User Defined Functions

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4 BOLTS W/STIFFENER&WEB DOUBLER MOMENT CONNECTION ANALYSIS

demand resistance check resistance demand ≥ OK Fails if :

A custom function to check demand versus capacity and output a message to the user

demand resistance UR demand resistance / 2 round (:

A custom function to display the utilization ratio of a specific check to the user

Ø.BH Holes.Punched No ≡ Ø.B 116 / in * + Holes.Punched Yes ≡ Ø.B 116 / in * + 2 mm * + N/A if if :

Bolt hole diameter

F.u Bolt.Grade A325 ≡ (Ø.B 1 in * ≤ (& 825 MPa * Bolt.Grade A325 ≡ (Ø.B 1 in * > (& 725 MPa * Bolt.Grade A490 ≡ 1035 MPa * N/A if if if :

Minimum specified tensile strength

f.bt Threads.Intercepted Yes ≡ 0.7 Threads.Intercepted No ≡ 1.0 N/A if if :

Bolt thread inclusion factor, S16-14 §13.12.1.2(c)

Edge.minDist Ø.BH 1 in * < 1 in * Ø.BH 1 in * ≥ 1.25 in * N/A if if :

Minimum edge distance

b.pe b.p b.b ≥ b.b 25.4 mm * + b.p b.b < b.p 0 mm * if if :

Effective plate width

The summary matrix to hold the connection capacity, display OK/NG, and the utilization ratio.

summary Check Description OK / NG UR Beam Stress Check check1 UR1 Beam Weld Check check2 UR2 Bolt Checks-Tension & Shear check3 UR3 End Plate Checks-Flexual & Shear check4 UR4 Column Flange Flexural & Shear Punching check5 UR5 Column Panel Zone Shear & Web Yield/Stability check6 UR6 Stiffeners - Strength, Welds, & Stability check7 UR7 Web Doublers check8 UR8 93 mat :

Inputs

Beam W310x60 :

Column W310x67 :

Section Properties Lookup

Reading the Section Properties from DataFile:

Designation datafile rfile 2 col :

Lookup Functions (JP):

j 1 : Beam Designation j el ≠ j j 1 + : while number.b j : 31 line

j 1 : Column Designation j el ≠ j j 1 + : while number.c j : 31 line

number.b 221

number.c 220

Beam Properties:

Beam_properties datafile rfile number.b row :

d.b Beam_properties 6 el mm * :

d.b mm 303

b.b Beam_properties 7 el mm * :

b.b mm 203

t.b Beam_properties 8 el mm * :

t.b mm 13.1

w.b Beam_properties 9 el mm * :

w.b mm 7.5

A.b Beam_properties 10 el mm 2^* :

A.b mm 2^7530

k.b Beam_properties 11 el mm * :

k.b mm 33

k.1b Beam_properties 12 el mm * :

k.1b mm 22

k.engb Beam_properties 13 el mm * :

k.engb mm 25.8

k1.engb k.engb t.b - w.b 2 / + :

k1.engb mm 16.45

Column Properties:

Column_properties datafile rfile number.c row :

d.c Column_properties 6 el mm * :

d.c mm 306

b.c Column_properties 7 el mm * :

b.c mm 204

t.c Column_properties 8 el mm * :

t.c mm 14.6

w.c Column_properties 9 el mm * :

w.c mm 8.5

A.c Column_properties 10 el mm 2^* :

A.c mm 2^8450

k.c Column_properties 11 el mm * :

k.c mm 34

k.1c Column_properties 12 el mm * :

k.1c mm 22

k.engc Column_properties 13 el mm * :

k.engc mm 27.3

k1.engc k.engc t.c - w.c 2 / + :

k1.engc mm 17

Beam Geometry

Beam W310x60

A.b mm 2^7530

d.b mm 303

b.b mm 203

t.b mm 13.1

w.b mm 7.5

Column Geometry

Column W310x67

d.c mm 306

b.c mm 204

t.c mm 14.6

w.c mm 8.5

k.engc mm 27.3

k1.engc mm 17

Design Decisions

e'.c 1000 mm * :

Distance from beam top flange to top of column?

Bolt Size and Properties

Ø.B 1 in * :

Bolt diameter

Rolt.ES 0 :

No. of extra shear bolts row

Bolt.ES 2 Rolt.ES * : 0

No. of extra shear bolts

Consider_Extra_Shear_Bolts_For_Axial_Load 1 :

Input 1 if extra shear bolts are not considered. Iuput 2 if extra shear bolts are considered to take some axial load.

No.bolts 8 Bolt.ES + : 8

Total number of bolts in connection

Bolt.Grade A325 :

Bolt grade (enter either "A325" or "A490")

Threads.Intercepted Yes :

Threads intercepted by shear plane? (enter either "Yes" or "No")

Holes.Punched No :

Bolt holes punched? (enter either "Yes" or "No")

Ø.BH in 1716 /

Effective bolt hole diameter

Bolt Spacing

p.ext 95 mm * :

Distance from flg. to outside edge of PL

p.fo 50 mm * :

Exterior bolt row spacing

p.fi 45 mm * :

Interior bolt row spacing

GA 130 mm * :

Bolt gauge

p.es 90 mm * :

Bolt pitch for additional shear bolts

Beam Welds

s.11 6 mm * :

Flange fillet leg size (side 1)

s.12 s.11 :

Flange fillet leg size (side 2)

s.2 6 mm * :

Web fillet leg size

End Plate Properties

t.p 25.4 mm * :

End plate thickness

b.p 230 mm * :

Plate width

NOTE: bpe may be less than the beam flange width

b.pe mm 228

Effective plate width

Edge.Dist p.ext p.fo - : mm 45

Plate edge distance

Edge.Dist_H b.p GA - 2 / : mm 50

Plate horizontal edge distance

Edge.minDist in 1.25

Edge.minDist mm 32

Plate Min. edge distance

NOTE: Plate width must be between

GA 2 Edge.minDist * + mm 194

and

b.b 25.4 mm * + mm 228

Full Depth Stiffener Properties

t.s 12.7 mm * :

Stiffener thickness

w.s 101.6 mm * :

Stiffener width

L.s d.c 2 t.c * - :

L.s mm 277

Stiffener length (calculated to fit in column web)

c 20 mm * :

Stiffener clip dimension

s.3 6 mm * :

Stiff. to col. flg. fillet weld leg size

s.4 6 mm * :

Stiff. to col. web fillet weld leg size

Web Doubler Plate Properties

No.doublers 1 :

Enter the number of web doublers (1 or 2)

t.d 38 / in * :

t.d mm 9.5

Web doubler thickness

s.5 6 mm * :

Doubler to stiffener weld

w.d 248 mm * :

Web doubler width

δ 38 / in * :

δ mm 9.5

Doubler plate to column groove weld depth

Applied Loads

Applied Shear & Axial Loads

A 80 kN * :

Applied axial tesnsion load, please input absolute value.

V.y 140 kN * :

Applied shear load, please input absolute value.

M.x 120 kN * m * :

Applied moment, please input absolute value

V.x 0 kN * :

Applied weak axis shear, please input absolute value

M.y 0 kN * m * :

Applied weak axis moment,please input absolute value

M.z 0 kN * m * :

Applied torsional moment,please input absolute value

Applied Loads to a Beam Framing into the Column Web

V.xst 0 kN * :

Applied weak axis shear, please input absolute value.

V.yst 0 kN * :

Applied strong axis shear, please input absolute value.

P.sh_tab 0 kN * :

Applied load from beam framing into shear tab, please input absolute value.

Material strength and resistance factors

Material Strengths

Material Resistance Factors

F.yb 350 MPa * :

Beam yield strength

φ 0.9 :

Structural steel

F.yc 350 MPa * :

Column yield strength

φ.u 0.75 :

Structural steel

F.uc 450 MPa * :

Column ultimate strength

φ.b 0.8 :

Bolts

F.yp 300 MPa * :

End plate yield strength

φ.bi 0.8 :

Beam web bearing, interior

F.up 450 MPa * :

End plate ultimate strength

φ.be 0.75 :

Bearm web bearing, exterior

F.ys 300 MPa * :

Stiffener yield strength

φ.br 0.8 :

Bearing of bolts on steel

F.yd 300 MPa * :

Web doubler plate yield strength

φ.w 0.67 :

Weld metal

F.ud 450 MPa * :

Web doubler plate ultimate strength

X.u 490 MPa * :

Weld electrode ultimate strength

E 200 GPa * :

Elastic modulus of steel (assumed)

G 77 GPa * :

Shear modulus of steel (assumed)

F.u MPa 825

Bolt ultimate strength (calculated in User Defined Functions, based on Inputs)

Load Distribution

Load Distribution

Factored Beam Flange Force:

Weak axis moment effect when stiffeners exist

Weak Axis Moment Effect W/ stifferners For Bolt/Col. Flange/End pl Check

N b.b b.p b.c 31 mat min : mm 203

σ.ybeam φ F.yb F.yc F.yp 31 mat min * : MPa 270

Bearing stress on end plate

a σ.ybeam t.b t.s 12 mat min * : N mm / 3429

b a N GA + (* - : kN 1141.857 -

c1 M.y :

y1 b - b 2^4 a * c1 * - sqrt + 2 a * / : mm 333

y2 b - b 2^4 a * c1 * - sqrt - 2 a * / : mm 0

y y1 0 > (y2 0 > (& y1 y2 12 mat min y1 y2 12 mat Max if :

y y N 2 / 12 mat min :

Limit y value not greater than N/2.

y mm 101.5

P.UF_weak M.y N GA + y - (2 / / :

