2011 Coastal Construction Manual (CCM) - Calculator The equations in this spreadsheet are equations in Volume 2 of the CCM In order to avoid the user from accidentally erasing the formula in a cell, all the cells in each of the worksheets, except those requiring user input, are protected (with no password). On each of the worksheets, the material on the right-hand side (Column J - Q) are reference material to help the user with input to the equation. Each of the worksheets is set to print only the left hand side (Columns A-I). List of equations included in this workbook is given in the "LIST" Worksheet. List of Equations - CCM Volume 2 Chapter 8 - Determining Site-Specific Loads Equation 8.1 Design Stillwater Flood Depth Equation 8.2. Design Flood Velocity Equation 8.3. Lateral Hydrostatic Load Equation 8.4. Vertical (Buoyant) Hydrostatic Force Equation 8.5. Breaking Wave Load on Vertical Piles Equation 8.6. Breaking Wave Load on Vertical Walls Equation 8.7. Lateral Wave Slam Equation 8.8. Hydrodynamic Load (for All Flow Velocities) Equation 8.9. Debris Impact Load Equation 8.10. Localized Scour Around a Single Vertical Pile Equation 8.11. Total Localized Scour Around Vertical Piles Equation 8.12. Total Scour Depth Around Vertical Walls and Enclosures Equation 8.13. Velocity Pressure Equation 8.14. Design Wind Pressure for Low-Rise Buildings Equation 8.15. Seismic Base Shear by Equivalent Lateral Force Procedure Equation 8.16. Vertical Distribution of Seismic Forces Chapter 10 - Designing the Foundation Equation 10.1. Sliding Resistance Equation 10.2. Ultimate Compression Capacity of a Single Pile Equation 10.3. Ultimate Tension Capacity of a Single Pile Equation 10.4. Load Application Distance for an Unbraced Pile Equation 10.5. Determination of Square Footing Size for Gravity Loads Equation 10.6. Determination of Soil Pressure Chapter 13 - Constructing the Building Equation 13.1. Pile Driving Resistance for Drop Hammer Pile Drivers Equation 8.1 Design Stillwater Flood Depth Equation 8.1 ds = Esw - GS where: ds = design stillwater flood depth (ft) Esw = design stillwater flood elevation in ft above datum (e.g., NGVD, NAVD) GS = lowest eroded ground elevation, in ft above datum, adjacent to a building, excluding effects of localized scour around the foundation Calculation Input: Esw = 10.10 ft GS = 5.50 ft Output: ds = 4.60 ft Eq. 8.1 Equation 8.2. Design Flood Velocity Equation 8.2 Lower bound Eq. 8.2A Upper bound V = (gds)0.5 Eq. 8.2B where: V = design flood velocity (ft/sec) ds = design stillwater flood depth (ft) - from Eq. 8.1 t = 1 sec. g = gravitational constant (32.2 ft/sec2 ) Calculation Input: ds = 4.60 ft g = 32.20 ft/sec2 Output: V = 4.60 ft/sec Eq. 8.2A Lower bound V = 12.17 ft/sec Eq. 8.2B Upper bound V =...... Equation 8.3. Lateral Hydrostatic Load Equation 8.3 fsta = (1/2) .wds2 Eq. 8.3 A Fsta = fsta (w) Eq. 8.3 B where: fsta = hydrostatic force per unit width (lb/ft) resulting from flooding against vertical element .w = specific weight of water (62.4 lb/ft3 for fresh water and 64.0 lb/ft3 for saltwater) ds = design stillwater flood depth (ft) - from Eq. 8.1 Fsta = total equivalent lateral hydrostatic force on a structure (lb) w = width of vertical element (ft) Calculation Input: ds = 4.60 ft .w = 64.00 lb/ft3 w = 0.67 ft Output: fsta = 677.12 lb/ft Eq. 8.3 A Fsta = 453.67 lb Eq. 8.3 B (flood load on only one side of vertical component) Equation 8.4. Vertical (Buoyant) Hydrostatic Force