USFOS. Joint Capacity. Theory Description of use Verification

Transcription

1 USFOS Joint Capacity Theory Description of use Verification

2 Table of Contents 1. INTRODUCTION General MSL variants Code variants THEORY Joint capacity formulas General Basic resistance, MSL Strength factor u Chord action factor f Strength check Design axial resistance for X and Y joints with joint cans Basic resistance, NORSOK N-004, Revision Strength factor u Chord action factor f Strength check Design axial resistance for X and Y joints with joint cans Basic resistance, NORSOK N-004 Revision Strength factor u Chord action factor f Strength check Design axial resistance for X and Y joints with joint cans Basic resistance, ISO 1990: Strength factor u Chord action factor f Strength check Design axial resistance for X and Y joints with joint cans Basic resistance, API RP A-WSD, ES3 Oct Strength factor u Chord action factor f Strength check Design axial resistance for X and Y joints with joint cans Joint classification Joint behaviour and ductility limits Joint P-D curves MSL Ductility limits USFOS Specific adjustments DESCRIPTION OF USE General Input description VERIFICATION K-Joints Gamma = 10, Beta =0.8, gap/t=

3 Gamma = 10, Beta = 0.8, gap/t = Gamma = 10, Beta = 0.8, gap/t = Gamma = 5, Beta = 0.8, gap/t = T/Y-Joints Gamma = 5, Beta = Gamma = 10, Beta = X-Joints Gamma = 5, Beta = Gamma = 10, Beta = Gamma = 10, Beta = REFERENCES... 68

4 4 1. INTRODUCTION 1.1 General The current joint capacity check included in USFOS covers simple tubular joint and is based on capacity formulas and description of the joint behaviour developed during the MSL Joint Industry Projects as described in /1/, //. In addition to the original MSL formulations, code variants from Norsok/3/and /6/, ISO 1990 /4/ and API RP A WSD /5/ are also implemented. 1. MSL variants The MSL Joint Industry Projects developed several sets of capacity formulas based on a large database of laboratory test results. The original MSL versions you find in USFOS includes: Mean Ultimate Characteristic Ultimate Characteristic First Crack Mean Ultimate represents the statistical mean failure of the joints tested (top of the force-displacement curve, "the most probable failure load"). Characteristic Ultimate is based on the same data, but the as the title say, the capacity is reduced in order to account for the spreading in the test results. Characteristic First Crack is in most cases equal to "Characteristic Ultimate" but is further reduced in some cases in order to avoid degradation of the joint for repeated loading. This version is recommended for structures subjected to repeated load actions, e.g. wave loading. 1.3 Code variants Note that the first crack characteristic capacity equations in the code variants are implemented in USFOS excluding the safety factors given in the codes. The additional safety level required by the code for the various limit states analysed must in USFOS be included on the load side (by increasing the applied loads). Norsok N-004 Revison, ISO: The MSL capacity check formulas have been adopted and adjusted by Norsok (rev ) and ISO. The code variants are based on the MSL First Crack capacity formulas. The ( u ) expressions are nearly identical, but the correction factor for chord utilisation differs from MSL. Also the interaction between axial force, in-

5 5 plane and out-of-plane bending differs, the code variants put more weight on the out-of plane bending component. API RP A: The formulas are also based on the MSL database, however, the database used to develop the latest joint capacity equations for API RPA are extended using results from FE analyses. API RPA (1 st edition) is currently (009) the most updated code with respect to joint capacity. Norsok N-004 Revision 3: The code is aligned with APIRPA (009) with some exceptions: -The basic capacity for X joints in axial tension follows OMAE /7/. In addition the expressions for chord utilisation factors are adjusted for X-joints.

6 6. THEORY.1 Joint capacity formulas.1.1 General The validity range for capacity equations given in Chapter and implemented in USFOS are as follows: 0. β γ θ 90 f y 500 MPa g 0.6 (for K joints) D The above geometry parameters are defined as d β =, D D γ =, T τ = t T Where d = brace diameter, D = Chord diameter, t = brace wall thickness, T = Chord thickness and g = gap between the two braces (for K-joints). d t d t D T crown Θ crown saddle L T Θ D

7 7 da d B d A d C BRACE A t A t B d B BRACE B A t A t B B C t C T Θ A g Θ B T Θ A Θ B Θ C D D g AB g BC Figure -1 Definition of joint geometry parameters.1. Basic resistance, MSL The resistances for simple tubular joints are defined as follows: N Rd f yt = sinθ u f M Rd Where f yt d = sinθ u f N Rd = the joint axial resistance M Rd = the joint bending moment resistance f y = the yield strength of the chord member at the joint For braces with axial forces with a classification that is a mixture of K, Y and X joints, a weighted average of N Rd based on the portion of each in the total action is used to calculate the resistance Strength factor u u varies with the joint and action type, as given in Table -1 to Table -3.

