Design of Offshore Structure

DESIGN OF OFFSHORE STRUCTURESINTRODUCTION • Offshore structures are constructed to explore the oil resources and for drilling purposes. • In the Gulf of Mexico, the first offshore structure was placed in 1945 in 6m water depth for drilling an exploration well. • The structure was made of timber and supported a converted land rig which drilled a dry hole. • In 1947 the first production well was drilled from a steel structure in 10m water depth. • In 1960 the first structure was installed in over 50m water depth and in 1967 the 100m barrier was broken in the Gulf of Mexico. • In 1976 first structure of 200m was installed in offshore California and 300m structure was installed in 1978, in Gulf of Mexico. • Various basic technologies involved in any offshore structural design is shown in Fig. 1 TECHNOLOGY Oceano graphy Foundation Engineering Wind Wave Current forces forces Tide Ice Soil Characteristic Vertical pile – soil characteristics Lateral pile – Soil characteristics Structural Engineering Materials selection and corrosion Stress analysis Marine Civil engineering Installation equipment Naval Architeure Flotation & Buoyancy Towing Installation methods Launching Welding Structural analysis Scour Navigation safety instrumentation Controlled flooding Design for fabrication and installation Appurtenances Fig.1 Technologies involved in offshore platform design . bottom-supported units (jacket type.CLASSIFICATION OF OFFSHORE PLATFORMS • Classification of the offshore platform can be done based on functional aspects. (Drill ships and semi-submersibles) . floating units. namely 1.gravity platforms…etc. geometric form.) 2. • The platforms can be classified into two main categories. construction and installation methods etc.. .a) Jacket Platforms • These are open steel trusses of tubular section pinned to the seabed with piles. • All the platforms in Bombay High are of this type. • It is used for offshore drilling and production operation. • Jacket platforms are also called template structures. • The piles are driven from above the water surface. a heavy concrete mat is laid on the seafloor. •Useful for scour protection and to facilitate grouting the foundation. •These skirts which in the form of short cylindrical shells provide resistance against horizontal sliding. •Over the concrete mat. with steel skirts attached to them. •In the CONDEEP platform construction.(b) Gravity Platform • Rests directly on the ocean floor. . cylindrical domed storage cells are mounted and three or more towers continue upward to support the deck. •The mat is provided with concrete skirt. (c) Jack-Up Platforms •The most widely used platforms now for exploration. • These are towed to location. hydraulic jacks or electric rack and pinion drives lower the legs to the sea floor •and then lift the hull above the sea surface to achieve the required clearance. . where pneumatic jacks. transport insures. •They are difficult to tow. •Depending on bottom mooring. •Much more expensive to build. •They are usually moored position with an elaborate system of anchors. chain and tensing devices. their depth capability is limited to shallow water depths (upto 450 m) than platform relying on dynamic positioning. the primary buoyancy is well below the water surface. .(d) Semi-Submersible •When they are floating. (e) Articulated Platform • It consists of a base plate resting on the ocean bottom. • The articulated platforms offer lower construction cost. • The column can be truss type in which case the buoyancy tanks are attached to the truss at convenient levels. fewer siting problems and an environmental cleaner method of loading. the buoyancy is offered by the watertight cylinders itself. a universal swivel joint and a column with buoyancy tanks. • If the column is cylindrical and water tight. •The cylindrical towers can be made of steel or concrete. . . • The base can partially penetrate the seabed. •The structure is held upright by several guy lines that run to clump weights on the ocean floor. • GT consist of a slender steel space frame and the vertical forces on the platform are taken by a foundation base. •GT and the TLP are the forms quite suitable to such depths. the weight and foundation requirements are less attractive than traditional offshore structures. •The guyed-tower considered to be applicable to water depths of about 600 m.