Equation 8.4 Fbuoy = .w (Vol) Eq. 8.4 where: Fbuoy = vertical hydrostatic force (lb) resulting from the displacement of a given volume of floodwater .w = specific weight of water (62.4 lb/ft3 for fresh water and 64.0 lb/ft3 for saltwater) Vol = Volume of floodwater displaced by a submerged object (ft3) Calculation Input: .w = 64.00 lb/ft3 Vol = 20.00 ft3 Output: Fbuoy = 1280.00 lb Eq. 8.4 Equation 8.5. Breaking Wave Load on Vertical Piles Equation 8.5 Fbrkp = (1/2) Cdb.wDHb2 Eq. 8.5 where: Fbrkp = drag force (lb) acting at the stillwater elevation Cdb = breaking wave drag coefficient (recommended value are 2.25 for square piles and 1.75 for round piles) .w = specific weight of water (62.4 lb/ft3 for fresh water and 64.0 lb/ft3 for saltwater) D = pile diameter (ft) for a round pile or 1.4 times the width of the pile or column for a square pile Hb = breaking wave height (0.78 ds) in ft. where ds = design stillwater depth in ft Calculation Input: "round" or "square" pile ? square if round pile, enter diameter of pile ft if square, enter the width of pile 0.67 ft .w = 64.00 lb/ft3 ds = 4.60 ft stillwater depth (From Eq 8.1) Output: Cdb = 2.25 square pile D = 0.94 ft (pile diameter or 1.4 * width of pile) Hb = 3.59 ft (0.78 * design stillwater depth, ds) Fbrkp = 869.44 lb Eq. 8.5 (on one pile) Equation 8.6. Breaking Wave Load on Vertical Walls Equation 8.6a (enclosed dry space behind wall) fbrkw = 1.1 Cp.wds2 + 2.4 .wds2 Eq. 8.6a Equation 8.6b (equal stillwater elevation on both sides of the wall) fbrkw = 1.1 Cp.wds2 + 1.9 .wds2 Eq. 8.6b Equation 8.6c Fbrkw = fbrkw (w) Eq. 8.6c where: fbrkw = total breaking wave per unit length of wall (lb/ft) acting at the stillwater elevation Cp = dynamic pressure coefficient from Table 8-1 .w = specific weight of water (62.4 lb/ft3 for fresh water and 64.0 lb/ft3 for saltwater) ds = design stillwater flood depth in ft (From Eq. 8.1) Fbrkw = total breakwater wave load (lb) acting at the stillwater elevation w = width of wall in ft Calculation Input: Cp = 2.8 .w = 64 lb/ft3 ds = 4.60 ft (From Eq 8.1) w = 2.00 ft Output: fbrkw = 7,421.24 lb/ft Eq. 8.6a enclosed dry space behind wall fbrkw = 6,744.12 lb/ft Eq. 8.6b equal stillwater elevation both sides Fbrkw = 14,842.47 lb Eq. 8.6c enclosed dry space behind wall Fbrkw = 13,488.23 lb Eq. 8.6c equal stillwater elevation both sides Equation 8.7. Lateral Wave Slam Equation 8.7 Fs = fsw = (1/2) .wCsdshw Eq. 8.7 where: Fs = lateral wave slam (lb) fs = lateral wave slam (lb/ft) Cs = slam coefficient incorporating effect of slam duration and surface stiffness for typical residential structure (recommended value is 2.0) .w = specific weight of water (62.4 lb/ft3 for fresh water and 64.0 lb/ft3 for saltwater) ds = design stillwater flood depth in ft (From Eq. 8.1) h = vertical distance (ft) the wave crest extends above the bottom of the floor joist or floor beam w = length (ft) of the floor joist or floor beam struck by wave crest Calculation Input: .w = 64.00 lb/ft3 Cs = 2.00 ds = 7.00 ft h = 0.90 ft w = 50.00 ft Output: fs = 403.20 lb/ft Fs = 20,160.00 lb Eq. 8.7 Equation 8.8. Hydrodynamic Load (for All Flow Velocities) Equation 8.8 Fdyn = (1/2) Cd.V2A Eq. 8.8 where: Fdyn = horizontal drag force (lb) acting on the stillwater mid-depth (half way between the stillwater level and the eroded ground surface) Cd = drag coefficient (recommended coefficient are 2.0 for square or rectangular piles and 1.2 for round piles; for other obstructions, see