot wide 330 foot long approach span which leads to a 130 foot long "T" pier. The two sections are separated by an expansion joint. The "T" pier steel fender units are separate from the pier and are designed to resist berthing and mooring loadings from various ferrys. Per code, the pier is designed to resist seismic loading based on a force based design (FBD) based on surviving a Life Safety design event (DE).

1. Precast non prestressed concrete 9" thick planks were chosen to reduced the amount of field fabrication and shoring as compared to cast in place decking. The three locations where cast in place concrete decking was employed was due to unique loading and geometry conditions. The amount of rebar in the deck planks was determined in part by considering corrosion. In order to reduce the long term effects of corrosion, the stresses in the rebar are kept low to reduce the potential crack size. In addition, all structural concrete members have 3 inches of cover.

2. Cracking due to concrete shrinkage is reduced by using pre cast planks. Temperature expansion and contraction is considered to be mitigated by the fact that the structure is located over water, where the temperature differential is greatly reduced. In addition, the lengths of the approach pier and the T pier sections are modest. Therefore the effects of temperature induced expansion and contraction, and the subsequent stresses associated are considered to be minimal.

CALCULATIONS

FOSU

Ft. Sumter Pier

Pier Replacement NBS

Sheet 2 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

CONSIDERATIONS (Continued)

5. Deck uniform allowable live load = 100 psf.

6. Deck allowable Concentrated load = 4000 lbs (Equivalent to H5 axle loading = 8000 lbs).

7. Vessel berthing forces are based on a 270 LT Ferry with a berthing velocity of 2 ft/s for the primary 4 cone fenders, and 1.5 ft/s for the smaller 2 cone fenders located directly in front of the pier. Note that berthing forces are not directed into the pier structure.

8. The fender frame "panel" and chain system will be designed by others as is not part of this calculation.

9. Mooring forces are based on a sustained wind speed of 25 knots with gusts up to 35 knots. It is expected that vessels will not be moored at higher wind speeds. All cleats are designed to resist loads based on the aforementioned wind speeds.

10. Required axial forces, moments and pile lengths are presented in the calculation fort both service loads and seismic loads.

The design of the prestressed concrete piles will be finalized by the pile fabricator, and verified by the EOR.

CALCULATIONS

CONCLUSION

Note: STAAD model files available upon request.

The calculation uses simple hand calcs and Excel spreadsheets, with the addition of STAAD software to model pile cap and pile loadings. All concrete design is based on LRFD procedures and References 5 and 7). Note that the pre cast concrete planks are also designed with reference to older "allowable stress" concrete design techniques that provide a clear picture of the level of cracking (and hence corrosion resistance) in the planks.

The proposed pier structure and fender units at Ft. Sumter are adequate for all service loads as well as seismic loading. The design also takes into account concerns related to corrosion by maintaining adequate concrete cover (3") and keeping stresses in the concrete under dead load and service loads to minimum levels to help reduce concrtete cracking.

CALCULATIONS

FOSU

Pier Replacement NBS

Sheet 3 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

16" square concrete prestressed pile b = 16 in f'c = 5000 psi

Ec = 4030509 psi

I = 5461.333 in4 z = 0.42 Fixed head adjustment per ASCE 61-14 Table 5-2

T determined using L-Pile load/deflection curves: Deflections and lateral shear loads from Ref. 1

Fixed head: Free head:

P = 1900 lbs P = Lateral load P = 300 lbs P = Lateral load

D = 1 in D = Deflection D = 1 in D = Deflection m = 4.92228 lbs/in m = P/386 m = 0.777202 lbs/in m = P/386 k = 1900 lbs/in k = P/D k = 300 lbs/in k = P/D

T = 0.320 s T = 2p(m/k)1/2 T = 0.320 s T = 2p(m/k)1/2

P = 3100 lbs P = Lateral load P = 500 lbs P = Lateral load

D = 2 in D = Deflection D = 2 in D = Deflection m = 8.031088 lbs/in m = P/386 m = 1.295337 lbs/in m = P/386 k = 1550 lbs/in k = P/D k = 250 lbs/in k = P/D

T = 0.452 s T = 2p(m/k)1/2 T = 0.452 s T = 2p(m/k)1/2

T determined using a simple cantilever analogy:

The pile length to fixity is iterated to achieve the same deflection as the L-Pile analysis

The "z" factor is applied to EI for the fixed head condition

This analysis is used only as a secondary check to compare to the Geotech L-Pile analysis results.

fixed head free head

P = 1900 lbs P = Lateral load P = 300 lbs P = Lateral load

L = 388 in L = Length of pile to fixity L = 604 in L = Length of pile to fixity m = 4.92228 slugs m = P/386 m = 0.777202 slugs m = P/386

D = 1.000368 in D = PL3/(12zEcI) D = 1.001042 in D = PL3/(3zEcI) k = 1899.301 lb/in k = 12zEcI/L 3 = P/D k = 299.6877 lb/in k = 3zEcI/L

3 = P/D

T = 0.320 s T = 2p(m/k)1/2 T = 0.320 s T = 2p(m/k)1/2 f = 3.13 Hz f = (121/2/(2p))(386zEcI/(PL3))1/2 f = 3.13 Hz f = (31/2/(2p))(386zEcI/(PL3))1/2

T = 0.320 s T = 1/f T = 0.320 s T = 1/f fixed head free head

P = 3100 lbs P = 500 lbs

L = 415 in L = 641 in m = 8.031088 slugs m = 1.295337 slugs

D = 1.997179 in D = 1.99418 in k = 1552.19 lb/in k = 250.7297 lb/in

T = 0.452 s T = 0.452 s f = 2.21 Hz f = 2.21 Hz

T = 0.452 s T = 0.452 s

CALCULATIONS

FOSU

Seismic

Sheet 4 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Note:

The L-pile analysis indicates that the depth to zero displacement is less for the free head condition.

It appears that the L-Pile analysis did not make a correction for the reduction in stiffness at the pile to pile cap interface for the fixed head condition.

Cast in place Planks:

L = 17.25 ft (16.25' clear span + 6" bearing distance each end)

LFD = 1.2

LFL = 1.6

h = 9 in d = 6.00 in 3" cover f'c = 5000 psi fv = 0.75 fVn = 7637 lbs/ft fVn = 2fvf'c 1/2(12)d wD = 137.50 psf wD = 150(2 +h)/12 h + 2" wearing surface

WD = 2371.88 lbs/ft WD = LwD Plank weight per foot of width with 2" topping

Uniform live loading:

wL = 100 psf wu = 325.00 lbs/ft wu = LFDwD + LFLwL

Ru = 2803.13 lbs/ft Ru = wuL/2

2803 < 7637 OK

FOSU

Ft. Sumter Pier

CALCULATIONS

Sheet 5 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

H5 wheel loading:

s = 4.98 ft s = 4 + 0.06(L - 1)

P = 4000 lbs/wheel

VuW = 1286.43 lbs/ft VuW = LFL(P/s) Wheel placed close to support

Ru = 2709.56 lbs/ft Ru = LFDWD/2 + VuW

2710 < 7637 OK

Ig = 729.00 in4 fr = 530.33 psi

Mcr = 7.16 ft-kips/ft

Uniform live loading:

MaD = 5.11 ft-kips/ft

MaD+L = 8.83 ft-kips/ft

MaD/Mcr = 0.71

MaD+L/Mcr = 1.23

Mu = 12.09 ft-kips/ft

H5 wheel loading:

MaD = 5.11 ft-kips/ft

MaD+P = 8.58 ft-kips/ft

MaD+P/Mcr = 1.20

Mu = 11.68 ft-kips/ft

From plank analysis:

12.09 < 21.7 OK #6 bars @ 6" spacing

FS = 1.3

y C T

14 144.2308 96.15385

36 384.6154 256.4103

Compression Load

335 0

335 40

CALCULATIONS

FOSU

Ft. Sumter Pier

Seismic

0 50 100 150 200 250 300 350 400 450

P ie l p en et ra ti o n in

C o o p er M at k

(f t)

Pile capacity (kips)

16" Concrete Pile Capacity (kips)