(f) Guyed Tower(GT) •Water depths more than 300 m. (g) Tension Leg Platform(TLP) •TLP consists of a buoyant structure held by tautly moored vertical or inclined cables. •. • A major advantage of the TLP concept is its relative cost insensitivity to increase water depths. . Figure 2 shows the other types of offshore structures and their features. • The anchor cables are held on the sea floor by large deadweight anchors or one large gravity type seabed. only Jacket platform is taken into consideration and discussed. (contnd. • Importance should also be given to environmental condition combined with appropriate dead and live loads.3.. however in this lecture.…) . • There are two methods to design any offshore platform structures and they are. • The primary methodology of design concepts any offshore structure are almost similar. DESIGN CONCEPTS • Any offshore platforms should be designed for the appropriate combination of loading condition. This allowable or working stress is obtained by dividing the material yield stress by a factor of safety. (b) Load and Resistance Factor Design (LRFD) method • • The design checked by. . applying separate load and resistance factors to nominal loads and nominal resistance. It considers the possible uncertainties in the applied loads and component resistances.(a) Working Stress Design (WSD) method • • The stresses produced by nominal loads(unfactored) compared with an allowable or working stress. axial compression. live. beam bending. etc. .In terms of API RP 2A-LRFD (1993). it has meant the replacement of the traditional one-third increase in allowable stresses by separate load factors () for dead. wind/wave/current and earthquake loads and resistance factors () which vary for pile capacity. 5. wind loads 3. 2. gravity loads. accidental loads occurring during its service life.ii) Design for In-place Conditions The platform should be designed to resist 1. current loads. . and 6. wave loads 4. earthquake loads. (a)Wind Forces •The wind speeds refer to values 30ft above the earth. • The wind speeds at other elevations, a one-seventh power law has generally been found to be adequate for elevations to about 600ft. • If V denotes the wind speed at an elevation y, and Vo denotes the wind speed at the 30ft elevation, then 1/ 7  y V = Vo  30  Where y is measured in feet.   •In the absence of information, over-water wind speeds are about 10% greater than those for nearby coastal stations are considered (contnd…) •The wind force acting on an ocean structure is the sum of the wind forces acting on its individual parts. •For structural member such as storage tank, deck house, etc., the wind force arises from the viscous drag of the air on the body and from the difference in pressure on the windward and leeward sides. •The net force on the object to be described by an equation of the form F= 1 CAV 2 2 (b) Waves •The forces exerted by waves are usually the dominant design criterion affecting fixed structures. • Waves are primarily caused by the action of wind on water, which through friction transmit energy from the wind into wave energy. •Figure 3 shows classification of waves. •A narrow range of wave periods from 5 to 15 sec, is usually more important. •Waves in this range are referred as gravity waves and share the highest part of total wave energy. (contnd…) . period and direction. •Figure 5 shows the relative percentages of wind and water wave forces on a typical template platform over its height. it is denoted as. •Mathematically. FI is the Inertial force and FD is the Drag force.•Design wave forces should be based on extreme environmental conditions (average expected recurrence interval of 100 years). •Figure 4 shows a typical example of orientation of structure and the wave loading. •The primary properties of the wave that affects the design are height. F= FI+FD Where. (c) Currents •Even when small in magnitude. •They exert horizontal pressures against structural surfaces and. •Influence on the movement of vessels and floating structures and on moorings. •They change the characteristics of waves. . due to the Bernoulli effect. develop uplift or downdrag forces on horizontal surfaces. have a significant effect on construction operations. as well as currents due to river discharge. •The vertical profile of currents is considered as decreasing with depth as a parabolic function. wind-driven and density currents. tethers. and piping. geostrophic. which may lead to scour and erosion of the soils. •Types of currents: oceanic circulation. (contnd…) .