P.UF_weak kN 0

Weak Axis Moment Effect W/ stifferners For Bolt/Col. Flange/End pl Check

Weak Axis Moment Effect W/ stifferners For Stiffeners Check

P.UF_weak_stiff M.y w.s w.c + c + / :

Weak Axis Moment Effect W/ stifferners For Stiffeners Check

P.UF_weak_stiff kN 0

Weak Axis Moment Effect W/ stifferners For Beam Flg. Check

b b.p b.b 12 mat min :

P.UF_weak_beam M.y b 2 / / :

Note: b/2 is the distance for plastic development

P.UF_weak_beam kN 0

Weak Axis Moment Effect W/ stifferners For Beam Weld Check

P.UF_weak_weld 3 M.y * b / :

Note: b/3 is the distance for elastic distribution

P.UF_weak_weld kN 0

P.UF_weak kN 0

Weak Axis Moment Effect W/ stifferners For Bolt/Col. Flange/End pl Check

P.UF_weak_stiff kN 0

Weak Axis Moment Effect W/ stifferners For Stiffeners Check

P.UF_weak_beam kN 0

Weak Axis Moment Effect W/ stifferners For Beam Flg. Check

P.UF_weak_weld kN 0

Weak Axis Moment Effect W/ stifferners For Beam Weld Check

P.UF M.x d.b t.b - / A 2 / + :

P.UF kN 454

Flange force W/O Weak Axis Moment Effect

A.web d.b 2 t.b * - (w.b * :

A.web mm 2^2076

Beam web area

NOTE: Axial force, A, is assumed to be proportioned to the top and bottom flange based on a 50-50 split, however, the axial load could be proportioned to the extra shear bolts based on the web area :total area ratio, as shown below.The existing assumption of the axial load only acting on the beam flanges is conservative.

P.shear_bolts A A.web A.b / * Rolt.ES sign * :

P.shear_bolts kN 0

Load on extra shear bolts if this distribution is used

P'.UF M.x d.b t.b - / A P.shear_bolts - 2 / + :

Flange force if this distribution is used W/O Weak Axis Moment Effect

P'.UF kN 454

Bolt Loads

Tension Flange Bolts

NOTE: (Weak axis shear load Vx consideration) All weak axis shear is taken by tension flg. bolts.

V.XT V.x M.z d.b t.b - / + :

Total lateral shear on tension flange bolts

NOTE: (Strong axis shear load Vy consideration) All shear is taken by compression flg. bolts and extra shear bolts(if present).

V.YT 0 kN * :

Strong axis shear on tension flange bolts from Vy

Pt.UF Consider_Extra_Shear_Bolts_For_Axial_Load 1 ≡ P.UF P.UF_weak + P'.UF P.UF_weak + if :

Pt.UF kN 454

Total tension on tension flange bolts W/ Weak Axis Moment Effect

Compression Flange Bolts:

V.XB M.z d.b t.b - / :

Total lateral shear on compression flange bolts

V.YC 4 V.y * 4 Bolt.ES + (/ :

Total axis shear on compression flange bolts from Vy

V.YC kN 140

Pc.UF A 2 / P.UF_weak + M.x d.b t.b - / - 021 mat Max :

Total tension on compression flange bolts

Pc.UF kN 0

Extra Shear Bolts

Vy.xtra V.y Bolt.ES (Bolt.ES 4 + (/ * :

Vy.xtra kN 0

Strong axis shear on extra shear bolts group from Vy

Tf.xbolt Consider_Extra_Shear_Bolts_For_Axial_Load 1 ≡ 0 P.shear_bolts Bolt.ES / if :

Tf.xbolt kN 0

Applied tension load per extra shear bolt

Factored Beam Flange Force W/O Weak Axis Moment Effect:

P.UF kN 454

Flange force if Load on extra shear bolts is not considered

P'.UF kN 454

Flange force if Load on extra shear bolts is considered

Weak Axis Moment Effect:

P.UF_weak kN 0

Weak Axis Moment Effect W/ stifferners For Bolt/Col. Flange/End pl Check

P.UF_weak_stiff kN 0

Weak Axis Moment Effect W/ stifferners For Stiffeners Check

P.UF_weak_beam kN 0

Weak Axis Moment Effect W/ stifferners For Beam Flg. Check

P.UF_weak_weld kN 0

Weak Axis Moment Effect W/ stifferners For Beam Weld Check

Bolt Loads:

Tension Flange Bolts:

NOTE: (Weak axis shear load Vx consideration) All weak axis shear is taken by tension flg. bolts.

V.XT kN 0

Total lateral shear on tension flange bolts

V.YT kN 0

Strong axis shear on tension flange bolts from Vy

Pt.UF kN 454

Total tension on tension flange bolts W/ Weak Axis Moment Effect

Compression Flange Bolts:

V.XB kN 0

Total lateral shear on compression flange bolts

NOTE: (Strong axis shear load Vy consideration) All shear is taken by compression flg. bolts and extra shear bolts(if present).

V.YC kN 140

Total axis shear on compression flange bolts from Vy

Pc.UF kN 0

Total tension on compression flange bolts W/ Weak Axis Moment Effect

Extra Shear Bolts:

Vy.xtra kN 0

Strong axis shear on extra shear bolts group from Vy

Tf.xbolt kN 0

Applied tension load per extra shear bolt

CHECK 1 - Beam Stress Checks

Rewrite the puf load if the axial load is considered to be taken by extra shear bolts or not

P.UF Consider_Extra_Shear_Bolts_For_Axial_Load 1 ≡ P.UF P'.UF if :

Beam Flange

Gross Tensile Yield (Check 1.1)S16-14 §13.2(a)-i

T.r_11 φ A.g * F.yb * :

b.bfw b.b b.pe 21 mat min :

b.b b.pe 21 mat mm 20322821 mat

where:

= min

b.bfw mm 203

A.g b.bfw t.b * :

A.g mm 2^2659.3

P.UF_beam P.UF P.UF_weak_beam + : kN 454

Gross tensile yield, S16-14 §13.2(a)-i

UR1.1 P.UF_beam T.r_11 UR :

Demand —»

P.UF_beam kN 454

P.UF_beam T.r_11 check OK

UR1.1 0.54

Resistance —»

T.r_11 kN 838

UR1.1 0.54

Gross Weak Axis Shear Yield (Check 1.2)S16-14 §21.12

V.r_12 φ 0.5 * A.g * F.yb * :

V.r_12 kN 419

NOTES: (1) Assumes all weak axis shear is applied to the top flg (2) 0.5Fy is the largest shear stress that steel can handle without adversely affecting its ability to resist tensile stress

UR1.2 V.XT V.r_12 UR :

Gross shear yield, S16-14 §21.12

Demand —»

V.XT kN 0

V.XT V.r_12 check OK

UR1.2 0

Resistance —»

V.r_12 kN 419

UR1.2 0

Beam Web

Strong Axis Shear Yield over Beam Web (Check 1.3) S16-14 §13.4.1.1(a)3)

V.r_13 φ 0.5 * A.web * F.yb * :

V.r_13 kN 327

NOTE: In lieu of a more thorough check, applied strong axis shear is assumed to be resisted over the height of the beam web. To account for the interaction of shear and normal stresses on the web, the shear strength is limited to 0.5 x the material strength.

UR1.3 V.y V.r_13 UR :

Beam web shear yield, S16-14 §13.4.1.1(a)

Demand —»

V.y kN 140

V.y V.r_13 check OK

UR1.3 0.43

Resistance —»

V.r_13 kN 327

UR1.3 0.43

FYI - Shear Yield over Effective Beam Web Length (Check 1.4) S16-14 §13.4.1.1(a)

NOTE: This FYI check follows the AISC DG 4 recommendation to reduce the shear resistance to below the endplate. This check is FYI and is NOT included in the Utilization Ratio for Check #1 or the Calculation Summary

s 12 / b.pe GA * sqrt * :

s mm 86

NOTE: S is used in the effective pitch calculation, see Check 4 - End Plate Flexural Yield for more info.

A.gv d.b 2 / t.b - (w.b * d.b 2 t.b * - p.fi - s - (w.b * 21 mat max :

d.b 2 / t.b - (w.b * d.b 2 t.b * - p.fi - s - (w.b * 21 mat mm 2^1038109221 mat

A.gv mm 2^1092

= max

V.r_sz φ A.gv * 0.66 * F.yb * :

V.r_sz kN 227

Beam web shear yield excluding tensile zone, S16-14 §13.4.1.1(a)

UR1.4 V.y V.r_sz UR :

Demand —»

V.y kN 140

V.y V.r_sz check OK

Resistance —»

V.r_sz kN 227

UR1.4 0.62

UR1.4 0.62

UR1 UR1.1 UR1.2 UR1.3 13 mat max :

Determines the critical UR for Check 1 and checks OK or NG

check1 UR1 1.0 check :

Summary

Description of Check

Capacity

Factored Applied Load

OK / N.G.