Compression

Tension

Load

Sheet 6 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

FS = 1.3

y C T

14 144.2308 96.15385

36 384.6154 256.4103

Tension Load

265 0

265 40

CALCULATIONS

FOSU

Ft. Sumter Pier

Seismic

0 50 100 150 200 250 300 350 400 450

P ie l p en et ra ti o n in

C o o p er M at k

(f t)

Pile capacity (kips)

16" Concrete Pile Capacity (kips)

Compression

Tension

Load

Sheet 7 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

16" Square Concrete Pile D = The depth the pile must penetrate into the Cooper Marl layer

FS = 1.3

ELCM = -64 Elevation of the top of the Cooper Marl layer ft kips kips Pile

D PC PT Tip EL

14 144 96 -78

15 155 103 -79

16 166 111 -80

17 177 118 -81

18 188 125 -82

19 199 133 -83

20 210 140 -84

21 221 147 -85

22 232 154 -86

23 243 162 -87

24 253 169 -88

25 264 176 -89

26 275 184 -90

27 286 191 -91

28 297 198 -92

29 308 205 -93

30 319 213 -94

31 330 220 -95

32 341 227 -96

33 352 235 -97

34 363 242 -98

35 374 249 -99

36 385 256 -100

37 396 264 -101

38 406 271 -102

39 417 278 -103

Pile Cap kips kips Pile Tip

Type C T EL (MLW)

1 242 182 -94

2 284 228 -101

3 52 0 -80

4 303 237 -102

5 309 243 -102

6 60 0 -80

7 334 267 -102 * FS = 1.3

8 328 265 -102 * FS = 1.3

9 183 125 -85

10 33 0 -80

11 123 106 -82

Non battered and 1:12 battered piles except on cap 11

C T EL

60 0 -80

FOSU

Ft. Sumter Pier

Sheet 8 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

16" Steel Pipe Piles D = The depth the pile must penetrate into the Cooper Marl layer

FS = 2.5

ELCM = -64 Elevation of the top of the Cooper Marl layer ft kips kips Pile

D PC PT Tip EL

17 74 49 -81

18 78 52 -82

19 82 55 -83

20 87 58 -84 16" SQUARE PRESTRESSED CONCRETE PILE DESIGN REQUIREMENTS

21 91 61 -85 PILE CAP AXIAL LOAD AXIAL LOAD TENSIONAXIAL LOAD COMP. MOMENT MINIMUM

22 95 64 -86 TYPE SERVICE SEISMIC SEISMIC SERVICE TIP ELEV.

23 100 67 -87 KIPS KIPS KIPS FT-KIPS MLW

24 104 69 -88 1 80 180 240 90 -94

25 109 72 -89 2 80 230 285 90 -101

26 113 75 -90 3 80 - - 90 -80

27 117 78 -91 4 80 235 305 90 -102

28 122 81 -92 5 80 240 310 90 -102

29 126 84 -93 6 80 - - 90 -80

30 130 87 -94 7 80 265 335 90 -102

31 135 90 -95 8 80 265 330 90 -102

32 139 93 -96 9 80 125 185 90 -85

33 144 96 -97 10 80 - - 90 -80

34 148 99 -98 11 80 110 125 90 -82

35 152 102 -99 1. NON BATTERED and 1:12 BATTERED PILES ON CAPS 2 TO 7 AND 10: TIP EL = -80

36 157 104 -100 2. CONCRETE COVER = 3"

37 161 107 -101

38 165 110 -102

39 170 113 -103

40 174 116 -104

41 179 119 -105

42 183 122 -106

43 187 125 -107

44 192 128 -108

45 196 131 -109

46 200 134 -110

CALCULATIONS

FOSU

Sheet 9 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Seismic Main Pier:

Reference 4: Fort Sumter and Fort Moultrie Geotechnical Report

Reference 9: ASCE 61-14

Reference 8: ASCE 7-16

Seismic Design

E Site class Conservatively considered as Soft clay soil Ref. 4, Table 3

Rc = I Risk Category Ref. 4, Table 3

Ss = 1.227 s Ref. 4, Table 3

S1 = 0.363 s Ref. 4, Table 3

Fa = 1.2 Ref. 4, Table 3

Fv = 2.548 Ref. 4, Table 3

SMS = 1.472 s SMS = FaSs Ref. 8, (11.4-1)

SM1 = 0.925 s SM1 = FvS1 Ref. 8, (11.4-2)

SDS = 0.982 s SDS = (2/3)SMS Ref. 8, (11.4-3)

SD1 = 0.617 s SD1 = (2/3)SM1 Ref. 8, (11.4-4)

TL = 6 s Ref. 8, Figure 22-14

PGA = 0.079 Ref. 8, Figure 22-9

Per Table 12.6-1, the Equivalent Lateral Force analysis Procedure is permitted (Section 12.8)

Ts = 0.628 s Ts = SD1/SDS

To = 0.126 s To = 0.2Ts

T = 0.452 s As determined from Ref. 1 pile analysis

0.452 < 6 Use Equation 12.8-3 also

R = 1 Table 5.1 ASCE 61-14

W = 1 Overstrength Factor Table 12.2-1

CD = 1 Deflection Amplification Factor Table 5.1 ASCE 61-14

Ie = 1 Importance Factor: Seismic Table 1.5-2

Cs1 = 0.982 Cs1 = SDS/(R/Ie) (12.8-2)

Cs2 = 1.364 Cs2 = SD1/[T(R/Ie)] (12.8-3)

Cs = 0.982 Cs = Minimum of SDS/(R/Ie) and SD1/[T(R/Ie)] Min. of (12.8-2) and (12.8-3) x = 130.25 ft x = Length of deck y = 24 ft y = Width of deck wD = 137.5 psf 9" Thick concrete deck + 2" wearing surface wL = 100 psf

WD = 461085.0 lbs WD = xy(wD + 0.1wL) Pier

WDp = 144000 lbs Pile caps

W = 605085.0 lbs W = WD + WDp Dead weight of structure for determining seismic forces

V = 593951 lbs V = CsW Lateral load at the top of braced frame (12.8-1)

CALCULATIONS

FOSU

Sheet 10 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Concrete Plank Deck Diaphragm Design:

The concrete deck system must be able to transfer seismic loads to the pile caps that have lateral load resistance.

There are 8 caps on the main pier with lateral capacity in the North/South direction.

They are spaced at 18.25 feet apart.

WD = 461085.0 lbs Main Pier

V = 452601 lbs V = CsWD Lateral load at the deck to cap interface.

Ldeck = 130.25 ft wv = 3474.9 lbs/ft wv = V/Ldeck x = 18.25 ft y = 24 ft

VR = 31708.1 lbs VR = wvx/2

M = 144668.4 ft-lbs M = wvx 2/8

C = T = 6289.9 lbs C = T = M/(y - 1) Chord Forces

For the chord tension force, use two #6 bars in the precast slab on the outshore face :

As = 0.44 in2 n = 2 nAs = 0.88 in2

Fy = 60000 psi fT = 0.9 fT = 47520.0 lbs fT = fnAsFy

47520.0 > 6289.9 OK

For shear at the end caps, use twelve #8 rebar dowels, cast into the cap and grouted into oversized pockets near the plank ends:

VR = 31708.1 lbs

As = 0.79 in2 n = 12 nAs = 9.48 in2

Fy = 60000 psi fV = 0.75 fV = 255960.0 lbs fV = 0.6fnAsFy

255960.0 > 31708.1 OK

From separate concrete shear breakout strength check, the anchor capacity is as follows:

fVn = 8270 lbs/anchor Concrete shear breakout strength (From separate calculation) nfVn = 99240.0 lbs

99240.0 > 31708.1 OK

Shear flow through plank side edge connectors:

s = 12.0 ft s = y/2 vf = 1981.8 lbs/ft vf = 6sVR(y - s)/y3 Shear flow at seam between adjacent planks z = 3.67 ft z = spacing between connectors

Vf = 7273.1 lbs/connector Vf = zvf

Ac = 84 in2/ft Ac = 12(h-2) h = 9" thick plank fv80Ac = 5040.0 lbs/ft

5040.0 > 1981.8 OK Shear strength of grouted shear key

FOSU

Ft. Sumter Pier

Seismic

CALCULATIONS

wv

C

T y x

Sheet 11 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

The edge shear connectors are 4"x3"x3/4" plates welded across the side of each adjacent plank: (Redundant to grouted key) t = 0.75 in b = 4 in

Fy = 36000 psi

A = 3.00 in2

Vall = 43200.00 lbs

43200.0 > 7273.1 OK Shear strength of grouted shear key

1/4" fillet weld:

f = 3708.00 lbs/inch f = 927(4) x = 12 in x = Length of weld fx = 44496.00 lbs

44496.0 > 7273.1 OK

Check four x 5/8" dia. A706 rebar anchors:

n = 4 # of bars

Fy = 60000 psi A706 weldable rebar

As = 0.31 in2 5/8" dia. rebar v = 1818.3 lbs/bar v = Vf/n fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs

9862.7 > 1818.3 OK

Note that for seismic loading in the East/West direction, the chord forces can be handled by the transverse bars in the plank near the ends, combined with the available tension capacity of the nearest to the plank end side connector.