•Create eddy patterns around structures. •They cause vortex shedding on piles. Tidal. • Other loads such as air-sea temperatures. •When the sun and moon are approximately 90o apart. that is. at the first and third quarter of the moon. marine growth and ice loading are also to be considered while designing. these are called neap tides. .(d) Tides •Tides result from the gravitational pull of the moon and the sun. the ranges are lower. • Due to the relative masses and distances the sun exerts only half the influence on the tides as the moon. for installation forces. •In the case of WSD method. (contd…) .(iii) Design for Construction Conditions •The offshore platform in general is fabricated on the shore and is transported to the desired offshore location by mean of a launch barge. •The loads that occur during the operation of moving the platform components and installing are to be considered. basic allowable stresses for member design may be increased by 1/3 in keeping with normal allowable stress condition. 3 Sheltered location. Table 1 Load factors for dynamic effects WSD LFRD Open. in design of platform.35 1.15 Location (contd…) . Exposed Sea 1. or lift onshore 1.The dynamic loading involved during the installation should also be considered.15 1. should be used in determining the motion of the tow. . • In that case. • Large jacket platforms will extend beyond the launch barge and will usually be subjected to submersion during tow. by selecting appropriate condition. the effects like slamming buoyancy and collapse forces due the submersion are to be considered. inertial and hydrodynamic loads and the components should be designed accordingly.•The environmental criteria. • All the structural components should be analyzed for the gravitational. iv) Strength and Stability Check (a) Axial Tension The axial tensile stress due to factored loads should not exceed the allowable tensile stress given in Table 2 Table 2: Allowable stress for axial tension Allowable Stress LRFD WSD t Fy 0. ft is the axial tensile stress due to factored loads .6 Fy t = resistance factor for axial tension=0.95 Fy = nominal yield strength and ft  allowable stress Where. Fcn = nominal axial compressive strength fc = axial compressive stress due to (factored) loads and Fa = allowable axial compressive strength i) Column Buckling The nominal axial compressive strength for tubular members subjected to column buckling should be determined from the equation given in Table 3.85 Where.(b) Axial Compression: The axial compressive stress due to (factored) loads should not exceed the allowable stress fc c Fcn c =0. .  Kl / r  1   2C  3Kl / r  5/ 3   8C Fa = 2 c c Fa  F  Kl / r  8C y 3 c 12π 2 E = 23 ( Kl / r ) 2  =column slenderness parameter = Kl  Fy  E K l r 3 = Young’s Modulus of elasticity = effective length factor = unbraced length = radius of gyration   π r  E  0 .0  0.Table 3: Nominal axial compressive strength (column buckling) LRFD   WSD Kl/r  Cc 2 2 Fcn = Fcn = 1.25 λ F 2 1 λ 2 Fy y 2 1/ 2 Cc = 12π 2 E    F  y  Kl / r  Cc Where.5 . 64 – 0.(ii) Local Buckling The nominal local buckling strength (stress units) values are given in Table 4. Fxe = nominal elastic local buckling strength C and Cx = critical elastic buckling coefficient D = Outside diameter t = wall thickness x = subscript for member longitudinal axis Fxc = nominal inelastic local buckling strength .23 (D / t)1/4] Fy  Fxe Where.23 (D/t)1/4]Fy Fxc = [1. Table 4 : Nominal axial compressive strength (local buckling) LRFD Elastic Local Buckling Inelastic Local Buckling D/t 60 D / t  60 WSD Fxe = 2CxE (t/D) Fxe = 2CE (t/D) Fxc = Fy Fxc = Fy Fxc = [1.64 – 0. 58  Fy Et   S  Fb = Fy D   0.(c) Bending For LRFD: fb   b Fbn and b = 0.75 Fy Fbn = Fy D  Z   1.76    Fy Et   S   Fb = Fy D   0.72  0.74  Fy Et   Fbn = Fy D   Z   0.84  1.95 Table 5: Allowable stress in bending LRFD D/t  10340 / Fy 10340 / Fy < D / t  20680 / Fy 20680 / Fy< D / t  300 Fbn = (Z / S)* Fy WSD Fb = 0.58  Fy Et   .94  0.13  2. Fy  3 .(d) Shear i) Beam Shear For LRFD: fv   Fvn where Fvn = nominal shear strength. in stress units fv = maximum shear stress due to factored loads V = beam shear due to factored loads A = cross sectional area and Fv = allowable beam shear stress . fvt = torsional shear stress due to factored loads fv = nominal torsional strength Fy  3 I = polar moment of inertia and Mt = torsional moment and Mvt = torsional moment due to factored load Fvt = allowable torsional shear stress Table 6: Maximum shear stress LRFD and WSD Beam Shear fv = Torsional Shear fvt = 2V A M vt D 2I p . Torsional stress For LRFD: fvtv Fvtn where.2. 