1) Beam Flange Gross Tensile Yield

T.r_11 kN 838

P.UF_beam kN 454

UR1.1 0.54

P.UF_beam T.r_11 check OK

2) Beam Flange Weak Axis Shear Yield

V.r_12 kN 419

V.XT kN 0

UR1.2 0

V.XT V.r_12 check OK

3) Beam Web Strong Axis Shear Yield

V.r_13 kN 327

V.y kN 140

UR1.3 0.43

V.y V.r_13 check OK

CHECK 2 - Beam Weld Checks

Flange

Fillet Weld Resistance (Check 2.1) S16-14 §13.13.2.2

V.rw_21 0.67 φ.w * A.w_21 * X.u * 1 0.5 θ.21 sin (1.5^* + (* :

P.UF_weld P.UF P.UF_weak_weld + : kN 454

R.w_21 P.UF_weld 2^V.XT (2^+ sqrt :

R.w_21 kN 454

Resultant force on weld

θ.21 V.XT 0 > P.UF_weld V.XT / atan 90 ° * if :

θ.21 ° 90

Load angle, typically 90 degrees

A.w_21 12 sqrt / b.eff * s.11 s.12 + (2 / * :

Weld area

NOTE: Typically s11 = s12

b.eff 2 b.b * w.b - (2 b.p * w.b - (2 GA 2 p.fo * + 2 p.fi * + (* 4 Ø.B 2 p.fo * + 2 p.fi * + (* 41 mat min :

where:

2 b.b * w.b - (2 b.p * w.b - (2 GA 2 p.fo * + 2 p.fi * + (* 4 Ø.B 2 p.fo * + 2 p.fi * + (* 41 mat mm 39845264086241 mat

= min

b.eff mm 398

NOTE: This assumes that a 2:1 dispersion slope defines the limit of the effective flexural length of the plate

A.w_21 mm 2^1691

V.rw_21 kN 558

Fillet weld resistance, S16-14 §13.13.2.2

UR2.1 R.w_21 V.rw_21 UR :

Demand —»

R.w_21 kN 454

R.w_21 V.rw_21 check OK

Resistance —»

V.rw_21 kN 558

UR2.1 0.81

UR2.1 0.81

PJP Groove Weld Combined with Fillet Welds at Beam Flange/Endplate Interface (Check 2.2)

NOTE: If the flange fillet weld capacity is exceeded, a PJP groove weld combined with fillet welds may be required. Below are the equations for the capacity for this weld type. This check is FYI and is NOT included in the Utilization Ratio of Check #2, or the Calculation Summary

x t.b 3 mm * - : mm 10

Groove weld leg size

s.f 6 mm * :

Fillet weld leg size

A.n1 b.b x 3 mm * - (* :

A.n1 mm 2^1441

Groove weld area

A.w1 b.b s.f 2 sqrt / * :

A.w1 mm 2^861

Fillet weld area one side

NOTE: Since the application expression in S16-14 §13.13.3.3 is only applied to the groove weld and fillet weld on both sides of plate, the capacity of the designed weld will be separated into two parts. The first term is for the one groove weld and one fillet weld; the second term is for one fillet weld another side of plate.

T.r_22 0.5 φ.w * F.up A.n1 * (2^X.u A.w1 * (2^+ sqrt * 0.67 φ.w * A.w1 * X.u * 1.5 * + :

T.r_22 kN 543

T.r_22 T.r_22 φ F.yb * A.g * 21 mat min :

φ.w F.up A.n1 * (2^X.u A.w1 * (2^+ sqrt * φ F.yb * A.g * 21 mat kN 51883821 mat

= min

T.r_22 kN 543

UR2.2 Pt.UF T.r_22 UR :

Weld details in design application expression

Partial joint penetration groove welds combined with a fillet weld, S16-14 §13.13.3.3

Demand —»

Pt.UF kN 454

UR2.2 0.84

Web

Resistance —»

T.r_22 kN 543

Pt.UF T.r_22 check OK

Web Weld Check (Check 2.3)

Web Weld Longtitude Stress:

τ.web_L

τ.web_L V.y d.b 2 t.b * - (2 * / :

τ.web_L kN mm / 0.2529

Web Weld Transvers Stress:

τ.web_T

τ.web_T P.UF_weld 4 / 0.5 * L.trib / :

NOTE: Weld transvers stress from single bolt force Puf/4 and assume the force act 50% on the web.

NOTE: In the second term of the cal. of tributary web weld length below, consider 2 to 1 ration out from bolt.

L.trib p.fi s 21 mat min P.real_pitch 2 / P.max_pitch 2 / 2 GA w.b - (2 / * 31 mat min + :

P.real_pitch Bolt.ES 0 ≠ p.es d.b 2 t.b * - 2 p.fi * - if :

P.max_pitch 4 s * :

d.b 2 t.b * - 2 p.fi * - mm 186.8

τ.web_T kN mm / 0.41

Web Weld Resultant Stress:

τ.web_demand τ.web_T 2^τ.web_L 2^+ sqrt :

τ.web_demand kN mm / 0.4817

θ.web τ.web_T τ.web_L / atan :

θ.web deg 58.3326

Web Weld Resistance:

R.web φ.w 0.67 * X.u * 1.0 0.5 θ.web sin (1.5^* + (* s.2 2 sqrt / * :

R.web kN mm / 1.2996

UR2.3 τ.web_demand R.web UR :

τ.web_demand kN mm / 0.4817

Demand —»

UR2.3 1.0 check OK

UR2.3 0.37

Resistance —»

R.web kN mm / 1.2996

UR2.3 0.37

This cal. was disabled (web weld check part)

Web Weld Resistance Over Effective Beam Web Shear Length (Check 2.3)

V.rw_23 0.67 φ.w * A.w * X.u * 1 0.5 θ.23 sin (1.5^* + (* :

where:

θ.23 0 :

NOTE: Load angle = 0 because axial load on shear bolts is assumed = 0 If axial load is taken by extra shear bolts, load angle =/= 0

A.w 2 d.b 2 / t.b - (* s.2 2 sqrt / * 2 d.b 2 t.b * - p.fi - s - (* s.2 2 sqrt / * 21 mat max :

2 d.b 2 / t.b - (s.2 * (* 2 sqrt / 2 d.b 2 t.b * - p.fi - s - (* s.2 * 2 sqrt / 21 mat mm 2^1812208021 mat

A.w mm 2^2080

= max

V.rw_23 0.67 φ.w * A.w * X.u * 1 0.5 θ.23 sin (1.5^* + (* :

V.rw_23 kN 458

NOTE: This weld is checked against Vy ONLY if there is no axial load assumed on the extra shear bolts. If axial load exists on the extra shear bolts, the weld should be checked on the resultant load from Vy and Axial Effect on Shear Bolts

UR2.3 V.y V.rw_23 UR :

Fillet weld resistance, S16-09 §13.13.2.2

Demand —»

V.y kN 250

V.y V.rw_23 check #

Resistance —»

V.rw_23 kN 458

UR2.3 0.55

Web Weld Resistance Over Effective Beam Web Tensile Length (Check 2.4)

NOTE: (1) As a minimum, the web fillet weld will be designed for: (a) 60% of the beam web tensile capacity (AISC Design Guide 4 recommendation) or (b) ¼PUF. Of the two, ¼PUF is the most critical. (2) The calculations assume that shear will never be taken in the tensile length unless the shear length is overloaded. (3) Another method to determine the proportioning of load to the web and flange welds is to consider a yield line analysis, similar to that completed in the Axially Loaded End Plate Design with Flanges Welded sample calc.

V.rw_24 0.67 φ.w * A.w * X.u * 1 0.5 θ.24 sin (1.5^* + (* :

where:

θ.24 90 ° * :

A.w 2 p.fi s + (* s.2 2 sqrt / * 2 d.b 2 / t.b - (* s.2 2 sqrt / * 21 mat min :

2 p.fi s + (* s.2 2 sqrt / * 2 d.b 2 / t.b - (* s.2 2 sqrt / * 21 mat mm 2^1545181221 mat

A.w mm 2^1545

= min

V.rw_24 0.67 φ.w * A.w * X.u * 1 0.5 θ.24 sin (1.5^* + (* :

V.rw_23 kN 458

P.UFbolt Pt.UF Pc.UF 21 mat max :

Pt.UF Pc.UF 21 mat kN 643021 mat

= max

P.UFbolt kN 643

V.f_24 P.UFbolt 4 / φ 0.6 * F.yb * p.fi s + (* w.b * P.UFbolt 4 / (2^V.y V.r_sz - (2^+ sqrt 31 mat max :

P.UFbolt 4 / φ 0.6 * w.b * F.yb * p.fi s + (* P.UFbolt 4 / (2^V.y V.r_sz - (2^+ sqrt 31 mat kN 16124319431 mat

= max

V.f_24 kN 243

UR2.4 V.f_24 V.rw_24 UR :

Fillet weld resistance, S16-09 §13.13.2.2

Demand —»

V.f_24 kN 243

V.f_24 V.rw_24 check OK

Resistance —»

V.rw_24 kN 510

UR2.4 0.48

s'.2 φ w.b * F.yb * 0.67 φ.w * 2 * X.u * 1.5 2 sqrt / * / :

FYI: Fillet weld leg size required to develop the beam web in tension

s'.2 mm 5.1

UR2 UR2.1 UR2.3 12 mat max :

Determines the critical UR for Check 2 and checks OK or NG

check2 UR2 1.0 check :

Summary

Description of Check

Capacity

Factored Applied Load

OK / N.G.