8 8 Table -1 Joint Classification Values for u, MSL Mean Ultimate Brace action Axial Tension Axial Compression In-plane Bending K ( β ) β gyy 1.3( β ) β gyy Y X β γ β ( ) β β β for β ( β ) β ( β - 0.9)( 37.6γ 364) for β > β γ 5.5β γ Out-of-plane bending 4.γ 4.γ 4.γ 0.5β 0.5β 0.5β Mean Ultimate represents the statistical mean failure of the joints tested (top of the force-displacement curve, "the most probable failure load"). Table - Joint Classification Values for u, MSL Characteristic Ultimate Brace action Axial Tension Axial Compression K ( β ) β g yy ( β ) β gyy In-plane Bending 4.5β γ Out-of-plane bending 3.γ 0.5β Y X 41 β ( ) β β β. for β 0.9 ( β ) β + ( β - 0.9)( 3γ 85) for β > β γ 4.5β γ 35 Characteristic Ultimate is based on the same data as for Mean Ultimate, the capacity is reduced in order to account for the spreading in the test results γ 3.γ 0.5β 0.5β Table -3 Joint Classification Values for u, MSL Characteristic First Crack Brace action Axial Tension Axial Compression K ( β ) β g yy ( β ) β gyy In-plane Bending 4.5β γ Out-of-plane bending 3.γ 0.5β Y X 30 β 0.5 ( β ) 3 1 β β for β 0.9 ( β ) β + ( β - 0.9)( 17γ 0) for β > β γ 4.5β γ 1 Characteristic First Crack is in most cases equal to "Characteristic Ultimate" but is further reduced in some cases in order to avoid degradation of the joint for repeated loading. This version is recommended for structures subjected to repeated load actions, e.g. wave loading. β is a geometric factor defined by: γ 3.γ 0.5β 0.5β

9 9 β 0.3 = for β > 0.6 β ( β ) β = 1.0 for β 0.6 g is a gap factor defined by: g 0.5 g g = 1.9 for.0,but g 1. 0 D T g 65 g T 0.5 = φγ for. 0 where φ = t f T f y,b y,c f y,b = yield strength of brace (or brace stub if present) f y,c = yield strength of chord (or chord can if present) g = linear interpolated value between the limiting values of the above expressions for g.0.0 T yy is an angle correction factor defined by: yy = 1.0 when θ 4θ 90 yy θ c θ t = 00 t when θ > 4θ 90 t where θ c and θ t is the angle between the compression / tension brace and the chord respectively. c c.1.. Chord action factor f f is a factor to account for the presence of factored actions in the chord. f where: = 1.0 λ U λ = for brace axial tension or compression = for brace in-plane bending moment = 0.01 for brace out-of-plane bending moment

10 10 The parameter U is defined as follows: 1 U = Γ where: q P C1 N P + C M M P ipb + C M M P opb 0.5 P = axial load in chord M = bending moment in chord, (ipb and opb) N P = axial capacity of chord M P = bending capacity of chord C 1, C = coefficients depending on joint and load type Γ q = assessment factor of safety, not to be taken greater than unity Table -4 Values for C 1 and C, MSL Joint Classification C 1 C T/Y joints under brace axial loading 5 11 DT/X joints under brace axial loading 5 43 K joints under balanced loading All joints under brace moment loading 5 43 The chord thickness at the joint should be used in the above calculations. The highest value of U for the chord on either side of the brace intersection should be used. Apart from X joints with β > 0.9, f may be set to unity if the magnitude of the chord axial tension stress is greater than the maximum combined stress due to chord moments Strength check Joint resistance shall satisfy the following interaction equation for axial force and/or bending moments in the brace: N N Sd Rd Where: M + M y,sd y,rd M + M z,sd z,rd 1 N Sd = N Rd = M y,sd = M z,sd = M y,rd = M z,rd = axial force in the brace member the joint axial resistance in-plane bending moment in the brace member out-of-plane bending moment in the brace member in-plane bending resistance out-of-plane bending resistance

11 Design axial resistance for X and Y joints with joint cans For Y and X joints with axial force and where a joint can is specified, the joint design resistance should be calculated as follows: N Rd Where = r + T T c n ( 1- r) Ncan, Rd N can,rd = N Rd based on chord can geometric and material properties T n = nominal chord member thickness = chord can thickness T c DT/X Joints: r = Lc/(.5D) for joints with β 0.9 ( 4β 3) Lc / 1. 5D for joints with β > 0.9 = [ ( )] Y/T Joints: r = Lc/(.0D) for joints with β 0.9 ( 5β /3 1)Lc / D for joints with β > 0.9 = [ ] Lc = effective total length of chord can, excluding taper, see Figure - In no case shall r be taken as greater than unity. Figure - Calculation of Lc The reduction for short can sections is currently not implemented in USFOS, and should be accounted for when selecting effective can section thickness.

12 1.1.3 Basic resistance, NORSOK N-004, Revision The resistances for simple tubular joints are defined as follows: N Rd f yt = sinθ u f M Rd Where f yt d = sinθ u f N Rd = the joint axial resistance M Rd = the joint bending moment resistance f y = the yield strength of the chord member at the joint For braces with axial forces with a classification that is a mixture of K, Y and X joints, a weighted average of N Rd based on the portion of each in the total action is used to calculate the resistance Strength factor u u varies with the joint and action type, as given in Table -3. Table -5 Joint Classification Values for u Brace action Axial Tension Axial Compression K ( β ) 0.5 β g ( β ) 0.5 β g Y X 30 β 0.5 ( β ) 3 1 In-plane Bending 4.5β γ β β for β 0.9 ( β ) β + ( β - 0.9)( 17γ 0) for β > β γ 4.5β γ Out-of-plane bending 3.γ 3.γ 3.γ 0.5β 0.5β 0.5β β is a geometric factor defined by: β 0.3 = for β > 0.6 β ( β ) β = 1.0 for β 0.6 g is a gap factor defined by: g 0.5 g g = 1.9 for.0,but g 1. 0 D T