Table 8-2) . = mass density of fluid (1.94 slugs/ft2 for fresh water and 1.99 slugs/ft2 for saltwater) V = Velocity of water (ft/sec); see Equation 8.2 A = surface area of obstruction normal to flow (ft2) = (w)(ds) if object is not fully immersed, see figure 8-13 or (w)(h) if the object is completely immersed h = the height of the object (ft) if the object is completely immersed in water ds = stillwater flood depth of the water (ft) if the object is not fully immersed Calculation Input: Cd = 2.00 . = 1.99 slugs/ft2 V = 12.20 ft/sec from Eq. 8.2 w = 0.67 ft h = ft Leave blank if object is not completely immersed. ds = 4.60 ft Output: A = 3.082 ft2 (A = ds*w or h*w) Fdyn = 912.86 lb Eq. 8.8 Equation 8.9. Debris Impact Load Equation 8.9 Fi = WVCDCBCStr Eq. 8.9 where: Fi = impact force acting at the stillwater elevation (lb) W = weight of the object (lb) V = velocity of water (ft/sec), approximated by 1/2(gds)1/2 CD = depth coefficient (see Table 8-3) CB = blockage coefficient (taken as 1.0 for no upstream screening, flow path greater than 30 ft; see below for more information) CStr = Building structure coefficient (sec/ft) 0.2 for timber pile and masonry column supported structures 3 stories or less in height above grade 0.4 for concrete pile or concrete or steel moment resisting frames 3 stories or less in height above grade 0.8 for reinforced concrete foundation walls (including insulated concrete forms) Calculation Input: W = 1000.00 lb V = 12.20 ft/sec CD = 0.75 CB = 1.00 CStr = 0.20 sec/ft Output: Fi = 1830.00 lb Eq. 8.9 Equation 8.10. Localized Scour Around a Single Vertical Pile Equation 8.10 Smax = 2.0a Eq. 8.10 where: Smax = maximum localized scour depth (ft) a = diameter of a round foundation element or the maximum diagonal cross- section dimension for a rectangular element Calculation Input: a = 0.88 ft Output: Smax = 1.76 ft Eq. 8.10 Equation 8.11. Total Localized Scour Around Vertical Piles Equation 8.11 STOT = 6a + 2 ft (if grade beam and/or slab-on-grade present) Eq. 8.11a STOT = 6a (if no grade beam or slab-on-grade present) Eq. 8.11b where: STOT = total localized scour depth (ft) a = diameter of a round foundation element or the maximum diagonal cross- section dimension for a rectangular element 2 ft = allowance for vertical scour due to presence of grade beam or slab-on- grade Calculation Input: a = 0.88 ft Output: STOT = 7.28 ft Eq. 8.11a STOT = 5.28 ft Eq. 8.11b Equation 8.12. Total Scour Depth Around Vertical Walls and Enclosures Equation 8.12 STOT = 0.15L Eq. 8.12 where: STOT = total localized scour depth (ft), maximum value is 10 ft L = horizontal length (ft) along the side of the building or obstruction exposed to flow and waves Calculation Input: L = 10.00 ft Output: STOT = 1.50 ft Eq. 8.12 Check Total localized scour depth is less than 10 ft - OK Equation 8.13. Velocity Pressure Equation 8.13 qz = 0.00256 KzKztKdV2 Eq. 8.13 where: qz = Velocity pressure evaluated at height z (psf) Kz = velocity pressure exposure coefficient evaluated at height z Kzt = topographic factor Kd = wind directionality factor V = basic wind speed (mph) (3-sec gust speed at 33 ft above ground in Exposure Category C) Calculation Input: Kz = 1.00 Kzt = 1.00 Kd = 0.85 V = 150.00 mph Output: qz = 48.96 psf Eq. 8.13 Equation 8.14. Design Wind Pressure for Low-Rise Buildings Equation 8.14 p = qh [GCpf - GCpi] Eq. 8.14 where: P = design wind pressure (psf) qh = Velocity pressure (psf) evaluated at mean rood