5  M  0.5  M  0. Elastic Hoop Buckling Stress(Fhe) Fhe = 2Ch Et/D where the critical hoop buckling coefficient Ch Table 7: Critical hoop buckling coefficient LRFD Ch 0.559) @ 1.5  M < 3.8 @ M  1.825 D/t 0.44 t/D + 0.579) 0.21D / t 3 @ 0. is defined as M = L 2D L = Length of cylinder between stiffening rings D t .6 D/t M4 0.736 / (M – 0.(e) Hoop Buckling Stress 1.5 0.8 for M  1.737 / (M – 0.21D / t 3 M 4 for 0.5 where the geometric parameter.755 / (M – 0.825 D/t 0.636) @ 3.825 D/t  M1.6 D/t 0.44 t/D @ M  1.6 D/t 0.6 D/t 0. M.5 for 1.44 t/D+ WSD for M  1.44 t/D 0.825 D/t M1. 2.45Fy + 0.31Fy  1.4  Fy Fhe = 0.6Fy < Fhe  6. Critical Hoop Buckling Stress Table 8: Critical hoop buckling stress LRFD Elastic Buckling Inelastic Buckling Fhc = Fhe 0.55 Fy Fhc = Fhe @ Fhe  0.55 Fy WSD @ Fhe  F   he  y  Fy    0.7 F @ Fhe > 0.15  Fy / Fhe  @ 1.18Fhe @ 0.55 Fy Fhc = 0.6Fy Fhc = 1.2Fy Fhc = Fy @ Fhe > 6.2Fy .55Fy < Fhe  1. 0. •a jacket is considered to have failed when any of the interaction ratios reach a value equal to 1. Fhc = critical hoop stress Faa = Fxe/SFx and Fha = Fhe/SFh SFb = safety factor for bending . fby.Cmz = reduction factors corresponding to the member y and z axes respectively Fey. resultant bending stress and hoop fh compression stress.Fez = Euler buckling strengths to member y and z axes (Fey = Fy/y2 and Fez = Fz/z2) y. fband = absolute value of acting axial.(f) Interaction Equations •Interaction ratios that are to be satisfied are given in Table 9. Cmy. respectively. fbz = bending stress about member y and z axes due to factored loads fa. z = column slenderness parameters for the members in y and z axes. 4. which cause the failure of the jacket platform. (a) (b) (c) (d) Marine Growth Wave Steepness Flooding of the Jacket Legs P-Delta Effect . PARAMETRIC STUDY A parametric study has been carried out by Sundaravadivelu and Manjeet Singh Chagar (2001) to ascertain the effect of following factors on the limiting wave height. 0 fa  Fa      C  C f   mx f bx    my by  fa   fa   1  1     Fe' x   Fe' y    1.0 fa  0.0 Fb f bx 2  f by2 fa   1.Table 9: Member Interaction Ratios LRFD Combined Axial Compression and Bending    fc 1  C my f by   φ c Fcn φ b Fbn   fe    1  φ F c ey    WSD 2         C mz f bz           1 f e          φ c Fez     2          π f   f by 2  f bz  c   φ b Fbn  2 φ c Fxc  0.0 Fa Fb (contd…) .5  1.5 when 1.6Fy Fb 0.0 0.15. Fa 2 2 fa f bx  fby   1. 5Fha   h Faa  0.0 Fxc Fy fh (SFh )  1.Combined tension And bending Combined Axial Compression Bending and Hydrostatic Pressure 1-cos   π f   f by 2  f bz t   φ b Fbn  2 φ t Fy   0.0 Fb where fbx and fby are computed bending tensile stresses fa  (0.5Fha  Fha     2 (contd…) .5φ h Fhe   h   1. fx > 0.5hFhe) 2  f  f x 0.6Fy f bx2  f by2  1.e.0 Fhe  f f x  0.0 when axial utilization exceeds 0.5 (i.5φ h Fhe φ h Fhe  fx = fc+fb+(0.5f h ) f (SFx )  b (SFb )  1.5fh) fa  0.5 2  1.0 φ cFxe  0. 3 =5- 4Fhc Fy SF fh (SFh ) Fhc = Poisson’s ratio = 0.0 Where where A= ft  f b  (0.0 A2 + B2 + 2AB 1.5f h ) f  f  (0.Combined Axial Tension Bending and Hydrostatic Pressure A2 + B2 + 2AB 1.3 = safety factor for axial tension SF = safety factor for h hoop compression x .5f h ) A= a b (SFx ) Fy φ t Fy fh B= φ h Fhc B=   = Poisson’s ratio=0. • Effect of marine growth is shown in Table 10.(a) Marine Growth • Marine growth is assumed to be uniform thickness from seabed to the mean sea level. • The limiting wave height causing the failure of the jacket obtained by using LRFD is about 2% more then the wave height obtained using WSD . • The surface finish of members is considered to be rough where marine growth is present and smooth where marine growth is absent. • Above the mean sea level no marine growth is assumed. Table 10: Effect of Marine growth Thickness of marine growth (mm) Limiting wave height (m) causing failure WSD Percentage reduction Ratio of wave height for LRFD & WSD LRFD Percentage reduction 0 24.022 50 24.1 1.021 250 21.476 3.276 6.2 22.3 1.4 21.626 8.000 3.4 1.022 100 23.040 13.8 1.021 .815 - 24.160 8.800 6.2 23.8 22.021 150 22.286 - 1.478 13. 6. •The limiting wave height causing the failure of the jacket increases with increase in wave steepness for the both LRFD and WSD.