V = 452601 lbs V = Cs(WD + WDc) n = 7 n = # of seismic lateral capacity pile cap secions x = 24 ft wv = 2694.1 lbs/ft wv = V/(nx) y = 18.25 ft

VR = 32328.6 lbs VR = wvx/2

M = 193971.9 ft-lbs M = wvx 2/8

C = T = 14639.4 lbs C = T = M/(y - 5) Chord Forces to the nearest side clip at plank ends

For the chord tension force, use two #4 bars in the precast slab adjacent to the nearest end side shear coupler :

As = 0.2 in2 n = 2 nAs = 0.40 in2

Fy = 60000 psi fT = 0.9 fT = 21600.0 lbs fT = fnAsFy

21600.0 > 14639.4 OK

Shear coupler:

fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs n = 2 n = # bars on one side of connection nfVn = 19725.3 lbs/connection

19725.3 > 14639.4 OK

Ft. Sumter Pier

Seismic

CALCULATIONS

FOSU

TT

Sheet 12 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Seismic Approach span:

Reference 4: Fort Sumter and Fort Moultrie Geotechnical Report

Reference 9: ASCE 61-14

Reference 8: ASCE 7-16

Seismic Design

E Site class Conservatively considered as Soft clay soil Ref. 4, Table 3

Rc = I Risk Category Ref. 4, Table 3

Ss = 1.227 s Ref. 4, Table 3

S1 = 0.363 s Ref. 4, Table 3

Fa = 1.2 Ref. 4, Table 3

Fv = 2.548 Ref. 4, Table 3

SMS = 1.472 s SMS = FaSs Ref. 8, (11.4-1)

SM1 = 0.925 s SM1 = FvS1 Ref. 8, (11.4-2)

SDS = 0.982 s SDS = (2/3)SMS Ref. 8, (11.4-3)

SD1 = 0.617 s SD1 = (2/3)SM1 Ref. 8, (11.4-4)

TL = 6 s Ref. 8, Figure 22-14

PGA = 0.079 Ref. 8, Figure 22-9

Per Table 12.6-1, the Equivalent Lateral Force analysis Procedure is permitted (Section 12.8)

Ts = 0.628 s Ts = SD1/SDS

To = 0.126 s To = 0.2Ts

T = 0.452 s As determined from Ref. 1 pile analysis

0.452 < 6 Use Equation 12.8-3 also

R = 1 Table 5.1 ASCE 61-14

W = 1 Overstrength Factor Table 12.2-1

CD = 1 Deflection Amplification Factor Table 5.1 ASCE 61-14

Ie = 1 Importance Factor: Seismic Table 1.5-2

Cs1 = 0.982 Cs1 = SDS/(R/Ie) (12.8-2)

Cs2 = 1.364 Cs2 = SD1/[T(R/Ie)] (12.8-3)

Cs = 0.982 Cs = Minimum of SDS/(R/Ie) and SD1/[T(R/Ie)] Min. of (12.8-2) and (12.8-3) x = 172.5 ft x = Length of plank deck y = 12 ft y = Width of deck wD = 137.5 psf 9" Thick concrete deck + 2" wearing surface wL = 100 psf

WD = 305325.0 lbs WD = xy(wD + 0.1wL) Pier

WDp = 187650 lbs Pile caps + cip sections

W = 492975.0 lbs W = WD + WDp Dead weight of structure for determining seismic forces

V = 483904 lbs V = CsW Lateral load at the top of braced frame (12.8-1)

CALCULATIONS

FOSU

Sheet 13 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Concrete Plank Deck Diaphragm Design:

The concrete deck system must be able to transfer seismic loads to the pile caps that have lateral load resistance.

There are 5 caps on the approach pier with lateral capacity in the East/West direction.

They are spaced at 37.5 feet apart with an intermediate cap at midspan, except for two caps at the finger pier where the east/west lateral load resistance caps are 18.75 feet apart.. The deck diaphragm at the midspan cap must be continuous.

W'D = 67850.0 lbs W'D = (2/9)WD Pier section load into worst case loaded pilecap

WDc = 25713 lbs Weight of cip deck section

V = 91841 lbs V = Cs(W'D + WDc) Lateral load at the deck to cap interface.

x = 37.5 ft wv = 2449.1 lbs/ft wv = V/Ldeck y = 12 ft

VR = 45920.7 lbs VR = wvx/2

M = 430506.8 ft-lbs M = wvx 2/8

C = T = 39137.0 lbs C = T = M/(y - 1) Chord Forces

For the chord tension force, use two #6 bars in the precast slab on the outshore face :

As = 0.44 in2 n = 2 nAs = 0.88 in2

Fy = 60000 psi fT = 0.9 fT = 47520.0 lbs fT = fnAsFy

47520.0 > 39137.0 OK Note that rebar couplers will be required at the intermediate pile cap

For shear at the end caps, use six #8 rebar dowels, cast into the cap and grouted into oversized pockets near the plank ends:

VR = 45920.7 lbs

As = 0.79 in2 n = 6 nAs = 4.74 in2

Fy = 60000 psi fV = 0.75 fV = 127980.0 lbs fV = 0.6fnAsFy

127980.0 > 45920.7 OK Note that rebar couplers will be required at the intermediate pile cap

From separate concrete shear breakout strength check, the anchor capacity is as follows:

fVn = 8270 lbs/anchor Concrete shear breakout strength (From separate calculation) nfVn = 49620.0 lbs

49620.0 > 45920.7 OK

Shear flow through plank side edge connectors:

s = 6.0 ft s = y/2 vf = 5740.1 lbs/ft vf = 6sVR(y - s)/y3 Shear flow at seam between adjacent planks z = 3.67 ft z = spacing between connectors

Vf = 21066.1 lbs/connector Vf = zvf

Ac = 84 in2/ft Ac = 12(h-2) h = 9" thick plank fv80Ac = 5040.0 lbs/ft

5040.0 < 5740.1 Added shear transfer required Shear strength of grouted shear key

FOSU

Ft. Sumter Pier

Seismic

CALCULATIONS

copy wv

C

T y x'

Sheet 14 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

The edge shear connectors are 4"x3"x3/4" plates welded across the side of each adjacent plank: (Redundant to grouted key) t = 0.75 in b = 4 in

Fy = 36000 psi

A = 3.00 in2

Vall = 43200.00 lbs

43200.0 > 21066.1 OK Shear strength of grouted shear key

1/4" fillet weld:

f = 3708.00 lbs/inch f = 927(4) x = 12 in x = Length of weld fx = 44496.00 lbs

44496.0 > 21066.1 OK

Check four x 5/8" dia. A706 rebar anchors:

n = 4 # of bars

Fy = 60000 psi A706 weldable rebar

As = 0.31 in2 5/8" dia. rebar v = 5266.5 lbs/bar v = Vf/n fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs

9862.7 > 5266.5 OK

Note that for seismic loading in the North/South direction, the chord forces can be handled by the transverse bars in the plank near the ends, combined with the available tension capacity of the nearest to the plank end side connector.