1) Beam Flange Fillet Weld Check

V.rw_21 kN 558

R.w_21 kN 454

UR2.1 0.81

R.w_21 V.rw_21 check OK

2) Beam Web Weld Check

R.web kN mm / 1.3

τ.web_demand kN mm / 0.48

UR2.3 0.37

UR2.3 1.0 check OK

CHECK 3 - Bolt Checks (No Prying)

Single Bolt Capacity

NOTE: Threads included / not included option in input tab

n 1 :

Number of bolts in connection

m 1 :

Number of faying surfaces or shear planes in a bolted joint

A.b π 4 / Ø.B 2^* :

A.b mm 2^507

Nominal area

V.r_bolt 0.6 f.bt * φ.b * n * m * A.b * F.u * :

V.r_bolt kN 140

Bolts in shear, S16-14 §13.12.1.1

Tr.bolt 0.75 φ.b * n * A.b * F.u * :

Tr.bolt kN 251

Bolts in tension, S16-14 §13.12.1.2

B.re 3 φ.br * n * F.yp * t.p * Ø.B * :

B.re kN 465

Bearing on end plate, S16-14 §13.12.1.1(a)

B.rc 3 φ.br * n * F.yc * t.c * Ø.B * :

B.rc kN 312

Bearing on column flange, S16-14 §13.12.1.1(a)

Vr.bolt V.r_bolt B.re B.rc 31 mat min :

V.r_bolt B.re B.rc 31 mat kN 14046531231 mat

= min

Vr.bolt kN 140

Governing shear/bearing capacity for single bolt

Bolt Shear and Tension Interaction

Tension Bolts (Check 3.1) S16-14 §13.12.1.4

Vf.bolt V.XT 2^V.YT 2^+ sqrt 4 / :

Vf.bolt kN 0

Shear per bolt

Tf.bolt Pt.UF 4 / :

Tf.bolt kN 113

Tension per bolt

i.1 Vf.bolt Vr.bolt / (2^Tf.bolt Tr.bolt / (2^+ :

i.1 0.2

Bolt shear and tension interaction

Vf.bolt Vr.bolt / (2^0

Tf.bolt Tr.bolt / (2^0.2

UR3.1 i.1 sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

Demand —»

i.1 0.2

UR3.1 1.0 check OK

UR3.1 0.45

Resistance —»

1.0

UR3.1 0.45

Extra Shear Bolts (Check 3.2)S16-14 §13.12.1.4

Vf.xbolt Vy.xtra Bolt.ES / :

Vf.xbolt kN 0

Shear taken by extra shear bolts, per bolt

Tf.xbolt kN 0

Tension per bolt if extra shear bolts take some axial load

i.2 Vf.xbolt Vr.bolt / (2^Tf.xbolt Tr.bolt / (2^+ :

i.2 0

Vf.xbolt Vr.bolt / (2^0

Tf.xbolt Tr.bolt / (2^0

UR3.2 i.2 sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

Demand —»

i.2 0

UR3.2 1.0 check OK

UR3.2 0

Resistance —»

1.0

UR3.2 0

Compression Bolts (Check 3.3)S16-14 §13.12.1.4

Vf.cbolt V.XB 2^V.YC 2^+ sqrt 4 / :

Vf.cbolt kN 35

Shear per bolt

Tfc.bolt Pc.UF 4 / :

Tfc.bolt kN 0

Tension per bolt

i.3 Vf.cbolt Vr.bolt / (2^Tfc.bolt Tr.bolt / (2^+ :

i.3 0.06

Vf.cbolt Vr.bolt / (2^0.06

Tfc.bolt Tr.bolt / (2^0

UR3.3 i.3 sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

Demand —»

i.3 0.06

UR3.3 1.0 check OK

UR3.3 0.25

Resistance —»

1.0

UR3.3 0.25

UR3 UR3.1 UR3.2 UR3.3 13 mat max :

Determines the critical UR for Check 3 and checks OK or NG

check3 UR3 1 check :

Summary

Description of Check

Capacity

Factored Applied Load

OK / N.G.

1) Tension Bolts Check Shear&Tension Interaction

UR3.1 0.45

i.1 1.0 check OK

2) Extra Shear Bolts Check Shear&Tension Interaction If Applicalble

UR3.2 0

UR3.2 1.0 check OK

3) Compression Bolts Check Shear&Tension Interaction

Vr.bolt kN 140

Vf.cbolt kN 35

UR3.3 0.25

UR3.3 1.0 check OK

CHECK 4 - Endplate Checks

Check of End Plate Prying - Use Yield Line Aproach

End Plate Flexural Yield (Check 4.1) AISC DG04

h.0 d.b 12 / t.b * - p.fo + :

h.0 mm 346

h.1 d.b 32 / t.b * - p.fi - :

h.1 mm 238

Y.P b.pe 2 / h.1 1 p.fi s 21 mat min / 1 s / + (* h.0 1 p.fo s 21 mat min / (* + 12 / - (* 2 GA / h.1 p.fi s 21 mat min s + (* (* + :

Y.P mm 2136

M.np 2 Tr.bolt * h.0 h.1 + (* :

M.np kN m * 293

NOTE: FYI, this is for a seismic check

1.11 M.np * φ F.yp * Y.P * / sqrt

FYI ONLY - this is the maximum plate thickness required as it develops the bolts with no prying for a seismic check.

1.11 M.np * φ F.yp * Y.P * / sqrt mm 23.8

Pt.UF φ 2 * F.yp * Y.P * h.0 h.1 + / (/ sqrt

The minimum plate thickness to transfer the loads flexurally through the plate

P.UF φ 2 * F.yp * Y.P * h.0 h.1 + / (/ sqrt mm 15.2

t.p mm 25.4

Plate thickness

P.UFr φ 2 * F.yp * t.p 2^* Y.P h.0 h.1 + (/ * :

P.UFr kN 1272

End plate flexural resistance

UR4.1 Pt.UF P.UFr UR :

End plate flexural resistance, Eq'n 3.10 of AISC Design Guide 4

UR4.1 0.36

Demand —»

Pt.UF kN 454

P.UF P.UFr check OK

Resistance —»

P.UFr kN 1272

UR4.1 0.36

Inputs for Prying Analysis

t t.p :

t mm 25

End Plate Thickness is the Flange Thickness

d.e p.ext p.fo - :

d.e mm 45

Edge distance

g p.fo p.fi + t.b + :

g mm 108

Bolt gauge

b g 2 d.e * + :

b mm 198

T-stub width

w t.b :

w mm 13

T-stub thickness

p b.p b.pe 21 mat min 2 / :

p mm 114.2

T-stub effective pitch

T.F Pt.UF 2 / :

T.F kN 227

Calculations for Prying Analysis

NOTE: If the pitch becomes too large, the yield line pattern will change and become a 2-way bending pattern about the bolts. Also, there is a certain level of practicality when selecting a maximum pitch, §22.3.3 of S16-09 gives some guidelines on the maximum edge distance that can also be applied here.

MaxPitch 2 b g * sqrt * :

MaxPitch mm 293

p p MaxPitch 21 mat min :

p mm 114

X.1 g w - s.11 - Ø.B - (2 / :

X.1 mm 32

X.2 X.2 1.25 g w - (2 / * Ø.B 2 / + 21 mat min :

X.2 b g - Ø.B + (2 / :

X2 is limited to a maximum value as per the CISC handbook recomendations.

X.2 1.25 g w - (2 / * Ø.B 2 / + 21 mat mm 587221 mat

= min

X.2 mm 58

End Plate Capacity (Check 4.2 T-STUB Model FYl )

P.r φ F.yp * t 2^* 2 p * Ø.BH - (g w - s.11 - Ø.B - / (* :

P.r kN 552

End plate flexural capacity Simply Mode FYl

T.F kN 227

Applied axial load on stem

UR4.2 T.F P.r UR :

End plate flexural capacity FYl

Demand —»

T.F kN 227

UR4.2 1.0 check OK

Resistance —»

P.r kN 552

UR4.2 0.41

Q.Max φ F.yp * t 2^* 4 / p Ø.BH - (X.2 / (* : kN 66

Maximum possible bolt prying force (per bolt) T-STUB

NOTE - This no prying force is for FYI only, and we will use (0.9*flexural cap.)

P.NP φ F.yp * t 2^* 2 / p X.1 / (* : kN 313

FYI. Maximum force that can be applied to the end plate (per row) for NO PRYING forces in the bolts. T-STUB

Current Excel Design Sheet Prying Force (FYI)

NOTE: Below are the equations used in the Excel Design Spreadsheet for the T-stub prying analysis. They do not affect the calculations on the left, and are only presented FYI.

Q_MAX assuming a T-Stub Model (NOTE: Bolt dia. error in E610):

Q'.Max φ F.yp * t.p 2^* b.pe 2 Ø.BH * - (8 d.e 1.25 p.fo * 21 mat min * 4 Ø.B * + (/ * :

Q'.Max kN 66

FYI.

P_NP assuming a T-Stub Model (NOTE: Yield stress error in E607):

P'.NP F.yc t.p 2^* 4 / b.pe p.fo s.11 2 / - (/ * 2 * :

P'.NP kN 549

FYI.

Q assuming a T-Stub Model

Q' Pt.UF P'.NP ≤ 0 kN * Q'.Max Pt.UF P'.NP - P.UFr P'.NP - / * if :

Q' kN 0

FYI.

Prying Analysis

T.F UR4.1 1.0 ≥ 0 kN * Pt.UF 2 / if :

NOTE - These checks only valid if the end plate flexural resistance (check above) is adequate. - Tf will change to 0 kN if end plate has failed.

NOTE: Maximum Puf force for no prying forces as per AISC DG #4 = 90% flexural resistance =

0.9 P.UFr * kN 1145

P.NP 0.9 P.UFr * 2 / :

Maximum force that can be applied to the end plate (per row) for NO PRYING forces in the bolts. Use 90% flexural resistance

P.NP kN 573

T.F kN 227

Applied axial load on stem (if Tf = 0, re-check end plate flexure)

Q T.F P.NP ≤ 0 kN * Q.Max T.F P.NP - P.UFr 2 / P.NP - / * if :

Q =

Q kN 0

Actual bolt prying force (per bolt)

T.f_bolt T.F 2 / Q + :

T.f_bolt kN 113

Bolt tension force (including prying effects)

f.p Pt.UF 4 / Q + Pt.UF 4 / / :

f.p 1

Bolt prying amplification factor

NOTE: The bolt prying amplification factor is calculated based on bolts on the tension side, but also used for extra shear bolts if the extra shear bolts are considered to take some axial load.