13 13 g 65 g T 0.5 = φγ for. 0 where φ = t f T f y,b y,c f y,b = yield strength of brace (or brace stub if present) f y,c = yield strength of chord (or chord can if present) g = linear interpolated value between the limiting values of the above expressions for g.0.0 T.1.3. Chord action factor f f is a factor to account for the presence of factored actions in the chord. f = 1.0 λ U Where: λ = for brace axial tension or compression = for brace in-plane bending moment = 0.01 for brace out-of-plane bending moment The parameter U is defined as follows: P U = C1 N P where: + C M M P ipb + C M M P = axial load in chord M = bending moment in chord, (ipb and opb) N P = axial capacity of chord M P = bending capacity of chord C 1, C = coefficients depending on joint and load type Table -6 Values for C 1 and C, NORSOK N-004 r P opb Joint Classification C 1 C T/Y joints under brace axial loading 5 11 DT/X joints under brace axial loading 0 K joints under balanced loading 0 All joints under brace moment loading

14 14 The chord thickness at the joint should be used in the above calculations. The highest value of U for the chord on either side of the brace intersection should be used Strength check Joint resistance shall satisfy the following interaction equation for axial force and/or bending moments in the brace: N N Sd Rd M + M y,sd y,rd + M M z,sd z,rd 1 where: N Sd = N Rd = M y,sd = M z,sd = M y,rd = M z,rd = axial force in the brace member the joint axial resistance in-plane bending moment in the brace member out-of-plane bending moment in the brace member in-plane bending resistance out-of-plane bending resistance Design axial resistance for X and Y joints with joint cans For Y and X joints with axial force and where a joint can is specified, the joint design resistance should be calculated as follows: N Rd Where = r + T T c n ( 1- r) Ncan, Rd N can,rd = N Rd based on chord can geometric and material properties T n = nominal chord member thickness T c = chord can thickness r = Lc/(.5D) for joints with β 0.9 = [( 4β 3) Lc /( 1. 5D) ] for joints with β > 0.9 Lc = effective total length of chord can, excluding taper, see Figure -3. In no case shall r be taken as greater than unity.

15 15 Figure -3 Calculation of Lc The reduction for short can sections is currently not implemented in USFOS, and should be accounted for when selecting effective can section thickness.

16 Basic resistance, NORSOK N-004 Revision The resistances for simple tubular joints are defined as follows: N Rd f yt = sinθ u f M Rd Where f yt d = sinθ u f N Rd = the joint axial resistance M Rd = the joint bending moment resistance f y = the yield strength of the chord member at the joint (or 0.8 of the tensile strength, if less) For braces with axial forces with a classification that is a mixture of K, Y and X joints, a weighted average of N Rd based on the portion of each in the total action is used to calculate the resistance Strength factor u u varies with the joint and action type, as given in Table -11. Table -7 Joint Classification K Y Values for u Brace action Axial Tension Axial Compression In-plane Bending ( γ)β 1. but 30 β 40β 1. g X (0.6β ) 6.4γ g ( γ)β 1. but 40β 1. g.8 + ( γ)β but β g 1.6 [.8 ( γ ) β ] β 1. ( γ)β 1. ( γ)β + 1. ( γ)β Out-of-plane bending.5 + ( γ)β.5 + ( γ)β.5 + ( γ)β β is a geometric factor defined by: β 0.3 = for β > 0.6 β ( β ) β = 1.0 for β 0.6 g is a gap factor defined by: g 3 = 1+ 0.[1.8 g D] for g D 0.05, but g 1.0

17 17 g = φγ 0.5 for g D where φ = t f T f y,b y,c f y,b = yield strength of brace (or brace stub if present) f y,c = yield strength of chord (or chord can if present) g = linear interpolated value between the limiting values of the above expressions for 0.05 g D Chord action factor f f is a factor to account for the presence of factored actions in the chord. f = 1. 0 P + C 1 N p M C M ipb p C 3 A The parameter A is defined as follows: P A = N P and: M M P M P ipb M + opb + P = axial load in chord M ipb = inplane bending moment in chord M opb = out of plane bending moment in chord N P = axial capacity of chord M P = bending capacity of chord C 1 = coefficient depending on joint and load type, see Table -1 C = coefficient depending on joint and load type, see Table -1 C 3 = coefficient depending on joint and load type, see Table

18 18 Table -8 Values for C 1 C and C 3 Joint Classification C 1 C C 3 T/Y joints under brace axial loading DT/X joints under brace axial loading, compression b 0.9* b=1* DT/X joints under brace axial loading, tension b 0.9* b=1* K joints under balanced loading All joints under brace moment loading *) Linear interpolation for 0.9 b 1.0 The chord thickness at the joint should be used in the above calculations. The average of the chord loads and bending moments on either side of the brace intersection should be used. Chord axial load is positive in tension, chord in-plane bending moment is positive when it produces compression on the joint footprint Strength check Joint resistance shall satisfy the following interaction equation for axial force and/or bending moments in the brace: N N Sd Rd M + M y,sd y,rd + M M z,sd z,rd 1 where: N Sd = N Rd = M y,sd = M z,sd = M y,rd = M z,rd = axial force in the brace member the joint axial resistance in-plane bending moment in the brace member out-of-plane bending moment in the brace member in-plane bending resistance out-of-plane bending resistance Design axial resistance for X and Y joints with joint cans For Y and X joints with axial force and where a joint can is specified, the joint design resistance should be calculated as follows: N Rd = r + T T c n ( 1- r) Ncan, Rd