V = 91841 lbs V = Cs(W'D + WDc) x = 12 ft wv = 7653.5 lbs/ft wv = V/x y = 37.5 ft

VR = 45920.7 lbs VR = wvx/2

M = 137762.2 ft-lbs M = wvx 2/8

C = T = 4238.8 lbs C = T = M/(y - 5) Chord Forces to the nearest side clip at plank ends

For the chord tension force, use two #4 bars in the precast slab adjacent to the nearest end side shear coupler :

As = 0.2 in2 n = 2 nAs = 0.40 in2

Fy = 60000 psi fT = 0.9 fT = 21600.0 lbs fT = fnAsFy

21600.0 > 4238.8 OK

Shear coupler:

fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs n = 2 n = # bars on one side of connection nfVn = 19725.3 lbs/connection

19725.3 > 4238.8 OK

Ft. Sumter Pier

Seismic

CALCULATIONS

Sheet 15 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Seismic Approach span:

Reference 4: Fort Sumter and Fort Moultrie Geotechnical Report

Reference 9: ASCE 61-14

Reference 8: ASCE 7-16

Seismic Design

E Site class Conservatively considered as Soft clay soil Ref. 4, Table 3

Rc = I Risk Category Ref. 4, Table 3

Ss = 1.227 s Ref. 4, Table 3

S1 = 0.363 s Ref. 4, Table 3

Fa = 1.2 Ref. 4, Table 3

Fv = 2.548 Ref. 4, Table 3

SMS = 1.472 s SMS = FaSs Ref. 8, (11.4-1)

SM1 = 0.925 s SM1 = FvS1 Ref. 8, (11.4-2)

SDS = 0.982 s SDS = (2/3)SMS Ref. 8, (11.4-3)

SD1 = 0.617 s SD1 = (2/3)SM1 Ref. 8, (11.4-4)

TL = 6 s Ref. 8, Figure 22-14

PGA = 0.079 Ref. 8, Figure 22-9

Per Table 12.6-1, the Equivalent Lateral Force analysis Procedure is permitted (Section 12.8)

Ts = 0.628 s Ts = SD1/SDS

To = 0.126 s To = 0.2Ts

T = 0.452 s As determined from Ref. 1 pile analysis

0.452 < 6 Use Equation 12.8-3 also

R = 1 Table 5.1 ASCE 61-14

W = 1 Overstrength Factor Table 12.2-1

CD = 1 Deflection Amplification Factor Table 5.1 ASCE 61-14

Ie = 1 Importance Factor: Seismic Table 1.5-2

Cs1 = 0.982 Cs1 = SDS/(R/Ie) (12.8-2)

Cs2 = 1.364 Cs2 = SD1/[T(R/Ie)] (12.8-3)

Cs = 0.982 Cs = Minimum of SDS/(R/Ie) and SD1/[T(R/Ie)] Min. of (12.8-2) and (12.8-3) x = 134 ft x = Length of plank deck y = 12 ft y = Width of deck wD = 137.5 psf 9" Thick concrete deck + 2" wearing surface wL = 100 psf

WD = 237180.0 lbs WD = xy(wD + 0.1wL) Pier

WDp = 182700 lbs Pile caps + widened section

W = 419880.0 lbs W = WD + WDp Dead weight of structure for determining seismic forces

V = 412154 lbs V = CsW Lateral load at the top of braced frame (12.8-1)

CALCULATIONS

FOSU

Sheet 16 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Concrete Plank Deck Diaphragm Design:

The concrete deck system must be able to transfer seismic loads to the pile caps that have lateral load resistance.

There are 3 caps on the approach pier with lateral capacity in the East/West direction.

They are spaced at 37.5 feet apart with an intermediate cap at midspan. The deck diaphragm at the midspan cap must be continuous.

W'D = 67765.7 lbs W'D = (2/7)WD Pier section load into worst case loaded pilecap

V = 66519 lbs V = CsWD' Lateral load at the deck to cap interface.

x = 37.5 ft wv = 1773.8 lbs/ft wv = V/Ldeck y = 12 ft

VR = 33259.4 lbs VR = wvx/2

M = 311807.0 ft-lbs M = wvx 2/8

C = T = 28346.1 lbs C = T = M/(y - 1) Chord Forces

For the chord tension force, use two #6 bars in the precast slab on the outshore face :

As = 0.44 in2 n = 2 nAs = 0.88 in2

Fy = 60000 psi fT = 0.9 fT = 47520.0 lbs fT = fnAsFy

47520.0 > 28346.1 OK Note that rebar couplers will be required at the intermediate pile cap

For shear at the end caps, use six #8 rebar dowels, cast into the cap and grouted into oversized pockets near the plank ends:

VR = 33259.4 lbs

As = 0.79 in2 n = 6 nAs = 4.74 in2

Fy = 60000 psi fV = 0.75 fV = 127980.0 lbs fV = 0.6fnAsFy

127980.0 > 33259.4 OK Note that rebar couplers will be required at the intermediate pile cap

From separate concrete shear breakout strength check, the anchor capacity is as follows:

fVn = 8270 lbs/anchor Concrete shear breakout strength (From separate calculation) nfVn = 49620.0 lbs

49620.0 > 33259.4 OK

Shear flow through plank side edge connectors:

s = 6.0 ft s = y/2 vf = 4157.4 lbs/ft vf = 6sVR(y - s)/y3 Shear flow at seam between adjacent planks z = 3.67 ft z = spacing between connectors

Vf = 15257.8 lbs/connector Vf = zvf

Ac = 84 in2/ft Ac = 12(h-2) h = 9" thick plank fv80Ac = 5040.0 lbs/ft

5040.0 > 4157.4 OK Shear strength of grouted shear key

FOSU

CALCULATIONS

Ft. Sumter Pier

Seismic wv

C

T y

Sheet 17 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

The edge shear connectors are 4"x3"x3/4" plates welded across the side of each adjacent plank: (Redundant to grouted key) t = 0.75 in b = 4 in

Fy = 36000 psi

A = 3.00 in2

Vall = 43200.00 lbs

43200.0 > 15257.8 OK Shear strength of grouted shear key

1/4" fillet weld:

f = 3708.00 lbs/inch f = 927(4) x = 12 in x = Length of weld fx = 44496.00 lbs

44496.0 > 15257.8 OK

Check four x 5/8" dia. A706 rebar anchors:

n = 4 # of bars

Fy = 60000 psi A706 weldable rebar

As = 0.31 in2 5/8" dia. rebar v = 3814.4 lbs/bar v = Vf/n fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs

9862.7 > 3814.4 OK

Note that for seismic loading in the North/South direction, the chord forces can be handled by the transverse bars in the plank near the ends, combined with the available tension capacity of the nearest to the plank end side connector.

V = 66519 lbs V = CsWD' x = 12 ft wv = 5543.2 lbs/ft wv = V/x y = 37.5 ft

VR = 33259.4 lbs VR = wvx/2

M = 99778.2 ft-lbs M = wvx 2/8

C = T = 3070.1 lbs C = T = M/(y - 5) Chord Forces to the nearest side clip at plank ends

For the chord tension force, use two #4 bars in the precast slab adjacent to the nearest end side shear coupler :

As = 0.2 in2 n = 2 nAs = 0.40 in2

Fy = 60000 psi fT = 0.9 fT = 21600.0 lbs fT = fnAsFy

21600.0 > 3070.1 OK

Shear coupler:

fVn = 9862.7 lbs/bar fVn = cos(45)fvFyAs n = 2 n = # bars on one side of connection nfVn = 19725.3 lbs/connection

19725.3 > 3070.1 OK

Seismic

CALCULATIONS

FOSU

Sheet 18 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

REINFORCED CONCRETE BEAM DESIGN (RECTANGULAR SECTION, TENSION STEEL ONLY)

Material properties:

Fy = 60000 psi Fy = Reinforcement yield Effective tension area of rebar f'c = 5000 psi f'c = Concrete strength y = Distance of row of bars from the bottom