(b) Wave Steepness •The analysis is carried out for waves with steepness varying from 1/7 to 1/30 •The variation in the wave height causing failure is compared with the Fig. . (c) Flooding of Jacket Legs •The effect of the flooding is to nullify the effect of hydrostatic pressure and allow the jacket platform to withstand higher waves. •All the legs of the platform are assumed to be flooded and the analysis is done to determine the limiting wave height causing the failure of the jacket platform. •The flooding causes 7% and 8% increase in the limiting wave height causing the failure of the jacket platform respectively for LRFD and WSD procedures (Table 11) . 193 1.443 23.07 WSD 25.872 24.Table 11: Effect of Flooding of Main legs Wave height (m) causing the Ratio of Wave height causing failure of the jacket failure of the jacket Main legs Flooded Main legs NonFlooded for Flooded condition to Non-Flooded condition Ratio of Wave height causing failure of the jacket for Flooded condition to Non-Flooded condition LRFD 25.586 1.08 . it may be necessary to perform a more accurate analysis. • The lateral deflection because of this are more as compared to the case when only lateral force or bending moment is present. •In such case additional bending moments due to the axial forces when the member deflects laterally should be considered. • This axial – flexural interaction is called the P – Delta effect. it is assumed that there is no interaction between axial forces and bending moments. (contd…) .(d) P – Delta Effect •In case of linear analysis. •If the axial forces are large or if the member is slender. The member forces and moments derived from the load combinations are used to check the stability in accordance with API RP 2A-LRFD (1993). The strength and stability interaction ratios are obtained using bending and axial stress interaction equations given in Table 9. API RP 2A-WSD (1993). 7.The deflections at the deck of the jacket platform were calculated for a wave height 24m. A best-fit line has been drawn for each case and the percentage variation from the equality line has been calculated as 31.2% for WSD and 0.27% for LRFD.3% . using WSD and LRFD and the effect of P – Delta is to increase the deflection by 0. The scatter diagrams of interaction ratios of WSD vs LRFD for all the members are shown in Fig. 0 Fy (11  1.5 /β) . The above rule can be considered satisfied for simple tubular joints when the following condition is obtained. Fy b (γτ sin )  1. CONNECTIONS The components are connected together to form structure and the connection may be at the ends of tension or compression members. The strength of connection should satisfy the design loads. and as the yield load for member primarily load in tension. but not less than 50% of the effective strength Effective strength:The buckling load for member loaded is either tension or compression.5. Air gap. The bottom of the lowest deck should be located at an elevation. water depth uncertainty.5m should be added to the crest elevation to allow for unexpected platform settlement. and for possibility of extreme waves. (contd…) . of at least 1.6. which will clear the calculated crest of the design wave with adequate allowance for safety. computed from appropriate wave theories. MINIMUM DECK CLEARANCE When waves strike a platform’s deck and equipment. The wave crest elevations. large forces exerted on it. above storm water level including guideline storm tide. When it is needed to position any component below the lower deck in the designated air gap. . An additional air gap should also be provided for any known or predicted long-term seafloor subsidence. then design wave crest pressure should also be considered in their design.This air gap decides the minimum acceptance elevation of the bottom beam of the deck to avoid waves striking the deck. Many offshore structural components are made of hollow steel pipes. ASTM A252. The minimum requirement for fabrication and service should satisfy API. ASTM A139. (AISC) and Det Norske Veritas (DNV). ASTM A381 or ASTM A671 codes. (contd…) . STRUCTURAL MATERIALS The offshore structural materials should be selected based on the recommendations provided by the (API).7. The structural steel materials for specific conditions can follow the detailed recommendations given in the above codes. At any cases.The concrete material are to be selected with due attention to their strength and durability in the marine environment. bond strength and workability for underwater placement including cohesiveness and flowability. the water cement ratio should be less than 0. The concrete mix to be selected on the basis of shear strength. In general.45. all structural material