19 19 where N can,rd = N Rd based on chord can geometric and material properties T n = nominal chord member thickness T c = chord can thickness r = Lc/(.5D) for joints with β 0.9 = [( 4β 3) Lc /( 1. 5D) ] for joints with β > 0.9 Lc = effective total length of chord can, excluding taper, see Figure -5. In no case shall r be taken as greater than unity. Figure -4 Calculation of Lc The reduction for short can sections is currently not implemented in USFOS, and should be accounted for when selecting effective can section thickness..1.5 Basic resistance, ISO 1990:007 The resistances for simple tubular joints are defined as follows: N Rd f yt = sinθ u f M Rd f yt d = sinθ u f Where N Rd = the joint axial resistance M Rd = the joint bending moment resistance f y = the yield strength of the chord member at the joint

20 0 For braces with axial forces with a classification that is a mixture of K, Y and X joints, a weighted average of N Rd based on the portion of each in the total action is used to calculate the resistance Strength factor u u varies with the joint and action type, as given in Table -5. Table -9 Joint Classification Values for u Brace action Axial Tension Axial Compression K ( β ) 0.5 β g ( β ) 0.5 β g Y X 30 β 0.5 ( β ) 3 In-plane Bending 4.5β γ β β for β 0.9 (.8 ( γ ) β ) β + ( β - 0.9)( 17γ 0) for β > β γ β γ Out-of-plane bending 3.γ 3.γ 3.γ 0.5β 0.5β 0.5β β is a geometric factor defined by: β 0.3 = for β > 0.6 β ( β ) β = 1.0 for β 0.6 g is a gap factor defined by: g = g g γ for.0,but g 1. 0 T T g 65 g T 0.5 = φγ for. 0 where φ = t f T f y,b y,c f y,b = yield strength of brace (or brace stub if present) f y,c = yield strength of chord (or chord can if present) g = linear interpolated value between the limiting values of the above expressions for g.0.0 T.1.5. Chord action factor f f is a factor to account for the presence of factored actions in the chord.

21 1 f = 1.0 λ U Where: λ = for brace axial tension or compression = for brace in-plane bending moment = 0.01 for brace out-of-plane bending moment The parameter U is defined as follows: U = γ where: R, q P C1 N P + C M M P ipb + C M M P = axial load in chord M = bending moment in chord, (ipb and opb) N P = axial capacity of chord M P = bending capacity of chord C 1, C = coefficients depending on joint and load type γ Rq = is the partial resistance factor for yield ( set to 1.0 in USFOS) Table -10 Values for C 1 and C, ISO 1990:007 Joint Classification C 1 C T/Y joints under brace axial loading 5 11 DT/X joints under brace axial loading 0 K joints under balanced loading All joints under brace moment loading 5 43 The chord thickness at the joint should be used in the above calculations. The highest value of U for the chord on either side of the brace intersection should be used Strength check Joint resistance shall satisfy the following interaction equation for axial force and/or bending moments in the brace: P opb 0.5 N N Sd Rd M + M y,sd y,rd + M M z,sd z,rd 1 where: N Sd = N Rd = M y,sd = M z,sd = axial force in the brace member the joint axial resistance in-plane bending moment in the brace member out-of-plane bending moment in the brace member

22 M y,rd = M z,rd = in-plane bending resistance out-of-plane bending resistance Design axial resistance for X and Y joints with joint cans For Y and X joints with axial force and where a joint can is specified, the joint design resistance should be calculated as follows: N Rd where = r + T T c n ( 1- r) Ncan, Rd N can,rd = N Rd based on chord can geometric and material properties T n = nominal chord member thickness T c = chord can thickness r = Lc/(.5D) for joints with β 0.9 = [( 4β 3) Lc /( 1. 5D) ] for joints with β > 0.9 Lc = effective total length of chord can, excluding taper, see Figure -5. In no case shall r be taken as greater than unity. Figure -5 Calculation of Lc The reduction for short can sections is currently not implemented in USFOS, and should be accounted for when selecting effective can section thickness..1.6 Basic resistance, API RP A-WSD, ES3 Oct. 007 The resistances for simple tubular joints are defined as follows:

23 3 N Rd = f yt FS sinθ u f M Rd = Where f yt d FS sinθ u f N Rd = the joint axial resistance M Rd = the joint bending moment resistance f y = the yield strength of the chord member at the joint (or 0.8 of the tensile strength, if less) FS = is the safety factor (Default set to 1.0 in USFOS for characteristic capacity) For braces with axial forces with a classification that is a mixture of K, Y and X joints, a weighted average of N Rd based on the portion of each in the total action is used to calculate the resistance Strength factor u u varies with the joint and action type, as given in Table -11. Table -11 Joint Classification K Y X Values for u Brace action Axial Tension Axial Compression In-plane Bending ( γ)β 1. but 30 β 40β 1. g g ( β - 0.9)( 17γ 0) for β > 0.9 ( γ)β 1. but 40β 1. g.8 + ( γ)β but β 3β for β 0.9 [.8 ( γ ) β ] β g ( γ)β 1. ( γ)β + 1. ( γ)β Out-of-plane bending.5 + ( γ)β.5 + ( γ)β.5 + ( γ)β β is a geometric factor defined by: β 0.3 = for β > 0.6 β ( β ) β = 1.0 for β 0.6 g is a gap factor defined by: g 3 = 1+ 0.[1.8 g D] for g D 0.05, but g 1.0 g = φγ 0.5 for g D -0.05