Es = 29000000 psi Es = Reinforcement modulus Row As y Asy

Ec = 4030509 psi Ec = 57000f'c 1/2 1 0.44 3 1.32 n = 7 n = Es/Ec (rounded) 2 0.44 3 1.32 b = 0.8 b = If f'c <= 4000, b = 0.85, otherwise 3 0 0 0 b = max of 0.65 or 0.85 - 0.05[(f'c/1000) - 4] 4 0 0 0

Concrete member geometry: 5 0 0 0 b = 12 in b = Section width 6 0 0 0 h = 9 in h = Section height 7 0 0 0 d = 6.000 in d = h - Y 8 0 0 0

As = 0.88 in2 As = Total area of reinforcement steel 9 0 0 0 dt = 6 in dt = Depth to extreme (deepest) tension steel 10 0 0 0

Ig = 729 in4 Ig = bh /12 11 0 0 0 fr = 530.33 psi fr = 7.5f'c 1/2 12 0 0 0

Mcr = 7.16 ft-kips Mcr = 2Igfr/(12000h) SAs = 0.88 SAsy = 2.64 rmin = 0.0033 rmin = 200/Fy (applies for beams) r = 0.012 r = As/(bd) Ok for beams Y = 3.000 in Y = SAsy/SAs k = 0.3369 in k = -rn + [(rn)2 + (2rn)]1/2 As max = 0.44 in2 As max = Area of largest bar kd = 2.02 in u = 2.000 u = SAs/As max

Icr = 131 in 4 Icr = b(kd)3/3 + nAs(d - kd)2 rbal = 0.034 rbal = 0.85b(f'c/Fy)[87000/(87000 + Fy)] rACI 1999 = 0.025 rACI 1999 = 0.75rbal rACI 1999 > r? Yes Under-reinforced, OK a = 1.04 in a = AsFy/(0.85bf'c) c = 1.29 in c = a/b q = 0.15 q = rFy/f'c Tension reinforcement index et = 0.011 in et = 0.003(dt - c)/c Strain in extreme tension steel

Tension controlled

Mcap = 24.12 ft-kips Mcap = f'cbd2q(1 - 0.59q)/12000

Ma = 5.11 ft-kips Ma = Dead Load Moment at section considered

Ma/Mcr = 0.71

Ie = 729 in4 Ie = Icr if Ma/Mcr > 3

If 1 < Ma/Mcr < 3, Ie = (Mcr/Ma )Ig + [1-(Mcr/Ma)

]Icr, otherwise Ig

A's = 0.20 in 2 A's = Area of compression steel r' = 0.003 r' = A's/(bd)

L = 207 in wD = 137.5 lbs/ft

Di = 0.093 in Di = Initial deflection from dead load only e = 2 e = Creep time factor:

3 Mon. = 1, 6 Mon. = 1.2, 1 Yr. = 1.4, 5 Yrs+ = 2

Dc&s = 0.164 in Dc&s = eDi/(1 + 50r') Dead load deflection caused by creep and shrinkage

SD = 0.257 in SD = Di + Dc&s

L/m: m = 806 Dead load only wL = 100 lbs/ft

DL = 0.068 in DL = Deflection from live load only

SD' = 0.325 in SD' = Di + Dc&s + DL Long term dead load dflection + short term live load deflection

CALCULATIONS

FOSU

Planks

Sheet 19 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Crack control:

B = 1.35 B = 1.2 for beams, 1.35 for slabs dc = 3 in dc = Distance from bottom steel to nearest edge fs = 14.000 ksi w = 4.104 mils w = Crack width: If dc <= 3,w = 0.076B(0.6Fy)(2dcYb/u) 1/3

, otherwise w = 0.076B(fs)(6Yb/u) 1/3 z = 40.00 z = w/(0.076B) z < 145, OK for exterior exposure z < 175, Ok for interior exposure

Curvature ductility ratio:

CDR = 4.74 CDR = [0.003/(a/0.85)]/{Fy/[Es(d - kd)]}

CDR > 4, OK for seismic criteria

Allowable stress design:

fs = 14 ksi fs = Allowable reinforcement steel stress: 20 ksi for Fy = 40, 24 ksi for Fy = 60 suggested

Mall = 5.47 ft-kips Mall = fsAs[d - (kd/3)]/12 Allowable moment tension side

Mall = 12.11 ft-kips Mall = (0.45f'c/2)bkd[d - (kd/3)]/12000 Allowable moment compression side

My = 23.44 ft-kips My = FyAsd[1 - (k/3)]/12000 Yield moment

Strength design:

Mn = 24.12 ft-kips Mn = AsFy[d - (a/2)]/12000 Nominal ultimate moment strength fv = 0.65 fv = Shear reduction factor = 0.7 for spiral, 0.65 for other f = 0.90 f = If fs = 0.65, MIN[0.9, fs + (et - 0.002)(250/3)] Flexural reduction factor otherwise f = MIN[0.9, 0.7 + (et - 0.002)(200/3)] and f need not be less than fv f = 0.90 Enter 0.9 if doubly reinforced fMn = 21.71 ft-kips Ultimate moment capacity

Ft. Sumter Pier

Planks

Sheet 20 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Berthing Analysis Ferry

Ship parameters: 270 LT = 604.80 kips

LOA LBP B DL CB

ft ft ft ft

110 110 32 6.7 0.358 z = 0.9 z = 1 for tankers/bulk carriers, 0.9 for other ships MD

MD = 600.40 kips MD = CBLBPBDL64/(z1000) 272.29 metric tons

Kc = 6 ft Kc = Under keel clearance to seabed

D = 6.70 ft D = DL PIANC Method

Kc/D = 0.895522

CM = 1.50 CM = 1.5 if Kc/D > 0.5, 1.8 if Kc/D < 0.1, otherwise CM = 1.875 - 0.75(Kc/D) x = 22.00 ft x = 0.2LOA

R1 = 23.13 ft R1 = x2/B + B/4

R2 = 36.67 ft R2 = [(LOA/2 - x)2 + B2/4]1/2

K = 19.58 ft K = (0.19CB + 0.11)LBP a = 10 deg a = Berthing angle y = 54.13 deg y = 90 - a - (180/p)ASIN[B/(2R2)]

CE = 0.49 CE = {K2 + [R2

2COS[(p/180)y]2]}/(K2 + R2

2)

CE = 0.49 CE = Eccentricity coefficient

VB = 2 ft/s VB = Vessel berthing velocity

CC = 1 CC = Berth configuration coefficient

CS = 1 CS = Softness coefficient

For KN-m: 1.356EN

EN = 27.41 ft-kips 37.17 KN-m EN = MDVB 2CMCECCCS/2/32.2 (ft-kips)

F.S. = 2 F.S. = Abnormal berthing energy (Factor of Safety)

EA = 54.82 ft-kips 74.33 KN-m EA = F.S. EN

CALCULATIONS

FOSU

Berthing

Sheet 21 of 105

Client Date 28-Mar-20

Project Computed by LPL

Subject Checked by

Berthing Analysis Ferry

Ship parameters: 270 LT = 604.80 kips

LOA LBP B DL CB

ft ft ft ft

110 110 32 6.7 0.358 z = 0.9 z = 1 for tankers/bulk carriers, 0.9 for other ships MD

MD = 600.40 kips MD = CBLBPBDL64/(z1000) 272.29 metric tons

Kc = 6 ft Kc = Under keel clearance to seabed

D = 6.70 ft D = DL PIANC Method

Kc/D = 0.895522

CM = 1.50 CM = 1.5 if Kc/D > 0.5, 1.8 if Kc/D < 0.1, otherwise CM = 1.875 - 0.75(Kc/D) x = 22.00 ft x = 0.2LOA

R1 = 23.13 ft R1 = x2/B + B/4

R2 = 36.67 ft R2 = [(LOA/2 - x)2 + B2/4]1/2

K = 19.58 ft K = (0.19CB + 0.11)LBP a = 10 deg a = Berthing angle y = 54.13 deg y = 90 - a - (180/p)ASIN[B/(2R2)]

CE = 0.49 CE = {K2 + [R2

2COS[(p/180)y]2]}/(K2 + R2

2)