should be selected with due consideration to chemical resistance. mechanical resistance and corrosion resistance. . splash and atmospheric. • Figure 9 shows the various corrosion zones. • Dry-corrosion: Even in the absence of water. the non-metallic materials are attacked by the chemical corrosive media •The three primary zones of corrosion in any typical offshore structure are immerse.8. • Wet-corrosion: Metals often corrode due to the electrochemical action. due to the action of water and the atmosphere. (contd…) . CORROSION •Almost all metals components suffer corrosion to some extent. . The splash zone is the most critical area of corrosion and it is desirable to minimize the steel in this area. which are positioned in the atmospheric zone. Zinc painting over the members would be sufficient. but frequent inspection of coatings is required. Either non-corrosion coverings or increasing thickness of steel member can be adopted as protective measures. The least corrosion rate occurs on the member.Galvanic corrosion predominates in the immersed zone and can be protected either by a system of sacrificial galvanized anodes or by impressed current generator–rectifier with inert anodes. Jacket platform consisting of the tower and deck are constructed separately. the jacket tower is erected at the site and then the upper deck is attached over it. . either by launch barge method or by flotation method. Initially. The transportation and installation of jacket tower can be done is two ways. offshore structures are fabricated near the coast and then transported to the offshore site and erected. TRANSPORTATION AND INSTALLATION Generally. In particular.9. Transportation and installation procedure for a jacket structure Transportation and installation procedure for a typical offshore jacket structure is shown in Fig. 10 a) b) c) d) e) f) g) h) Load out Towing Launching Floating Upending Vertical position Piling Deck mating . Jacket towers of long length can not be launched by means of barge.The fabricated jacket tower is loaded out in the launch barge. the platform is positioned at the site for the pilling to be installed. . The horizontally floating platform is selectively ballasted to bring it into vertical position. Launch barge is a rectangular floating vessel with controlled ballasting and de-watering system for draft of floatation. which may be extending the length of the barge. The positioning of the jacket on the barge required predesigned structural arrangements to avoid sinking of barge. After upending. As an alternate to the launch barge method. The tower would be made to float by large diameter tubes to offer sufficient buoyancy to the tower floating horizontally. the jacket is allowed to skid or slide. a newly developed method in which floating pontoon is used. Once the tower floats.The loaded barge with jacket is then towed to the site where the platform to be launched. by means of tiling the barge. then the tower is towed by means of two or more tugboats. The pontoon consists of large diameter circular tubes that provides necessary buoyancy. . At the site. 5. 8. Jr. Dawson. 20th Edition. American Petroleum Institute (1993). Department of the Army. Vol. API RP 2A-WSD. Gulf Publishing Company. Graff. “Comparison of LRFD and WSD procedures for Jacket Platform”. “Offshore Structural Engineering”. API RP 2A-LRFD. American Petroleum Institute (1993). 1984. US army corps of Engineers. 4. Inc. Prentice-Hall. Designing and Constructing Fixed Offshore Platforms-Working Stress Design. Ben C. 3. Det Norske Vertitas. April 23-26... . 2. 1993. pp. Sundaravadivelu. Thomas H. Gerwick.I and Vol. Rules for Classification of Fixed Offshore Installations. Designing and Constructing Fixed Offshore Platforms-Load and Resistance Factor Design. CRC Press.Tech Thesis.II. “Comparison of LRFD and WSD procedures for Jacket Platforms”. Manjeet Singh Chagar. Recommended practice for Planning. 51-56. Proceedings of First Asia Pacific Conference on Offshore Systems (APCOS). Department of Ocean Engineering. 6. Recommended practice for Planning. 9. “Introduction to Offshore Structures: Design. 1998. Part 3 Chapter 1. REFERENCES 1. Second Edition. Fabrication and Installation”. Structures. Fourth Edition.J. 2001. M. Indian Institute of Technology Madras. Shore Protection Manual. Malaysia.10. “Construction of Marine and Offshore Structures”. W. 1st Edition. 2001. 7. R and Manjeet Singh Chagar. wave and other loads .5 Relative values of wind.Fig.