24 4 where φ = t f T f y,b y,c f y,b = yield strength of brace (or brace stub if present) f y,c = yield strength of chord (or chord can if present) g = linear interpolated value between the limiting values of the above expressions for 0.05 g D Chord action factor f f is a factor to account for the presence of factored actions in the chord. f = 1. 0 FS P + C 1 N p FS M C M p ipb C 3 A The parameter A is defined as follows: FSP A = N P and: FSM + MP FS + M ipb M opb P P = axial load in chord M ipb = inplane bending moment in chord M opb = out of plane bending moment in chord N P = axial capacity of chord M P = bending capacity of chord C 1 = coefficient depending on joint and load type, see Table -1 C = coefficient depending on joint and load type, see Table -1 C 3 = coefficient depending on joint and load type, see Table -1 FS = is the safety factor (Default set to 1.0 in USFOS for characteristic capacity) 0.5 Table -1 Values for C 1 C and C 3 Joint Classification C 1 C C 3 T/Y joints under brace axial loading DT/X joints under brace axial loading b 0.9* b=1* K joints under balanced loading All joints under brace moment loading *) Linear interpolation for 0.9 b 1.0

25 5 The chord thickness at the joint should be used in the above calculations. The average of the chord loads and bending moments on either side of the brace intersection should be used. Chord axial load is positive in tension, chord in-plane bending moment is positive when it produces compression on the joint footprint Strength check Joint resistance shall satisfy the following interaction equation for axial force and/or bending moments in the brace: N N Sd Rd M + M y,sd y,rd + M M z,sd z,rd 1 where: N Sd = N Rd = M y,sd = M z,sd = M y,rd = M z,rd = axial force in the brace member the joint axial resistance in-plane bending moment in the brace member out-of-plane bending moment in the brace member in-plane bending resistance out-of-plane bending resistance Design axial resistance for X and Y joints with joint cans For Y and X joints with axial force and where a joint can is specified, the joint design resistance should be calculated as follows: N Rd where = r + T T c n ( 1- r) Ncan, Rd N can,rd = N Rd based on chord can geometric and material properties T n = nominal chord member thickness T c = chord can thickness r = Lc/(.5D) for joints with β 0.9 = [( 4β 3) Lc /( 1. 5D) ] for joints with β > 0.9 Lc = effective total length of chord can, excluding taper, see Figure -5. In no case shall r be taken as greater than unity.

26 6 Figure -6 Calculation of Lc The reduction for short can sections is currently not implemented in USFOS, and should be accounted for when selecting effective can section thickness.. Joint classification The joints are classified based on the axial force flow in the joint. This means that a brace in a joint with a K-joint topology can be classified as a T-joint if only one of the braces carry axial loads. Typically braces in complex joints will be classified as partly K, X and T joints. The ultimate capacity of each individual brace is based on the classification. The joint classification may change during an analysis if the axial force flow changes..3 Joint behaviour and ductility limits.3.1 Joint P-D curves The following expressions show the original MSL proposed relationship between the joint force/moments and joint displacements/rotations as described in //. P φ Pu 1 A δ exp B A φ f F D = y M 1 A θ exp B A φ f F = φ M u y

27 7 Table -13 Coefficients A and B Joint Load Type Coefficient Type A B T/Y Compression (( γ 4)sin 3 θ) / β Tension β IPB β OPB β DT/X Compression ( +10) / 100 K Tension γ 90000βγ 3900β for β ( β 0.9) γ for 0.9 < β 1.0 IPB β OPB β Balanced axial P, M = brace load at joint P u, M u = mean strength ϕ( γ 7) /18 where but ϕ = ζ < ϕ < 0.5 ψ (13 + 4γ ) where but ψ = ζ 170 ψ 30 IPB β OPB β φ = strength scaling factor (P char /P u) δ = joint deformation (pr brace) θ = joint rotation (radians, pr brace) D = chord diameter A = constant for given joint geometry and load type B = dimensional constant in units of MPa for given joint geometry and load type γ = D/(T) chord diameter / ( chord wall thickness) ζ = (g/d) gap between brace toes / chord diameter.3. MSL Ductility limits

28 8 Table -14 show the MSL proposed ductility limits as described in //. Table -14 Ductility limits for axial deflection Joint Type Mean Characteristic X T/Y K δ = β D δ = D δ = 0.06 D δ = β D δ = D δ = D In USFOS, the ductility limit is implemented by reducing the axial joint capacity to a small number for deformations larger than the ductility limit. No formulations are identified for mean and characteristic fracture criteria related to other degrees of freedom..3.3 USFOS Specific adjustments The Joint load-deformation curves described in.3.1 are developed with the mean capacity in mind. The scaling factor φ is intended to scale the curve when characteristic capacities are used, in a way that preserves the initial joint stiffness. However in some cases the produced curves are much softer near the characteristic capacity and the ductility limit is reached before the characteristic capacity. In order to avoid this, the B factors are increased for axial tension for the Norsok, API and ISO variants. B = B 1.5 is used.