height h, (see Fig 8-18 for an illustration of mean roof height) GCPf = External pressure coefficient for C & C loads or MWFRS loads per low- rise building provisions, as applicable GCPi = External pressure coefficient based on exposure classification as applicable, GCPi for enclosed building is +/- 0.18 Calculation Input: qh = 29.38 psf GCPf = -0.69 GCPi = 0.18 Output: P = -25.56 psf Eq. 8.14 Equation 8.15. Seismic Base Shear by Equivalent Lateral Force Procedure Equation 8.15 V = CsW Eq. 8.16a Eq. 8.16b where: V = Seismic base shear (lb) Cs = Seismic response coefficient S1 = the mapped maximum considered earthquake spectral response acceleration parameter SDS = design spectral response acceleration parameter in the short period range, 5 percent damped SD1 = the design spectral response acceleration parameter at a period of 1.0 second R = response modification factor I = occupancy importance factor W = effective seismic weight, kip T = the fundamental period of the structure(s) TL = long-period transition period(s) Calculation Input: S1 = 0.2 g SDS = 0.33 g SD1 = 0.13 g R = 6.00 I = 1.00 W = 6816.00 kips T = 0.35 sec TL = 8.00 sec Output: Cs = 0.055 Eq. 8.15b Use Check Cs (see right hand side) Cs = 0.055 V = 374.88 kips Eq. 8.15a ....=......(....) Equation 8.16. Vertical Distribution of Seismic Forces Equation 8.16 Fx = CvxV Eq. 8.16a Eq. 8.16b where: Fx = lateral seismic force induced at any level Cvx = vertical distribution factor V = seismic base shear (kips) wi and wx = portion of the total effective seismic weight of the structure (w) located or assigned to level i or x hi and hx = height (ft) from the base to Level i or x k = exponent related to the structure period; for structures having a period of 0.5 sec or less, k=1 n = Number of storys (assume not more than 2 storys in this worksheet) Calculation Input: For two-story structure, 1 is the lowest level V = 374.88 kips k = 1.00 w1 = 0.33 w2 = 0.33 h1 = 13 ft h2 = 26 ft Output: w1h1k = 4.29 w2h2k = 8.58 Cvx1 = 0.33 Fx1 = 124.96 kips Cvx2 = 0.67 Fx2 = 249.92 kips ......=....h.... ........=1h.... Equation 10.1. Sliding Resistance Equation 10.1 F = tan(.) (N) Eq. 10.1 where: F = resistance to sliding (lb) f = angle of internal friction in degrees N = normal force on the footing (lb) Calculation Input: f = 10.00 degree N = 3000.00 lb Output: F = 528.98 psf Eq. 10.1 Equation 10.2. Ultimate Compression Capacity of a Single Pile Equation 10.2 QULT = PTNqAT + . KHCP0Ds tan(d) Eq 10.2 . - summation over the different layers of soil. Set at maximum of 4 in this worksheet Where: Qult = ultimate load capacity in compression (lb) PT = effective vertical stress at pile tip (lb/ft2) Nq = bearing capacity factor (see Table 10-4) AT = area of pile tip (ft2) KHC = earth pressure coefficient in compression (see Table 10-5) P0 = effective vertical stress over the depth of embedment, D (lb/ft2) d = friction angle between pile and soil in degrees (see Table 10-6) s = surface area of pile per unit length (ft2) D = depth of embedment (ft) Calculation Input: PT = 975 lb/ft2 Nq = 21 AT = 0.79 ft2 Enter soil information from top layer down. Leave blank if less than 4 layers Soil Layer KHC P0 (lb/ft2) d(degree) s(ft2/ft) D(ft) KHCP0Dstan(d) 1 (Top) 1.00 975.00 22.50 3.14 15.00 19021.72 2 0.00 3 0.00 4 0.00 Total = 19021.72 Output: Qult = 35196.97 lb Eq. 10.2 Qall = 11732.32 lb Allowable compression capacity with a safety factor of 3 Equation 10.3. Ultimate Tension Capacity