Re-check Flange Bolts Shear/Tension Interaction Including Effects of Prying Forces from Endplate

Tension Bolts (Check 4.3)S16-14 §13.12.1.4

Vf.bolt 0

Shear per bolt

Tf.bolt f.p Pt.UF * 4 / :

Tf.bolt kN 113

Amplified tension per bolt

i.PT Vf.bolt Vr.bolt / (2^Tf.bolt Tr.bolt / (2^+ :

i.PT 0.2

Vf.bolt Vr.bolt / (2^0

Tf.bolt Tr.bolt / (2^0.2

UR4.3 i.PT sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

T.1 Tf.bolt :

Demand —»

i.PT 0.2

i.PT 1.0 check OK

Resistance —»

1.0

UR4.3 0.45

Bolt tension is re-defined as T1 to be checked in bolt shear punching (check #5.6)

Compression Bolts (Check 4.4)S16-14 §13.12.1.4

Vf.cbolt kN 35

Shear per bolt

Tfc.bolt f.p Pc.UF * 4 / :

Tfc.bolt kN 0

Amplified tension per bolt

i.PC Vf.cbolt Vr.bolt / (2^Tfc.bolt Tr.bolt / (2^+ :

i.PC 0.06

Vf.cbolt Vr.bolt / (2^0.06

Tfc.bolt Tr.bolt / (2^0

UR4.4 i.PC sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

Demand —»

i.PC 0.06

i.PC 1.0 check OK

Resistance —»

1.0

UR4.4 0.25

Extra Shear Bolts (Check 4.7)S16-14 §13.12.1.4

Vf.xbolt kN 0

Shear taken by extra shear bolts, per bolt

Tf.xbolt f.p Tf.xbolt * : kN 0

Amplified tension per bolt

i.Px Vf.xbolt Vr.bolt / (2^Tf.xbolt Tr.bolt / (2^+ :

i.Px 0

Vf.xbolt Vr.bolt / (2^0

Tf.xbolt Tr.bolt / (2^0

UR4.7 i.Px sqrt :

Bolts in combined shear and tension, S16-14 §13.12.1.4

Demand —»

i.PC 0.06

i.PC 1.0 check OK

Resistance —»

1.0

UR4.7 0

T.2 Tf.xbolt :

Bolt tension is re-defined as T2 to be checked in bolt shear punching (Check #5.6)

End Plate Shear Yield - adjacent to beam flange and web (Check 4.5 & 4.6)

Flange check

V.r_45 φ 0.5 * F.yp * b.p b.b 12 mat min * t.p * :

V.r_45 kN 696

V.f_45 Pt.UF 2 / (2^V.XT 2^+ sqrt :

V.f_45 kN 227

Endplate shear yield, S16-14 Clause 21.12

Demand —»

V.f_45 kN 227

V.f_45 V.r_45 check OK

UR4.5 V.f_45 V.r_45 UR :

Resistance —»

V.r_45 kN 696

UR4.5 0.33

Web check

V.r_46 φ 0.5 * F.yp * 2 * d.b * t.p * :

V.r_46 kN 2078

V.f_46 V.y :

V.f_46 kN 140

Endplate shear yield, S16-14 Clause 21.12

UR4.6 V.f_46 V.r_46 UR :

Demand —»

V.f_46 kN 140

V.f_46 V.r_46 check OK

Resistance —»

V.r_46 kN 2078

UR4.6 0.07

End Plate Shear Rupture FYI

V.r_48 φ.u 0.6 * F.u * b.p b.b 12 mat min 2 Ø.BH * - (* t.p * :

V.r_48 kN 1405

Endplate shear rupture

FYI

UR4.8 T.F V.r_46 UR :

Demand —»

T.F kN 227

UR4.8 1.0 check OK

Resistance —»

V.r_48 kN 1405

UR4.8 0.1

NOTE: Endplate end tear check is not included in this sheet because this will not govern usually.

UR4 UR4.1 UR4.3 UR4.5 UR4.6 UR4.7 UR4.4 16 mat max :

Determines the critical UR for Check 4 and checks OK or NG

check4 UR4 1.0 check :

Summary

Description of Check

Capacity

Factored Applied Load

OK / N.G.

1) End Plate Flexural Yield Check

P.UFr kN 1272

Pt.UF kN 454

UR4.1 0.36

UR4.1 1.0 check OK

2) Tension Flg. Bolts Recheck Including Prying From endplate yield line analysis

UR4.3 0.45

UR4.3 1.0 check OK

3) Compresssion Flg. Bolts Recheck Including Prying From endplate yield line analysis

UR4.4 0.25

UR4.4 1.0 check OK

4) Extra Shear Bolts Recheck Including Prying From endplate yield line analysis

UR4.7 0

UR4.7 1.0 check OK

5) End Plate Shear Yield Along Flange Check

V.r_45 kN 696

V.f_45 kN 227

UR4.5 0.33

V.f_45 V.r_45 check OK

6) End Plate Shear Yield Along Web Check

V.r_46 kN 2078

V.f_46 kN 140

UR4.6 0.07

V.f_46 V.r_46 check OK

CHECK 5 - Column Flange Checks

Unstiffened Column Flange Flexural Yield FYI

Unstiffened Column Flange Flexural Yield (Check 5.1) FYI

tc.reqd M.f φ F.yc * Y.c * / sqrt :

M.f P.UF M.y GA / + (h.0 h.1 + (* 2 / :

where:

M.f kN m * 133

Eq'n 2-9 of AISC Design Guide 16

b'.c b.c 14 / 9 GA * 5 w.c * - (* 21 mat min :

b.c 14 / 9 GA * 5 w.c * - (* 21 mat mm 20428221 mat

= min

b'.c mm 204

Effective column flange width

c.b p.fo p.fi + t.b + :

c.b mm 108

c.y c.b :

c.y mm 108

s 12 / b'.c GA * sqrt * :

s mm 81

NOTE: ec > 2s, therefore this is an interior condition. Yc is based on Table 3.4 - AISC DG 4 If ec ≤ 2s, an exterior condition exists. Yc will be based on Table 3.4 - AISC DG 4:

Y.c e'.c 2 s * > b'.c 2 / (h.1 s / h.0 s / + (* 2 GA / (h.1 s 3 c.y 4 / * + (* h.0 s c.y 4 / + (* + c.y 2^2 / + (* + GA 2 / (+ h.0 h.1 + (b'.c GA / sqrt * e'.c 2 s * 21 mat min b'.c + (GA / + if :

Y.c mm 2061

tc.reqd mm 14.3

Minimum column flange thickness required to transfer loads

FYI only Unstiffened column flange flexural resistance from AISC DG 4

R.cf φ F.yc * Y.c * t.c 2^* d.b t.b - / :

R.cf kN 477

FYI

Unstiffened column flange flexural resistance S16-09 §21.3 b) Future

R.cf 2 φ * F.yc * t.c 2^* b'.c GA / sqrt c.b 2 s * e'.c 12 mat min + GA / + (* :

R.cf kN 448

UR5.1 P.UF M.y GA / + R.cf UR :

Stiffen_note P.UF M.y GA / + R.cf check Fails ≡ Stiffeners required Stiffeners not req'd if :

Unstiffened column flg. flexural resistance FYI

Demand —»

P.UF M.y GA / + kN 454

P.UF M.y GA / + R.cf check Fails

Resistance —»

R.cf kN 448

UR5.1 1.01

Col Flg. Thickness Req'd —»

tc.reqd mm 14.3

Stiffen_note Stiffeners required

Col Flg. Actual Thickness —»

t.c mm 14.6

FYI - Minimum Flange Thickness Req'd for No Prying Forces

tc.min 1.11 M.np * φ F.yc * Y.c * / sqrt :

Eq'n 3.10 of AISC Design Guide 4 (for seismic applications)

where:

M.np 2 Tr.bolt * h.0 h.1 + (* :

M.np kN m * 293

tc.min 1.11 M.np * φ F.yc * Y.c * / sqrt :

FYI

tc.min mm 22.4

Min Col Flg. Thickness for no prying —»

tc.min mm 22.4

Actual Column Flange Thickness —»

t.c mm 14.6

Evaluation of Bolt Prying Forces for Flange Bolts for Unstiffened Column FYI

P.UF M.y GA / + kN 454

Q.cf Q.MAXcf P.UF M.y GA / + NP.cf - (R.cf NP.cf - (/ * :

Flange bolt column flange prying force

where:

k.eng k.engc :

Minimum k distance as reported by AISC

k1.eng k1.engc :

k1.eng mm 17

Conversion from k to k1

t.factor b.c GA / sqrt c.b 2 GA * / + (2 s * c.b + Ø.BH - (GA w.c 2 / - k1.eng - Ø.B - (/ (/ sqrt 2 sqrt * :

t.factor 1.07

Calculation of flange thickness factor to convert flange to equivalent T-stub model

t.factor t.factor 121 mat max :

t.factor 121 mat 1.07 121 mat

= max

t.factor 1.07

Factor must be greater than 1

Pseudo flange thickness to convert column flange to equivalent T-stub

t'.c t.factor t.c * :

t'.c mm 15.6

NOTE:

e'.c mm 1000

| | —» |

ec > 2s, therefore interior condition, however, if ec < 2s (exterior condition), QMAX_cf is defined below:

2 s * mm 163

Q.MAXcf e'.c 2 s * > 12 / φ * F.yc * t'.c 2^* s 12 / c.b * + Ø.BH - (b'.c GA - Ø.B + (/ * 12 / φ * F.yc * t.c 2^* e.c 12 / c.b * + Ø.BH - (b'.c GA - Ø.B + (/ * if :

Max prying force per bolt (for interior condition)

Max prying force per bolt (for exterior condition)

Q.MAXcf kN 42

NP.cf 0.9 R.cf * :

NP.cf kN 403

Prying force on bolts from unstiffened flange prying

φ F.yc * t'.c 2^* s 12 / c.b * + GA w.c 2 / - k1.eng - Ø.B - / * kN 124

FYI. No Prying force from Waiward Engineering STD

Q.cf kN 47

Column flange prying force, per bolt

Column flange check w/ stiffeners

Stiffened Column Flange Flexural Capacity (Check 5.2)

NOTE: Full width of column flange is assumed to participate in the stiffened column flange's flexural resistance.