29 9 3. DESCRIPTION OF USE 3.1 General When using the USFOS CHJOINT record, additional elements are inserted in the FEmodel, see Figure 3-1 The elements have properties representing both the stiffness and capacity of the tubular joint braces according to the selected rule. Beam Two extra elements Beam Two extra node Beam Beam Conventional joint model Joint with capacity check included Figure 3-1 Tubular joint representation A sample input for the joint given in Figure 3- is shown in Table 3-1. Section 3. describes the most relevant input records in order to include joint check in an USFOS analysis.

30 30 Figure 3- Tubular Joint Table 3-1 Joint check input ' nodex chord1 chord geono CapRule CapLevel CHJOINT MSL FCrack ' JNTCLASS 1! 0=OFF 1=ON

31 31 3. Input description Below is given a selection of the most relevant input records in order to include joint check in an USFOS analysis. CHJOINT nodex elnox1 elnox geono irule Parameter Description Default nodex elnox1 elnox geono irule External node number referring to the joint where shell effects should be considered External element number defining one of the two elements connected to the node External element number defining the second CHORD element Geometry reference number defining the diameter and thickness of the chord at the joint (canned joint). If omitted or equal to 0, the data for elnox1 is used. Capacity rule switch: irule = MSL : MSL non-linear joint characteristics, (see next pages). irule = NORSOK : Norsok N-004, rev non-linear joint characteristics. irule = NOR_R3 : Norsok N-004, rev 3 non-linear joint characteristics irule = ISO: ISO 1990:007 non-linear joint characteristics. irule = API-WSD: API RP A WSD ES3 (non-linear joint characteristics. 0 Norsok Historic, not recommended: irule = -1 : API-LRFD (no more data required) irule = - : DoE (no more data required) irule = -3 : User defined capacity and surface definition, more data required, (see next pages). Irule = -101 : User defined Joint Springs, more data required, (see next pages). With this record, the capacity of each brace/chord connection at the tubular joint will be checked according to a selected joint capacity formulation. This check will impose restrictions on the load transfer through each brace/chord connection at the specified joint. The generated capacities are printed in the '.jnt' or the.out file (Historic options), and the peak capacities will be printed using the Verify/Element/Information option in Xact.

32 3 Beam Two extra elements Beam Two extra node Beam Beam Conventional joint model Joint with capacity check included

33 33 CHJOINT nodex elnox1 elnox geono CapRule CapLevel f _SafetyCoeff Parameter Description Default nodex elnox1 elnox geono CapRule External node number referring to the joint where joint capacity and nonlinear joint behaviour should be considered External element number defining one of the two CHORD elements connected to the node External element number defining the second CHORD element Geometry reference number defining the diameter and thickness of the chord at the joint (canned joint). If omitted or equal to 0, the data for elnox1 is used. Capacity rule: MSL : MSL non-linear joint characteristics CapLevel Capacity level or capacity multiplier. mean : use mean ultimate joint capacities char : use characteristic ultimate joint capacities fcrack : use characteristic first crack joint capacities scalfact : joint capacities are set to mean value capacities multiplied by scalfact, (where scalfact is a positive real number). This option is only available with the MSL joint formulation. mean f _Safety Coeff The f factor for joint capacities includes a safety factor (or partial safety coefficient) in the chord stress utilization factor. With this record, the capacity of each brace/chord connection at the tubular joint will be checked according to a selected joint capacity equation This check will impose restrictions on the load transfer through each brace/chord connection at the specified joint, and the non-linear joint characteristics will be included in the USFOS analysis. Extra elements will be introduced in the FE model, and the behavior of these elements assigned according to the selected joint capacity rule or specified joint capacity, and the FE formulation selected for the joint elements. The joint capacity rule or joint capacity is specified by the CHJOINT record(s). The FE formulation for the joint elements is selected automatically. (JNT_FORM record is not needed to specify)

34 34 JOINTGAP Gap NodeID Brace1 Brace Parameter Description Default Gap NodeID Brace_i.. Actual Gap specified in current length unit Actual Joint, (CHJOINT must be specified for this joint) The actual gap should be applied to the Braces (Elem ID s) specified. NOTE 1: If no node is specified, all joints defined get the actual gap. NOTE : If no braces are specified, all braces get the actual gap. With this record the user may override the gaps between braces, which are computed based on the structural model, (member coordinates and offsets). This is a useful option if the structural model does not describe correct gaps (f ex a model without member eccentricities/offsets). This record may be repeated. Gap (NodID) Example 1: JOINTGAP This will force a gap = to be used in all relevant capacity calculations for all joints with CHJOINT applied (does not influence T/Y capacities). Gap NodID Example : JOINTGAP JOINTGAP JOINTGAP JOINTGAP This will force a gap = to be used in all relevant capacity calculations for all joints except for joints 1010, 010 and 3010, which will use a gap of Gap NodID Brace1 Brace Brace3 Example 3: JOINTGAP JOINTGAP This will force a gap = to be used in all relevant capacity calculations for all joints except for joint 1010, where the braces 0100, 0101 and 010, which will use a gap of The other braces connected to joint 1010 will use a gap of Gap NodID Brace1 Brace Brace3 Example 4: JOINTGAP This will force a gap=0.070 to be used for joint 1010, braces 0100, 0101 and 010. The other braces connected to joint 1010 as well as all other joints with ChJoint specified will use the gap computed on basis on the structural model (coordinates and eventual offsets).