of a Single Pile Equation 10.3 Tult = . KHTP0Ds tan(d) Eq. 10.3 . - summation over the different layers of soil. Set at maximum of 4 in this worksheet Where: Tult = ultimate load capacity in tension (lb) KHT = earth pressure coefficient in tension (see Table 10-5) P0 = effective vertical stress over the depth of embedment, D (lb/ft2) d = friction angle between pile and soil in degrees (see Table 10-6) s = surface area of pile per unit length (ft2/ft or ft) D = depth of embedment (ft) Calculation Input: Enter soil information from top layer down. Leave blank if less than 4 layers. Soil Layer KHT P0 (lb/ft2) d(degree) s(ft2/ft) D(ft) KHTP0 Dstan(d) 1 (Top) 0.60 975.00 22.50 3.14 15.00 11413.03 2 0.00 3 0.00 4 0.00 Total = 11413.03 Output: Tult = 11413.03 lb Eq. 10.3 Tallow = 3804.34 lb Allowable tension capacity with a safety factor of 3.0 Equation 10.4. Load Application Distance for an Unbraced Pile Equation 10.4 L = H + d/12 Eq 10.4 where: L = distance between the location where the lateral force in applied and the point of fixity (i.e., moment arm) (ft) d = depth from grade to inflection point (in); E = modulus of elasticity of the pile material, (lb/in2) I = moment of inertia of pile material (in4) nh = modulus of subgrade reaction (lb/in3), see Table 10-8 H = distance above grade where the lateral load is applied (ft) Calculation Input: E = 1500000 lb/in2 I = 322 in4 nh = 700 lb/in3 H = 11.3 ft Output: d = 26.49 in L = 13.51 ft Eq. 10.4 d = 1.8......h1/5 Equation 10.5. Determination of Square Footing Size for Gravity Loads Equation 10.5 Eq. 10.5 where: L = square footing dimension (ft) Pa = gravity load on pier (lb) hcol = height of pier above grade (ft) x = distance from grade to bottom of footing (ft) Wcol = column width (ft) tcol = column thickness (ft) wc = unit weight of column and footing material (lb/ft3) q = soil bearing pressure (psf) tfoot = footing thickness (ft) Calculation Input: Pa = 500.00 lb hcol = 12.00 ft x = 5.00 ft Wcol = 2.00 ft tcol = 2.00 ft wc = 150.00 lb/ft3 q = 2000.00 psf tfoot = 1.00 ft Output: L = 2.34 ft Eq. 10.5 L =....+h......+.. -................................ - ..............0.5 Equation 10.6. Determination of Soil Pressure Equation 10.6 Eq. 10.6 where: q = minimum and maximum soil bearing pressures at the edges of the footing (lb/ft2) Pt = total vertical load for the load combination being analyzed (lb) M = applied moment Pl (hcol+ x) (ft-lbs) where x and hcol are as defined in Figure 10-21 and Pl is the lateral load applied at the top of the column Calculation Input: Pt = 10710.00 lbs input negtive for uplift load (.) Pl = 989.00 lbs lateral force L = 8.50 ft footing dimension hcol = 13.30 ft height of pier above grade x = 1.50 ft length below grade Output: M = 14637.20 ft-lbs (Pl * (hcol+x)) qmax = 291.24 lb/ft2 Eq. 10.6 qmin = 5.23 lb/ft2 Eq. 10.6 Check eccentricity (see Figure 10-21) e = eccentricity, cannot exceed L/6 Output: e = 1.37 ft L/6 = 1.42 ft e < L/6 - acceptable downward load, no need to check uplift resistance ..=...... ..=......2±6....3 Equation 13.1. Pile Driving Resistance for Drop Hammer Pile Drivers Equation 13.1 Eq. 13.1 Where: Qall = allowable pile capacity (lb) W = weight of the striking parts of the hammer (lb) H = effective height of the fall (ft) S = average net penetration, given as in per blow for the last 6 in. of driving Calculation Input: W = 1000.00 lb H = 5.00 ft S = 1.00 ft Output: Qall = 5000.00 lb Eq. 13.1 ........=2....(..+1)