R.cfs 2 φ * F.yc * t.c 2^* Y.c * h.1 h.0 + (/ :

Table 3.4 AISC Design Guide 4

FYI

Y.c b.c 2 / h.1 1 s / 1 p.fi / + (* h.0 1 s / 1 p.fo / + (* + (* 2 GA / h.1 s p.fi + (* h.0 s p.fo + (* + (* + :

where:

Y.c mm 3144

FYI

R.cfs 2 φ * F.yc * t.c 2^* Y.c * h.1 h.0 + (/ :

R.cfs kN 722

FYI

c.so p.fo :

c.so mm 50

c.si p.fo t.b + t.s - :

c.si mm 50

c.so c.so s 21 mat min :

p.fo s 21 mat mm 508121 mat

= min

c.so mm 50

c.si c.si s 21 mat min :

p.fo t.b + t.s - s 21 mat mm 508121 mat

= min

c.si mm 50

Stiffened Column Flange Flexural Capacity Waiward Engineering STD'S,

R.cfs e'.c 2 s * > 2 φ * F.yc * t.c 2^* 2 b.c GA / sqrt * c.so c.si + GA / + b.c 4 / 1 c.so / 1 c.si / + (* + (* 2 φ * F.yc * t.c 2^* e'.c c.so + GA / b.c 4 c.so * / + b.c GA / sqrt + b.c 4 c.si * / + c.si GA / + (* if :

R.cfs kN 713

UR5.2 Pt.UF R.cfs UR :

Stiffened column flg. flexural resistance check

Demand —»

Pt.UF kN 454

P.UF R.cfs check OK

Resistance —»

R.cfs kN 713

UR5.2 0.64

Prying Forces on Bolts With Column Flange Stiffener Present

NOTE: Prying forces will be calculated assuming the "T-Stub" analogy where the stiffener acts as the web element and the point where prying forces start to occur will be taken as 90% of Rcfs.

NP.cfs 0.9 R.cfs * :

NP.cfs kN 642

Pt.UF NP.cfs > Q.cfs Q.MAXcfs Pt.UF NP.cfs - (R.cfs NP.cfs - (/ * : Q.cfs 0 : if

Calculate Pseudo flange thickness to convert column flange to equivalent T-stub From Waiward STD

t''.c e'.c 2 s * > 2 sqrt t.c * 2 b'.c GA / sqrt * c.so c.si + GA / + b'.c 4 / 1 c.so / 1 c.si / + (* + 4 s * 2 c.so c.si + (* + Ø.BH - GA w.c 2 / - k1.eng - Ø.B - / / sqrt * 2 sqrt t.c * e'.c c.so + GA / b'.c 4 c.so * / + 2 e'.c * 2 c.so * + Ø.BH - GA w.c 2 / - k1.eng - Ø.B - / / sqrt * if : mm 19.4406

where:

Q.MAXcfs e'.c 2 s * > 12 / φ * F.yc * t''.c 2^* 2 s * c.so + c.si + Ø.BH - b'.c GA - Ø.B + / * 12 / φ * F.yc * t''.c 2^* e.c c.so + Ø.BH - (b'.c GA - Ø.B + (/ * if :

Q.MAXcfs kN 141

NOTE:

e'.c mm 1000

| | —» |

ec > 2s, therefore interior condition, however, if ec < 2s (exterior condition)

2 s * mm 163

Q.cfs kN 0

FYI only Prying Forces on Bolts With Column Flange Stiffener Present Waiward Engineering STD'S,

T.r_np φ F.yc * t''.c 2^* 2 s * c.si + c.so + (GA w.c 2 / - k1.eng - Ø.B - / * : kN 375.7763

NP.cfs kN 642

Re-check Col, Flange Bolts Shear/Tension Interaction Including Effects of Prying Forces from Stiffened or Unstiffened Column

Q.bolt Q.cfs :

Q.bolt kN 0

f.p Pt.UF 4 / Q.bolt + Pt.UF 4 / / :

f.p 1

Bolt prying amplification factor

Tension Flange (Check 5.3)S16-14 §13.12.1.4

Vf.bolt kN 0

Tf.bolt Pt.UF 4 / f.p * :

Tf.bolt kN 113

Nominal bolt tension plus column flange prying force

i.4 Vf.bolt Vr.bolt / (2^Tf.bolt Tr.bolt / (2^+ :

i.4 0.2

Bolts in combined shear and tension, S16-14 §13.12.1.4

Vf.bolt Vr.bolt / (2^0

Tf.bolt Tr.bolt / (2^0.2

Demand —»

i.4 0.2

i.4 1.0 check OK

UR5.3 i.4 sqrt :

Resistance —»

1.0

UR5.3 0.45

T.3 Tf.bolt :

Bolt tension is re-defined as T3 to be checked in bolt shear punching (Check #5.6)

Compression Flange (Check 5.4)S16-14 §13.12.1.4

Vf.cbolt kN 35

Tfc.bolt 0 :

Tfc.bolt kN 0

Nominal bolt tension plus column flange prying force

i.5 Vf.cbolt Vr.bolt / (2^Tfc.bolt Tr.bolt / (2^+ :

i.5 0.06

Bolts in combined shear and tension, S16-14 §13.12.1.4

Vf.cbolt Vr.bolt / (2^0.06

Tfc.bolt Tr.bolt / (2^0

Demand —»

i.5 0.06

i.5 1.0 check OK

UR5.4 i.5 sqrt :

Resistance —»

1.0

UR5.4 0.25

Extra Shear Bolts (Check 5.7)S16-14 §13.12.1.4

NOTE: This check is conservative because shear bolt prying would be less.

Vf.xbolt kN 0

Shear taken by extra shear bolts, per bolt

Tf.xbolt Consider_Extra_Shear_Bolts_For_Axial_Load 1 ≡ 0 P.shear_bolts Bolt.ES / f.p * if :

Rewrite the tension per bolt on extra shear bolt

Tf.xbolt kN 0

Amplified tension per bolt

i.6 Vf.xbolt Vr.bolt / (2^Tf.xbolt Tr.bolt / (2^+ :

i.6 0

Bolts in combined shear and tension, S16-14 §13.12.1.4

Vf.xbolt Vr.bolt / (2^0

Tf.xbolt Tr.bolt / (2^0

Demand —»

i.6 0

i.6 1.0 check OK

UR5.7 i.6 sqrt :

Resistance —»

1.0

UR5.7 0

T.4 Tf.xbolt :

Bolt tension is re-defined as T4 to be checked in bolt shear punching (Check #5.6)

Column Flange Edge Tear - against weak axis shear (Check 5.5)S16-14 §13.11

NOTE: Conservative check which likely won't govern

V.r_55 φ.u 0.6 * t.c * b.c GA - (* F.yc F.uc + (2 / * 2 * :

V.r_55 kN 389

NOTE: Weak axis shear is assumed to be resisted at the top flange only, therefore column flange edge tear capacity is multiplied by 2 rows of bolts at top flg.

UR5.5 V.XT V.r_55 UR :

Column flange edge tear, S16-14 §13.11

Demand —»

V.XT 0

V.x V.r_55 check OK

Resistance —»

V.r_55 kN 389

UR5.5 0

Bolt Shear Punching (Check 5.6)

NOTE: This check is analogous to the check on the end plate shear strength at the yield line, it ensures that the column flange has enough shear strength to transfer the bolt forces and engage the assumed yield lines in the flange.

C.w 2 π * Ø.B * :

C.w mm 160

Assumed washer circumference, and 75% is assumed to be effective

V.r_56 φ 0.66 * F.yc * t.c * 0.75 * C.w * :

V.r_56 kN 363

V.f_56 T.1 T.2 T.3 T.4 41 mat max :

T.1 T.2 T.3 T.4 41 mat kN 1130113041 mat

Vf_56: Max bolt tension including prying effects T1 - Bolt tension in tension flg. bolts (includes prying from endPL) T2 - Bolt tension in extra shear bolts (including prying from endPL) T3 - Bolt tension in tension flg. bolts (includes prying from col. flg.) T4 - Bolt tension in extra shear bolts (including prying from col. flg.)

= max

V.f_56 kN 113

Bolt shear punching

UR5.6 V.f_56 V.r_56 UR :

Demand —»

V.f_56 kN 113

V.f_56 V.r_56 check OK

Resistance —»

V.r_56 kN 363

UR5.6 0.31

UR5 UR5.2 UR5.3 UR5.5 UR5.6 UR5.7 UR5.4 16 mat max :

check5 UR5 1.0 check :

Summary

Description of Check

Capacity

Factored Applied Load

OK / N.G.