35 35 JNTCLASS interval Parameter Description Default interval Joints will be (re)classified according to geometry and force state at specified intervals during the analysis. The joint capacities will be updated according to the revised classification, P-δ curves for each joint degree of freedom and the f factor will be updated. 0 : No joint classification. 1 : Continuous joint (re)classification. Joint capacities, nonlinear joint characteristics and the f factor will be updated at every step in the USFOS analysis. n >1 : Joints will be (re)classified at every n th step. Joint capacities, non-linear joint characteristics and the f factor will be updated at every n th step in the USFOS analysis. 1 If the record is not given, the default value of one (classified every step) is used for the MSL, Norsok, ISO and API-WSD variants. This record is given once

36 36 4. VERIFICATION 4.1 K-Joints P P Ax gap Figure 4-1 Simple K-Joint with gap

37 Gamma = 10, Beta =0.8, gap/t=.5 Table 4-1 Joint data Input Joint type Value K Geometry [mm] db 30 tb 0 Dc 400 Tc 0 theta 90 gap 50 Material [MPa] fyb 350 fy 350 Chord loads [N] -Axial -1.30E+06 Chord Capacity Np 8.357E+06 Mp 1.01E+09 Table 4- Expected capacities [N, mm] Results for Joint Type: K MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 5.103E E E E E E E+06 f Nrd.c*f 5.017E E E E E E E+06 Nrd.t 5.103E E E E E E E+06 f Nrd.t*f 5.017E E E E E E E+06 Mipb 6.33E E E E E E E+08 f Mipb*f 5.953E E E E E E E+08 Mopb 3.931E E E E E E E+08 f Mopb*f 3.849E+08.93E+08.93E+08.93E+08.93E E E+08

38 38 Table 4-3 USFOS results [N, m] 1 MSL mean 4.000E E E % K E E E+05 9% T 3.4E E E % => 4.55E E E K E E E MSL characteristic 4.000E E E % K E E E+05 9% T.538E E E % => 3.519E E E K E E E MSL first crack 4.000E E E % K E E E+05 9% T.538E E E % => 3.519E E E K E E E Norsok N-004 Rev 4.000E E E % K E E E+05 9% T.538E E E % => 3.519E E E K E E E ISO E E E % K E E E+05 9% T.538E E E % => 3.519E E E K E E E API RPA-WSD 1st ES E E E % K E E E+05 9% T 3.135E E E % => 3.155E E E K E E E

39 39 1 Norsok N-004 R E E E % K E E E+05 9% T 3.135E E E % => 3.155E E E K E E E

40 Gamma = 10, Beta = 0.8, gap/t = -0.5 Table 4-4 Joint data Input Joint type Value K Geometry [mm] Db 30 Tb 0 Dc 400 Tc 0 Theta 90 gap -10 Material [MPa] fyb 350 fy 350 Chord loads [N] -Axial -1.30E+06 Chord Capacity Np 8.357E+06 Mp 1.01E+09 Table 4-5 Expected capacities [N, mm] Results for Joint Type: K MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 6.467E E E E E E E+06 f Nrd.c*f 6.40E E E E E E E+06 Nrd.t 6.467E E E E E E E+06 f Nrd.t*f 6.40E E E E E E E+06 Mipb 6.33E E E E E E E+08 f Mipb*f 6.065E E E E E E E+08 Mopb 3.931E E E E E E E+08 f Mopb*f 3.88E E E E E E E+08

41 41 Table 4-6 USFOS Results [N, m] 1 MSL mean 4.000E E E % K E E E+05 9% T 3.4E E E % => 5.517E E E K E E E MSL characteristic 4.000E E E % K E E E+05 9% T.538E E E % => 4.61E E E K E E E MSL first crack 4.000E E E % K E E E+05 9% T.538E E E % => 4.61E E E K E E E Norsok N-004 Rev 4.000E E E % K E E E+05 9% T.538E E E % => 4.61E E E K E E E ISO E E E % K E E E+05 9% T.538E E E % => 4.61E E E K E E E API RPA-WSD 1st ES E E E % K E E E+05 9% T 3.135E E E % => 4.99E E E K E E E

42 4 1 Norsok N-004 R E E E % K E E E+05 9% T 3.135E E E % => 4.99E E E K E E E

43 Gamma = 10, Beta = 0.8, gap/t = -.5 Table 4-7 Joint data Input Joint type Value K Geometry [mm] db 30 tb 0 Dc 400 Tc 0 theta 90 gap -50 Material [MPa] fyb 350 fy 350 Chord loads [N] -Axial -1.30E+06 Chord Capacity Np 8.357E+06 Mp 1.01E+09 Table 4-8 Expected Capacities [N,mm] Results for Joint Type: K MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 7.11E E E E E E E+06 f Nrd.c*f 7.139E E E E E E E+06 Nrd.t 7.11E E E E E E E+06 f Nrd.t*f 7.139E E E E E E E+06 Mipb 6.33E E E E E E E+08 f Mipb*f 6.065E E E E E E E+08 Mopb 3.931E E E E E E E+08 f Mopb*f 3.88E E E E E E E+08