CE = 0.49 CE = Eccentricity coefficient

VB = 1.5 ft/s VB = Vessel berthing velocity

CC = 1 CC = Berth configuration coefficient

CS = 1 CS = Softness coefficient

For KN-m: 1.356EN

EN = 15.42 ft-kips 20.91 KN-m EN = MDVB 2CMCECCCS/2/32.2 (ft-kips)

F.S. = 2 F.S. = Abnormal berthing energy (Factor of Safety)

EA = 30.84 ft-kips 41.81 KN-m EA = F.S. EN

CALCULATIONS

FOSU

Berthing

Sheet 22 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

Bracket assembly Design

1. Tension Brackets

Tension across bracket section:

Fy = 36000 psi Fy = Plate yield strength

Fu = 58000 psi Fu = Plate tensile strength

Fa1 = 18000 psi Fa1 = 0.6Fy

Fa2 = 29000 psi Fa2 = 0.5Fu tp = 1 in tp = Bracket thickness (Design) d = 2 in d = Hole diameter bmin = 6 in bmin = Minimum bracket section

An = 6 in2 An = tpb

Ae = 4 in2 Ae = tp(b - d)

T = 30000 lbs T = Pipe load fa1 = 5000 psi fa1 = T/An < 18000 OK fa2 = 7500 psi fa2 = T/Ae < 29000 OK

Bearing at pin hole:

x = 2 in 1.5d

Le = 3 in Le = x + d/2 >= 3 OK

R = 139200 lbs R = 1.2Fudtp > 30000 OK

Stress in bracket:

Tx = 30000 lbs 90o

Ty = 0 lbs 90o b = 6 in ex = 0 in ey = 3 in

My = 90000 in-lbs My = Txey - Tyex

Sy = 6 in3 Sy = tpb 2/6

Ap = 6 in2 Ap = tpb fa = 0 psi fa = Ty/Ap fby = 15000 psi fby = My/Sy

INT = 0.833 INT = fa/Fa1 + fby/Fa1 < 1 OK

CALCULATIONS

FOSU

Ft. Sumter Pier

Fender Bracket

Ty b b/2 y

Tx ey

T a

Sheet 23 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

V1 = 25 knots/hr

Vmax = 35 knots/hr

V1 = 28.8 mph V1 = 1.151V1

Vmax = 40.3 mph Vmax = 1.151Vmax

V1 = 42.2 ft/s V1 = (5280/3600)V1

Vmax = 59.1 ft/s Vmax = (5280/3600)Vmax

CD = 0.8

A1 = 960 ft2 Small private vessel Estimated

F1 = 1632.0 lbs F1 = 0.0034CDV1 2 A1

Fmax = 3198.7 lbs Fmax = 0.0034CDVmax 2 A1

L = 110 ft Small cruise ship (Low Country)

H = 30 ft

A1 = 3300.0 ft2 A1 = LH Approximate

F1 = 5610.0 lbs F1 = 0.0034CDV1 2 A1

Fmax = 10995.6 lbs Fmax = 0.0034CDVmax 2 A1

CALCULATIONS

FOSU

Mooring wind loads

Sheet 24 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

REINFORCED CONCRETE BEAM DESIGN (RECTANGULAR SECTION, TENSION STEEL ONLY)

Material properties:

Fy = 60000 psi Fy = Reinforcement yield Effective tension area of rebar f'c = 5000 psi f'c = Concrete strength y = Distance of row of bars from the bottom

Es = 29000000 psi Es = Reinforcement modulus Row As y Asy

Ec = 4030509 psi Ec = 57000f'c 1/2 1 0.44 3 1.32 n = 7 n = Es/Ec (rounded) 2 0.44 3 1.32 b = 0.8 b = If f'c <= 4000, b = 0.85, otherwise 3 0 0 0 b = max of 0.65 or 0.85 - 0.05[(f'c/1000) - 4] 4 0 0 0

Concrete member geometry: 5 0 0 0 b = 12 in b = Section width 6 0 0 0 h = 11 in h = Section height 7 0 0 0 d = 8.000 in d = h - Y 8 0 0 0

As = 0.88 in2 As = Total area of reinforcement steel 9 0 0 0 dt = 8 in dt = Depth to extreme (deepest) tension steel 10 0 0 0

Ig = 1331 in 4 Ig = bh

/12 11 0 0 0 fr = 530.33 psi fr = 7.5f'c 1/2 12 0 0 0

Mcr = 10.69 ft-kips Mcr = 2Igfr/(12000h) SAs = 0.88 SAsy = 2.64 rmin = 0.0033 rmin = 200/Fy (applies for beams) r = 0.009 r = As/(bd) Ok for beams Y = 3.000 in Y = SAsy/SAs k = 0.2998 in k = -rn + [(rn)

+ (2rn)] 1/2 As max = 0.44 in

2 As max = Area of largest bar kd = 2.40 in u = 2.000 u = SAs/As max

Icr = 248 in 4 Icr = b(kd)

/3 + nAs(d - kd) rbal = 0.034 rbal = 0.85b(f'c/Fy)[87000/(87000 + Fy)] rACI 1999 = 0.025 rACI 1999 = 0.75rbal rACI 1999 > r? Yes Under-reinforced, OK a = 1.04 in a = AsFy/(0.85bf'c) c = 1.29 in c = a/b q = 0.11 q = rFy/f'c Tension reinforcement index et = 0.016 in et = 0.003(dt - c)/c Strain in extreme tension steel

Tension controlled

Mcap = 32.92 ft-kips Mcap = f'cbd q(1 - 0.59q)/12000

Ma = 5 ft-kips Ma = Dead Load Moment at section considered

Ma/Mcr = 0.47

Ie = 1331 in 4 Ie = Icr if Ma/Mcr > 3

If 1 < Ma/Mcr < 3, Ie = (Mcr/Ma 3)Ig + [1-(Mcr/Ma)

3]Icr, otherwise Ig

A's = 0.20 in2 A's = Area of compression steel r' = 0.002 r' = A's/(bd)

L = 216 in wD = 137.5 lbs/ft

Di = 0.061 in Di = Initial deflection from dead load only e = 2 e = Creep time factor:

3 Mon. = 1, 6 Mon. = 1.2, 1 Yr. = 1.4, 5 Yrs+ = 2

Dc&s = 0.110 in Dc&s = eDi/(1 + 50r') Dead load deflection caused by creep and shrinkage

SD = 0.170 in SD = Di + Dc&s

L/m: m = 1269 Dead load only wL = 100 lbs/ft

DL = 0.044 in DL = Deflection from live load only

SD' = 0.214 in SD' = Di + Dc&s + DL Long term dead load dflection + short term live load deflection

Crack control:

B = 1.35 B = 1.2 for beams, 1.35 for slabs dc = 3 in dc = Distance from bottom steel to nearest edge fs = 10.000 ksi w = 2.932 mils w = Crack width: If dc <= 3,w = 0.076B(0.6Fy)(2dcYb/u)1/3, otherwise w = 0.076B(fs)(6Yb/u)1/3 z = 28.57 z = w/(0.076B) z < 145, OK for exterior exposure z < 175, Ok for interior exposure

Curvature ductility ratio:

CDR = 6.67 CDR = [0.003/(a/0.85)]/{Fy/[Es(d - kd)]}

CDR > 4, OK for seismic criteria

Allowable stress design:

fs = 10 ksi fs = Allowable reinforcement steel stress: 20 ksi for Fy = 40, 24 ksi for Fy = 60 suggested

Mall = 5.28 ft-kips Mall = fsAs[d - (kd/3)]/12 Allowable moment tension side

Mall = 19.43 ft-kips Mall = (0.45f'c/2)bkd[d - (kd/3)]/12000 Allowable moment compression side

My = 31.68 ft-kips My = FyAsd[1 - (k/3)]/12000 Yield moment

Strength design:

Mn = 32.92 ft-kips Mn = AsFy[d - (a/2)]/12000 Nominal ultimate moment strength fv = 0.65 fv = Shear reduction factor = 0.7 for spiral, 0.65 for other f = 0.90 f = If fs = 0.65, MIN[0.9, fs + (et - 0.002)(250/3)] Flexural reduction factor otherwise f = MIN[0.9, 0.7 + (et - 0.002)(200/3)] and f need not be less than fv f = 0.90 Enter 0.9 if doubly reinforced fMn = 29.63 ft-kips Ultimate moment capacity