1) Column Flange Flexural Yield Check

R.cfs kN 713

Pt.UF kN 454

UR5.2 0.64

UR5.2 1.0 check OK

2) Tension Flg. Bolts Recheck Including Prying From col. flange yield line analysis

UR5.3 0.45

UR5.3 1.0 check OK

3) Compression Flg. Bolts Recheck Including Prying From col. flange yield line analysis

UR5.4 0.25

UR5.4 1.0 check OK

4) Extra Bolts Recheck Including Prying From col. flange yield line analysis

UR5.7 0

UR5.7 1.0 check OK

5) Column Flange Edge Tear - against weak axis shear

V.r_55 kN 389

V.XT kN 0

UR5.5 0

V.XT V.r_55 check OK

6) Bolt Shear Punching

V.r_56 kN 363

V.f_56 kN 113

UR5.6 0.31

V.f_56 V.r_56 check OK

CHECK 6 - Column Stiffener Check

Unstiffened column web check and provide stiffeners design loads

Column Web Strength Limit State

Web Yielding (Check 6.1)AISC DG 4

B.r_61 φ C.ty * 6 k.engc * N + (* F.yc * w.c * :

Eq'n 3.24 of AISC Design Guide 4

where:

C.ty e'.c d.c < 0.5 e'.c 75 mm * - 2 d.c 75 mm * - (* / + 1.0 if :

C.ty 1

C.t e'.c d.c < 0.5 e'.c 75 mm * - 2 d.c 2 / 75 mm * - (* / + 1.0 if :

C.t 1

NOTE: Ct and Cty are the factors that account for the end effect on an unstiffened column - if they equal 1.0 then there is no effect (interior connection)

N t.b s.11 + s.12 + 2 t.p * + :

N mm 76

B.yield B.r_61 :

B.r_61 kN 982

UR6.1 P.UF B.r_61 UR :

Column web yielding, eq'n 3.24 of AISC DG 4

Demand —»

P.UF kN 454

P.UF B.r_61 check OK

Resistance —»

B.r_61 kN 982

UR6.1 0.46

Panel Zone Shear (Check 6.2)AISC DG 13

NOTE: As we typically do not know shear load and axial load in the column, we do not consider it when calculating the column web shear capacity

V.r_62 φ 0.6 * w.c * F.yc * d.c * :

V.r_62 kN 492

P.UF_PZ M.x d.b t.b - / :

NOTE: This check assumes axial load does not contribute to panel zone shear

P.UF_PZ kN 414

UR6.2 P.UF_PZ V.r_62 UR :

Panel zone shear, eq'n 2.2-1 of AISC DG 13

Demand —»

P.UF_PZ kN 414

UR6.2 1.0 check OK

Resistance —»

V.r_62 kN 492

UR6.2 0.84

Column Web Stability Limit State

NOTE: This check is to make sure that the web stability not affect web shear yielding.

Local Buckling (Check 6.3)

F.yc F.yc MPa / :

NOTE: Fyc is non-dimensionalized for the purposes of this check

Limit.1 d.c 2 t.c * - t.c / :

Limit.1 19

Limit.2 670 F.yc sqrt / :

Limit.2 36

UR6.3 Limit.1 Limit.2 UR :

Local buckling, S16-14 Table 1

Demand —»

Limit.1 19

Limit.1 Limit.2 check OK

Resistance —»

Limit.2 36

UR6.3 0.53

F.yc F.yc MPa * :

Fyc is re-defined with units

Crippling (Check 6.4)AISC DG 4

Design Philosophy Note: AISC Design Guide 4 uses N = tb + Df1 +Df2. We feel the use of N = tb + Df1 +Df2 + 2tp is justified based on crippling guidance givenin AISC 360-05 Section J10.2 & J10.3

B.r_64 C.t 1 ≥ 0.75 0.8 * C.t * w.c 2^* 13 N d.c / (* w.c t.c / (1.5^* + (* E F.yc * t.c w.c / * sqrt ((* N d.c / 0.2 ≤ 0.75 0.4 * C.t * w.c 2^* 13 N d.c / (* w.c t.c / (1.5^* + (* E F.yc * t.c w.c / * sqrt ((* N d.c / 0.2 > 0.75 0.4 * C.t * w.c 2^* 14 N d.c / * 0.2 - (w.c t.c / (1.5^* + (* E F.yc * t.c w.c / * sqrt ((* 0 if if if :

AISC Design Guide 4 - Eq'n 3.29

B.r_64 kN 632

B.crippling B.r_64 :

Web crippling, eq'n 3.29 of AISC DG 4

UR6.4 P.UF B.r_64 UR :

Demand —»

P.UF kN 454

P.UF B.r_64 check OK

Resistance —»

B.r_64 kN 632

UR6.4 0.72

UR6 UR6.1 UR6.2 UR6.3 UR6.4 14 mat max :

Determines the critical UR for Check 6 and checks OK or NG

check6 UR6 1.0 check :

Column Stiffener Check

Column Reinforcement Load Distribution

Flexural Yielding of Flange

P.UF kN 454

P.s_FY P.UF R.cf - 021 mat max :

P.s_FY kN 6

Web Yielding

P.UF kN 454

P.s_WY P.UF B.yield - 021 mat max :

P.s_WY kN 0

Web Crippling

P.UF kN 454

P.s_WC P.UF B.crippling - 021 mat max :

P.s_WC kN 0

Web Buckling

P.UF kN 454

P.s_WB 0 :

P.s_WB kN 0

Web Panel Zone Shear

P.UF_PZ kN 414

P.s_PZ P.UF_PZ V.r_62 - 021 mat max :

P.s_PZ kN 0

Weak Axis Moment

M.y kN m * 0

P.s_WM P.UF_weak_stiff 2 / :

P.s_WM kN 0

NOTE: MC on one side of column only, Web Buckling check does not apply

Shear Tab Force

P.sh_tab kN 0

Additional applied loads to a beam framing into the column web with a shear tab welded to the MC stiffeners Note: Edit this value in Applied Loads area

Stiffener Load

P.s P.s_FY P.s_WY P.s_WC P.s_PZ 41 mat max :

P.s_FY P.s_WY P.s_WC P.s_PZ 41 mat kN 600041 mat

= max

P.s kN 6

NOTE: In lieu of taking the minimum stiffener load to be 40%Puf, below is a YL theory based on either an exterior or interior condition

e'.c mm 1000

| | —» |

ec > 2s, therefore interior condition, however, if ec < 2s, minimum load in stiffener = P'min

2 s * mm 163

y p.fo p.fi t.b + t.s - 21 mat min :

p.fo p.fi t.b + t.s - 21 mat mm 504521 mat

= min

y mm 45

Distance from bolt hole to top edge of stiffener

Tf.bolt Pt.UF 4 / :

Tf.bolt kN 113

Force in one bolt

b b'.c :

Minimum load in stiffener (based on stiffness at ultimate)

NOTE: The first term of the equation below is for the exterior bolt and the second term is for the interior bolt.

P.min e'.c 2 s * > Tf.bolt b 2 y * / b 2 y * / 2 y s + (* GA / + / b 2 y * / b 2 y * / 2 y P.real_pitch 2 / P.max_pitch 2 / 12 mat min + (* GA / + / + (* Tf.bolt b 2 y * / b 2 y * / y e'.c + (2 * GA / + / b 2 y * / b 2 y * / 2 y P.real_pitch 2 / P.max_pitch 2 / 12 mat min + (* GA / + / + (* if :

P.min kN 119

P.stiff P.s_WM P.s 2 / + P.min 21 mat max V.xst + :

Conservatively proportion all of the weak axis shear in the beam with the shear tab into one stiffener

P.s_WM P.s 2 / + P.min 21 mat kN 311921 mat

= max

V.xst kN 0

P.stiff kN 119

Full Depth Stiffener Strength Limit State Checks

Full Depth Stiffener Geometry

A.sf t.s w.s c - (* :

A.sf mm 2^1036

Area of stiffener edge 1 or 2 (stiffener/flange interface)

A.sw t.s L.s 2 c * - (* :

A.sw mm 2^3007

Area of stiffener edge 3 (stiffener/web interface)

Note: 25 mm accounts for minimum thickness of shear tab (13 mm) and minimum fillet weld leg size on both sides (6 mm) in the calculation below.

A.swt A.sw 2 w.s * 25 mm * + (t.s * 21 mat min :

t.s L.s 2 c * - (* 2 w.s * 25 mm * + (t.s * 21 mat mm 2^3007289821 mat

A.swt mm 2^2898

= min

e.s w.s c - (2 / c + :

e.s mm 61

Eccentricity between Pstiff and web interface

V.s P.stiff e.s * L.s / :

V.s kN 26

Couple forces to balance eccentric Pstiff

V.1_1 V.s 0.25 P.sh_tab * 1.2 * + :

V.1_1 kN 26

Total force at stiffener/flg. interface

NOTE: (1) 0.25 factor is the % of Psh_tab assigned to each stiffener/flange interface (2) 1.2 factor is a load distribution uncertainty factor to account for any varaiation in load distribution from what has been assumed

Section 1-1 (Interface between column flange and stiffener) (Check 7.1)

NOTE: If Section 1-1 Criteria is satisfied, Section 2-2 need not be checked

τ V.1_1 A.sf / :

τ MPa 25

Stiffener shear stress

τ.Limit φ 0.66 * F.ys * :

τ.Limit MPa 178

Stiffener shear stress resistance, S16-14 §13.

Demand —»

τ MPa 25

τ τ.Limit check OK

UR7.1 τ τ.Limit UR :

Resistance —»

τ.Limit MPa 178

UR7.1 0.14

σ.n1 P.stiff A.sf / :

σ.n1 MPa 115

Stiffener normal stress

σ.Limit φ F.ys * :

σ.Limit MPa 270

Stiffener normal stress limit

Normal/Shear Stress Interaction (Check 7.2)

NOTE: In order to assess the potential interaction between the shear stress, τ_w, and the normal stress, σ_N, the following equation is used. Refer to Waiward Engineering sample calculation document “Assessment of Combined Stresses” for more information, but roughly the intent of the following is to take advantage of the allowable shear and normal stress combination suggested by clause 13.4.2 of S16-09.