44 44 Table 4-9 USFOS Results [N, m] 1 MSL mean 4.000E E E % K E E E+05 9% T 3.4E E E % => 6.043E E E K E E E MSL characteristic 4.000E E E % K E E E+05 9% T.538E E E % => 4.666E E E K E E E MSL first crack 4.000E E E % K E E E+05 9% T.538E E E % => 4.666E E E K E E E Norsok N-004 Rev 4.000E E E % K E E E+05 9% T.538E E E % => 4.666E E E K E E E ISO E E E % K E E E+05 9% T.538E E E % => 4.666E E E K E E E API RPA-WSD 1st ES E E E % K E E E+05 9% T 3.135E E E % => 5.553E E E K E E E

45 45 1 Norsok N-004 R E E E % K E E E+05 9% T 3.135E E E % => 5.553E E E K E E E

46 Gamma = 5, Beta = 0.8, gap/t = 6.5 Table 4-10 Joint data Input Joint type Value K Geometry [mm] db 30 tb 8 Dc 400 Tc 8 theta 90 gap 50 Material [MPa] fyb 350 fy 350 Chord loads [N] -Axial -1.05E+06 Chord Capacity Np 3.448E+06 Mp 4.303E+08 Table 4-11 Expected Capacities [N,mm] Results for Joint Type: K MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 8.164E E E E E E E+05 f Nrd.c*f 7.845E E E E E E E+05 Nrd.t 8.164E E E E E E E+05 f Nrd.t*f 7.845E E E E E E E+05 Mipb 1.577E E E E E E E+08 f Mipb*f 1.41E E E E E E E+08 Mopb 8.433E E E E E E E+07 f Mopb*f 8.01E E E E E E E+07

47 47 Table 4-1 USFOS Results [N, m] 1 MSL mean 4.000E E E % K E E E+04 9% T 5.158E E E % => 7.84E E E K E+06.30E E MSL characteristic 4.000E E E % K E E E+04 9% T 4.061E E E % => 5.630E E E K E E E MSL first crack 4.000E E E % K E E E+04 9% T 4.061E E E % => 5.630E E E K E E E Norsok N-004 Rev 4.000E E E % K E E E+04 9% T 4.061E E E % => 5.630E E E K E E E ISO E E E % K E E E+04 9% T 4.061E E E % => 5.630E E E K E E E API RPA-WSD 1st ES E E E % K E E E+04 9% T 6.70E E E % => 6.950E E E K E E E

48 48 1 Norsok N-004 R E E E % K E E E+04 9% T 6.70E E E % => 6.950E E E K E E E

49 49 4. T/Y-Joints P Ax Figure 4- Simple T/Y-Joint

50 Gamma = 5, Beta =0.8 Table 4-13 Joint data Input Joint type Value T/Y Geometry [mm] db 30 tb 8 Dc 400 Tc 8 theta 90 gap 0 Material fyb 350 fy 350 Chord loads [N] -Axial -1.03E+06 Chord Capacity Np 3.448E+06 Mp 4.303E+08 Table 4-14 Expected capacities [N, mm] Results for Joint Type: T MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 5.158E E E E E E E+05 f Nrd.c*f 4.809E E E E E E E+05 Nrd.t 1.15E E E E E E E+05 f Nrd.t*f 1.074E E E E E E E+05 Mipb 1.577E E E E E E E+08 f Mipb*f 1.417E E E E E E E+08 Mopb 8.433E E E E E E E+07 f Mopb*f 8.035E E E E E E E+07

51 51 Table 4-15 USFOS results [N, m] (compression) 1 MSL mean 4.000E E E T 5.158E E E MSL characteristic 4.000E E E T 4.061E E E MSL first crack 4.000E E E T 4.061E E E Norsok N-004 Rev 4.000E E E T 4.061E E E ISO E E E T 4.061E E E API RPA-WSD 1st ES E E E T 6.70E E E Norsok N-004 R E E E T 6.70E E E

52 5 Table 4-16 USFOS results [N, m] (tension) 1 MSL mean 4.000E E E T 1.149E E E MSL characteristic 4.000E E E T 6.593E E E MSL first crack 4.000E E E T 5.375E E E Norsok N-004 Rev 4.000E E E T 5.376E E E ISO E E E T 5.376E E E API RPA-WSD 1st ES E E E T 5.376E E E Norsok N-004 R E E E T 5.376E E E

53 Gamma = 10, Beta =0.8 Table 4-17 Joint data Input Joint type Value T/Y Geometry [mm] Db 30 Tb 0 Dc 400 Tc 0 theta 90 gap 0 Material fyb 350 fy 350 Chord loads [N] -Axial -.51E+06 Chord Capacity Np 8.357E+06 Mp 1.01E+09 Table 4-18 Expected capacities [N, mm] Results for Joint Type: T MSL Mean MSL Char MSL Fcrack NORSOK R ISO API NORSOK R3 Nrd.c 3.4E E E E E E E+06 f Nrd.c*f 3.006E E E E E+06.67E+06.67E+06 Nrd.t 7.0E E E E E E E+06 f Nrd.t*f 6.715E E E E E E E+06 Mipb 6.33E E E E E E E+08 f Mipb*f 5.60E E E E E E E+08 Mopb 3.931E E E E E E E+08 f Mopb*f 3.745E E E E E E E+08