CALCULATIONS

FOSU

CIP Jib Crane Slab

Sheet 25 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

REINFORCED CONCRETE BEAM DESIGN (RECTANGULAR SECTION, TENSION STEEL ONLY)

Material properties:

Fy = 60000 psi Fy = Reinforcement yield Effective tension area of rebar f'c = 5000 psi f'c = Concrete strength y = Distance of row of bars from the bottom

Es = 29000000 psi Es = Reinforcement modulus Row As y Asy

Ec = 4030509 psi Ec = 57000f'c 1/2 1 0.31 3 0.93 n = 7 n = Es/Ec (rounded) 2 0.31 3 0.93 b = 0.8 b = If f'c <= 4000, b = 0.85, otherwise 3 0 0 0 b = max of 0.65 or 0.85 - 0.05[(f'c/1000) - 4] 4 0 0 0

Concrete member geometry: 5 0 0 0 b = 12 in b = Section width 6 0 0 0 h = 11 in h = Section height 7 0 0 0 d = 8.000 in d = h - Y 8 0 0 0

As = 0.62 in 2 As = Total area of reinforcement steel 9 0 0 0 dt = 8 in dt = Depth to extreme (deepest) tension steel 10 0 0 0

Ig = 1331 in4 Ig = bh3/12 11 0 0 0 fr = 530.33 psi fr = 7.5f'c 1/2 12 0 0 0

Mcr = 10.69 ft-kips Mcr = 2Igfr/(12000h) SAs = 0.62 SAsy = 1.86 rmin = 0.0033 rmin = 200/Fy (applies for beams) r = 0.006 r = As/(bd) Ok for beams Y = 3.000 in Y = SAsy/SAs k = 0.2589 in k = -rn + [(rn)2 + (2rn)]1/2 As max = 0.31 in2 As max = Area of largest bar kd = 2.07 in u = 2.000 u = SAs/As max

Icr = 188 in 4 Icr = b(kd)3/3 + nAs(d - kd)2 rbal = 0.034 rbal = 0.85b(f'c/Fy)[87000/(87000 + Fy)] rACI 1999 = 0.025 rACI 1999 = 0.75rbal rACI 1999 > r? Yes Under-reinforced, OK a = 0.73 in a = AsFy/(0.85bf'c) c = 0.91 in c = a/b q = 0.08 q = rFy/f'c Tension reinforcement index et = 0.023 in et = 0.003(dt - c)/c Strain in extreme tension steel

Tension controlled

Mcap = 23.67 ft-kips Mcap = f'cbd2q(1 - 0.59q)/12000

Ma = 4 ft-kips Ma = Dead Load Moment at section considered

Ma/Mcr = 0.37

Ie = 1331 in4 Ie = Icr if Ma/Mcr > 3

If 1 < Ma/Mcr < 3, Ie = (Mcr/Ma )Ig + [1-(Mcr/Ma)

]Icr, otherwise Ig

A's = 0.20 in 2 A's = Area of compression steel r' = 0.002 r' = A's/(bd)

L = 216 in wD = 137.5 lbs/ft

Di = 0.061 in Di = Initial deflection from dead load only e = 2 e = Creep time factor:

3 Mon. = 1, 6 Mon. = 1.2, 1 Yr. = 1.4, 5 Yrs+ = 2

Dc&s = 0.110 in Dc&s = eDi/(1 + 50r') Dead load deflection caused by creep and shrinkage

SD = 0.170 in SD = Di + Dc&s

L/m: m = 1269 Dead load only wL = 100 lbs/ft

DL = 0.044 in DL = Deflection from live load only

SD' = 0.214 in SD' = Di + Dc&s + DL Long term dead load dflection + short term live load deflection

Crack control:

B = 1.35 B = 1.2 for beams, 1.35 for slabs dc = 3 in dc = Distance from bottom steel to nearest edge fs = 11.000 ksi w = 3.225 mils w = Crack width: If dc <= 3,w = 0.076B(0.6Fy)(2dcYb/u) 1/3

, otherwise w = 0.076B(fs)(6Yb/u) 1/3 z = 31.43 z = w/(0.076B) z < 145, OK for exterior exposure z < 175, Ok for interior exposure

Curvature ductility ratio:

CDR = 10.02 CDR = [0.003/(a/0.85)]/{Fy/[Es(d - kd)]}

CDR > 4, OK for seismic criteria

Allowable stress design:

fs = 11 ksi fs = Allowable reinforcement steel stress: 20 ksi for Fy = 40, 24 ksi for Fy = 60 suggested

Mall = 4.15 ft-kips Mall = fsAs[d - (kd/3)]/12 Allowable moment tension side

Mall = 17.03 ft-kips Mall = (0.45f'c/2)bkd[d - (kd/3)]/12000 Allowable moment compression side

My = 22.66 ft-kips My = FyAsd[1 - (k/3)]/12000 Yield moment

Strength design:

Mn = 23.67 ft-kips Mn = AsFy[d - (a/2)]/12000 Nominal ultimate moment strength fv = 0.65 fv = Shear reduction factor = 0.7 for spiral, 0.65 for other f = 0.90 f = If fs = 0.65, MIN[0.9, fs + (et - 0.002)(250/3)] Flexural reduction factor otherwise f = MIN[0.9, 0.7 + (et - 0.002)(200/3)] and f need not be less than fv f = 0.90 Enter 0.9 if doubly reinforced fMn = 21.30 ft-kips Ultimate moment capacity

CALCULATIONS

FOSU

Sheet 26 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

REINFORCED CONCRETE BEAM DESIGN (RECTANGULAR SECTION, TENSION STEEL ONLY)

Material properties:

Fy = 60000 psi Fy = Reinforcement yield Effective tension area of rebar f'c = 5000 psi f'c = Concrete strength y = Distance of row of bars from the bottom

Es = 29000000 psi Es = Reinforcement modulus Row As y Asy

Ec = 4030509 psi Ec = 57000f'c 1/2 1 0.2 3 0.6 n = 7 n = Es/Ec (rounded) 2 0.2 3 0.6 b = 0.8 b = If f'c <= 4000, b = 0.85, otherwise 3 0 0 0 b = max of 0.65 or 0.85 - 0.05[(f'c/1000) - 4] 4 0 0 0

Concrete member geometry: 5 0 0 0 b = 12 in b = Section width 6 0 0 0 h = 11 in h = Section height 7 0 0 0 d = 8.000 in d = h - Y 8 0 0 0

As = 0.4 in2 As = Total area of reinforcement steel 9 0 0 0 dt = 8 in dt = Depth to extreme (deepest) tension steel 10 0 0 0

Ig = 1331 in 4 Ig = bh

/12 11 0 0 0 fr = 530.33 psi fr = 7.5f'c 1/2 12 0 0 0

Mcr = 10.69 ft-kips Mcr = 2Igfr/(12000h) SAs = 0.4 SAsy = 1.2 rmin = 0.0033 rmin = 200/Fy (applies for beams) r = 0.004 r = As/(bd) Ok for beams Y = 3.000 in Y = SAsy/SAs k = 0.2141 in k = -rn + [(rn)2 + (2rn)]1/2 As max = 0.2 in2 As max = Area of largest bar kd = 1.71 in u = 2.000 u = SAs/As max

Icr = 131 in 4 Icr = b(kd)

/3 + nAs(d - kd) rbal = 0.034 rbal = 0.85b(f'c/Fy)[87000/(87000 + Fy)] rACI 1999 = 0.025 rACI 1999 = 0.75rbal rACI 1999 > r? Yes Under-reinforced, OK a = 0.47 in a = AsFy/(0.85bf'c) c = 0.59 in c = a/b q = 0.05 q = rFy/f'c Tension reinforcement index et = 0.038 in et = 0.003(dt - c)/c Strain in extreme tension steel

Tension controlled

Mcap = 15.53 ft-kips Mcap = f'cbd q(1 - 0.59q)/12000

Ma = 1 ft-kips Ma = Dead Load Moment at section considered

Ma/Mcr = 0.09

Ie = 1331 in 4 Ie = Icr if Ma/Mcr > 3

If 1 < Ma/Mcr < 3, Ie = (Mcr/Ma 3)Ig + [1-(Mcr/Ma)

3]Icr, otherwise Ig

A's = 0.20 in2 A's = Area of compression steel r' = 0.002 r' = A's/(bd)

L = 216 in wD = 137.5 lbs/ft

Di = 0.061 in Di = Initial deflection from dead load only e = 2 e = Creep time factor:

3 Mon. = 1, 6 Mon. = 1.2, 1 Yr. = 1.4, 5 Yrs+ = 2

Dc&s = 0.110 in Dc&s = eDi/(1 + 50r') Dead load deflection caused by creep and shrinkage

SD = 0.170 in SD = Di + Dc&s

L/m: m = 1269 Dead load only wL = 100 lbs/ft

DL = 0.044 in DL = Deflection from live load only

SD' = 0.214 in SD' = Di + Dc&s + DL Long term dead load dflection + short term live load deflection

Crack control:

B = 1.35 B = 1.2 for beams, 1.35 for slabs dc = 3 in dc = Distance from bottom steel to nearest edge fs = 5.000 ksi w = 1.466 mils w = Crack width: If dc <= 3,w = 0.076B(0.6Fy)(2dcYb/u)1/3, otherwise w = 0.076B(fs)(6Yb/u)1/3 z = 14.29 z = w/(0.076B) z < 145, OK for exterior exposure z < 175, Ok for interior exposure

Curvature ductility ratio:

CDR = 16.47 CDR = [0.003/(a/0.85)]/{Fy/[Es(d - kd)]}

CDR > 4, OK for seismic criteria

Allowable stress design:

fs = 5 ksi fs = Allowable reinforcement steel stress: 20 ksi for Fy = 40, 24 ksi for Fy = 60 suggested

Mall = 1.24 ft-kips Mall = fsAs[d - (kd/3)]/12 Allowable moment tension side

Mall = 14.32 ft-kips Mall = (0.45f'c/2)bkd[d - (kd/3)]/12000 Allowable moment compression side

My = 14.86 ft-kips My = FyAsd[1 - (k/3)]/12000 Yield moment

Strength design:

Mn = 15.53 ft-kips Mn = AsFy[d - (a/2)]/12000 Nominal ultimate moment strength fv = 0.65 fv = Shear reduction factor = 0.7 for spiral, 0.65 for other f = 0.90 f = If fs = 0.65, MIN[0.9, fs + (et - 0.002)(250/3)] Flexural reduction factor otherwise f = MIN[0.9, 0.7 + (et - 0.002)(200/3)] and f need not be less than fv f = 0.90 Enter 0.9 if doubly reinforced fMn = 13.98 ft-kips Ultimate moment capacity

CALCULATIONS

FOSU

Sheet 27 of 105

Client Date 29-Mar-24

Project Computed by LPL

Subject Checked by

REINFORCED CONCRETE BEAM DESIGN (RECTANGULAR SECTION, TENSION STEEL ONLY)

Material properties:

Fy = 60000 psi Fy = Reinforcement yield Effective tension area of rebar f'c = 5000 psi f'c = Concrete strength y = Distance of row of bars from the bottom

Es = 29000000 psi Es = Reinforcement modulus Row As y Asy

Ec = 4030509 psi Ec = 57000f'c 1/2 1 0.6 3 1.8 n = 7 n = Es/Ec (rounded) 2 0.6 3 1.8 b = 0.8 b = If f'c <= 4000, b = 0.85, otherwise 3 0 0 0 b = max of 0.65 or 0.85 - 0.05[(f'c/1000) - 4] 4 0 0 0

Concrete member geometry: 5 0 0 0 b = 12 in b = Section width 6 0 0 0 h = 11 in h = Section height 7 0 0 0 d = 8.000 in d = h - Y 8 0 0 0

As = 1.2 in 2 As = Total area of reinforcement steel 9 0 0 0 dt = 8 in dt = Depth to extreme (deepest) tension steel 10 0 0 0

Ig = 1331 in 4 Ig = bh

/12 11 0 0 0 fr = 530.33 psi fr = 7.5f'c 1/2 12 0 0 0

Mcr = 10.69 ft-kips Mcr = 2Igfr/(12000h) SAs = 1.2 SAsy = 3.6 rmin = 0.0033 rmin = 200/Fy (applies for beams) r = 0.013 r = As/(bd) Ok for beams Y = 3.000 in Y = SAsy/SAs k = 0.3399 in k = -rn + [(rn)

+ (2rn)] 1/2 As max = 0.6 in

2 As max = Area of largest bar kd = 2.72 in u = 2.000 u = SAs/As max

Icr = 315 in 4 Icr = b(kd)

/3 + nAs(d - kd) rbal = 0.034 rbal = 0.85b(f'c/Fy)[87000/(87000 + Fy)] rACI 1999 = 0.025 rACI 1999 = 0.75rbal rACI 1999 > r? Yes Under-reinforced, OK a = 1.41 in a = AsFy/(0.85bf'c) c = 1.76 in c = a/b q = 0.15 q = rFy/f'c Tension reinforcement index et = 0.011 in et = 0.003(dt - c)/c Strain in extreme tension steel

Tension controlled

Mcap = 43.75 ft-kips Mcap = f'cbd q(1 - 0.59q)/12000

Ma = 14 ft-kips Ma = Dead Load Moment at section considered

Ma/Mcr = 1.31

Ie = 768 in 4 Ie = Icr if Ma/Mcr > 3

If 1 < Ma/Mcr < 3, Ie = (Mcr/Ma 3)Ig + [1-(Mcr/Ma)

3]Icr, otherwise Ig

A's = 0.20 in2 A's = Area of compression steel r' = 0.002 r' = A's/(bd)

L = 216 in wD = 137.5 lbs/ft

Di = 0.105 in Di = Initial deflection from dead load only e = 2 e = Creep time factor:

3 Mon. = 1, 6 Mon. = 1.2, 1 Yr. = 1.4, 5 Yrs+ = 2

Dc&s = 0.190 in Dc&s = eDi/(1 + 50r') Dead load deflection caused by creep and shrinkage

SD = 0.295 in SD = Di + Dc&s

L/m: m = 732 Dead load only wL = 100 lbs/ft

DL = 0.076 in DL = Deflection from live load only

SD' = 0.371 in SD' = Di + Dc&s + DL Long term dead load dflection + short term live load deflection

Crack control:

B = 1.35 B = 1.2 for beams, 1.35 for slabs dc = 3 in dc = Distance from bottom steel to nearest edge fs = 20.000 ksi w = 5.863 mils w = Crack width: If dc <= 3,w = 0.076B(0.6Fy)(2dcYb/u)1/3, otherwise w = 0.076B(fs)(6Yb/u)1/3 z = 57.15 z = w/(0.076B) z < 145, OK for exterior exposure z < 175, Ok for interior exposure

Curvature ductility ratio:

CDR = 4.61 CDR = [0.003/(a/0.85)]/{Fy/[Es(d - kd)]}

CDR > 4, OK for seismic criteria

Allowable stress design:

fs = 20 ksi fs = Allowable reinforcement steel stress: 20 ksi for Fy = 40, 24 ksi for Fy = 60 suggested

Mall = 14.19 ft-kips Mall = fsAs[d - (kd/3)]/12 Allowable moment tension side

Mall = 21.70 ft-kips Mall = (0.45f'c/2)bkd[d - (kd/3)]/12000 Allowable moment compression side

My = 42.56 ft-kips My = FyAsd[1 - (k/3)]/12000 Yield moment

Strength design:

Mn = 43.76 ft-kips Mn = AsFy[d - (a/2)]/12000 Nominal ultimate moment strength fv = 0.65 fv = Shear reduction factor = 0.7 for spiral, 0.65 for other f = 0.90 f = If fs = 0.65, MIN[0.9, fs + (et - 0.002)(250/3)] Flexural reduction factor otherwise f = MIN[0.9, 0.7 + (et - 0.002)(200/3)] and f need not be less than fv f = 0.90 Enter 0.9 if doubly…