σ.Limit1 τ τ.Limit > CHECK SHEAR STRESS τ 0.5 φ * F.ys * < φ F.ys * 254 / 0.66 φ * F.ys * τ - (* if if :

UR7.2 σ.n1 σ.Limit1 UR :

NOTE: If τ > 0.5φFy, the normal stress limit should be reduced to: 25 / 4 * ( 0.66*φ*Fy - τ ) as shown in the interaction diagram below.

Normal / shear stress interaction

Stiffener normal stress resistance, S16-14 §13.2 & 13.11

Demand —»

σ.n1 MPa 115

σ.n1 σ.Limit1 check OK

Resistance —»

σ.Limit1 MPa 270

UR7.2 0.43

τ/ΦFy

Section 3-3 (Interface between column web and stiffener) (Check 7.3)

τ P.stiff A.sw / :

τ MPa 40

Stiffener shear stress

τ.Limit φ 0.66 * F.ys * :

τ.Limit MPa 178

Stiffener shear stress resistance, S16-14 §13.

Demand —»

τ MPa 40

τ τ.Limit check OK

UR7.3 τ τ.Limit UR :

Resistance —»

τ.Limit MPa 178

UR7.3 0.22

σ.n2 0.5 P.sh_tab A.swt / * 1.2 * :

σ.n2 MPa 0

Stiffener normal stress

σ.Limit φ F.ys * :

σ.Limit MPa 270

Stiffener normal stress limit

Normal/Shear Stress Interaction (Check 7.4)

σ.Limit2 τ τ.Limit > CHECK SHEAR STRESS τ 0.5 φ * F.ys * < φ F.ys * 254 / 0.66 φ * F.ys * τ - (* if if :

Stiffener normal stress resistance, S16-14 §13.2 & 13.11

UR7.4 σ.n2 σ.Limit2 UR :

Demand —»

σ.n2 MPa 0

σ.n2 σ.Limit2 check OK

Resistance —»

σ.Limit2 MPa 270

UR7.4 0

Full Depth Stiffener Weld Limit State Checks

Full Depth Stiffener Weld Geometry

s.3 mm 6

s.4 mm 6

A.w_s3 12 sqrt / s.3 * w.s c - (* 2 * :

A.w_s3 mm 2^692

Area for weld 3 and 4 include weld on both sides of the stiffener

A.w_s4 12 sqrt / s.4 * L.s 2 c * - (* 2 * :

A.w_s4 mm 2^2009

Section 1-1 (Interface Between Column Flange and Stiffener) (Check 7.5)

V.r_75 0.67 φ.w * X.u * A.w_s3 * 1 0.5 θ.75 sin (1.5^* + (* :

θ.75 P.stiff V.1_1 / atan :

where:

θ.75 ° 78

Load angle

R.sf_75 P.stiff 2^V.1_1 2^+ sqrt :

R.sf_75 kN 122

Resultant load

UR7.5 R.sf_75 V.r_75 UR :

Fillet weld resistance, S16-14 §13.13.2.2

Demand —»

R.sf_75 kN 122

R.sf_75 V.r_75 check OK

Resistance —»

V.r_75 kN 226

UR7.5 0.54

Section 3-3 (Interface Between Column Web and Stiffener) (Check 7.6)

V.r_76 0.67 φ.w * A.w_s4 * X.u * 1 0.5 θ.76 sin (1.5^* + (* :

where:

θ.76 0.5 P.sh_tab * 1.2 * P.stiff / atan :

θ.76 ° 0

R.sf_76 0.5 P.sh_tab * 1.2 * (2^P.stiff (2^+ sqrt :

R.sf_76 kN 119

Resultant load

UR7.6 R.sf_76 V.r_76 UR :

Fillet weld resistance, S16-14 §13.13.2.2

Demand —»

R.sf_76 kN 119

R.sf_76 V.r_76 check OK

Resistance —»

V.r_76 kN 442

UR7.6 0.27

Full Depth Stiffener Stability Limit State Checks

Local Buckling (Check 7.7)Refer to Gilbet book equation 11.86 "Design of Steel Structure"

t.s_reqd w.s 188 / F.ys MPa / sqrt * :

t.s_reqd mm 9.4

Local Buckling

Demand —»

t.s_reqd mm 9.4

t.s_reqd t.s check OK

UR7.7 t.s_reqd t.s UR :

Resistance —»

t.s mm 12.7

UR7.7 0.74

Overall Buckling (Check 7.8)

k.x 0.75 :

k.y 0.75 :

k.z 0.75 :

C.w 0 :

L.x L.s :

L.y L.s :

L.z L.s :

n 1.34 :

C.r φ A.s * F.y * 1 λ 2 n *^+ (1 n / -^* :

web_potion e'.c 12 w.c * > 2512 if :

As per S16-14 §14.4.2

NOTE: For interior condition (ec' > 12wc),25, for exterior condition, 12

A.s web_potion w.c 2^* 2 w.s * t.s * + :

A.s mm 2^4387

where:

I.x w.c web_potion w.c * (3^* 12 / 2 w.s * t.s 3^* 12 / + :

I.x mm 4^6831642

I.y t.s 2 w.s * w.c + (3^* 12 / web_potion w.c * t.s - (w.c 3^* 12 / + :

I.y mm 4^10051412

J 2 w.s * t.s 3^* (3 / web_potion w.c 4^* (3 / + :

J mm 4^182244

r.x I.x A.s / sqrt :

r.x mm 39

r.y I.y A.s / sqrt :

r.y mm 48

r.0 r.x 2^r.y 2^+ sqrt :

r.0 2^mm 2^3849

—»

F.y F.ys F.yc 21 mat min :

F.ys F.yc 21 mat MPa 30035021 mat

= min

F.y MPa 300

F.ex π 2^E * k.x L.x * r.x / (2^/ :

F.ey π 2^E * k.y L.y * r.y / (2^/ :

F.ex MPa 71325

F.ey MPa 1105^*

F.ez π 2^E * C.w * k.z L.z * (2^/ G J * + (A.s r.0 2^* / :

F.ez MPa 831

F.e F.ex F.ey F.ez 31 mat min :

F.ex F.ey F.ez 31 mat MPa 713251105^* 83131 mat

= min

F.e MPa 831

λ F.y F.e / sqrt :

λ 0.6

C.r_78 φ A.s * F.y * 1 λ 2 n *^+ (1 n / -^* :

Stiffener stability, S16-14 §13.3.1

C.r_78 kN 1000

Demand —»

2 P.stiff * kN 238

2 P.stiff * C.r_78 check OK

UR7.8 2 P.stiff * C.r_78 UR :

Resistance —»

C.r_78 kN 1000

UR7.8 0.24

UR7 UR7.1 UR7.2 UR7.3 UR7.4 UR7.5 UR7.6 UR7.7 UR7.8 18 mat max :

Determines the critical UR for Check 7 and checks OK or NG

check7 UR7 1.0 check :

Summary

Factored Applied Load

Description of Check

Capacity

OK / N.G.

1) Stiffener Normal&Shear Interaction Section 1-1

σ.Limit1 MPa 270

σ.n1 MPa 115

UR7.2 0.43

σ.n1 σ.Limit1 check OK

2) Stiffener Normal&Shear Interaction Section 3-3

σ.Limit2 MPa 270

σ.n2 MPa 0

UR7.4 0

σ.n2 σ.Limit2 check OK

3) Full Depth Stiffener Weld Checks Weld to Col. Flange

V.r_75 kN 226

R.sf_75 kN 122

UR7.5 0.54

R.sf_75 V.r_75 check OK

4) Full Depth Stiffener Weld Checks Weld to Col. Web

V.r_76 kN 442

R.sf_76 kN 119

UR7.6 0.27

R.sf_76 V.r_76 check OK

5) Full Depth Stiffener Stability Checks Local Buckling

UR7.7 0.74

t.s_reqd t.s check OK

6) Full Depth Stiffener Stability Checks Overall Buckling

C.r_78 kN 1000

2 P.stiff * kN 238

UR7.8 0.24

2 P.stiff * C.r_78 check OK

CHECK 7 - Web Doubler Checks

Web Doubler Design Loads

NOTE: The load from stiffeners to web doubler goes through the weld#5, and assume min. load is Pstiff/2.

P.doubler P.s_PZ No.doublers / P.stiff 2 / 12 mat Max :

P.doubler kN 59

Design force for one web doubler

V.doubler P.doubler d.b t.s - w.d / * :

V.doubler kN 70

δ' δ :

NOTE: Effective fusion depth assumed equal to groove weld depth

h.d d.b 2 t.s * - :

h.d mm 278

Web doubler height

Web Doubler Strength Checks

Section 1-1 (Interface Between Column Flange and Web Doubler Plate) (Check 8.10)

V.r_810 0.8 φ * 0.66 * h.d * t.d * F.yd * :

V.r_810 kN 377

V.f_810 V.doubler V.yst 2 / + :

Gross shear yield, S16-09 §13.4.2

V.f_810 kN 70

Demand —»

V.f_810 kN 70

V.f_810 V.r_810 check OK

UR8.10 V.f_810 V.r_810 UR :

Resistance —»

V.r_810 kN 377

UR8.10 0.18

Section 2-2 (Interface Between Stiffener and Web Doubler Plate) (Check 8.11)

V.r_811 0.8 φ * 0.66 * w.d * t.d * F.yd * :

V.r_811 kN 337

Gross shear yield, S16-14 §13.4.2

Demand —»

P.doubler kN 59

P.doubler V.r_811 check OK

UR8.11 P.doubler V.r_811 UR :

Resistance —»

V.r_811 kN 337

UR8.11 0.18

Web Doubler Weld Checks

Interface Between Column Flange and Web Doubler Plate

Square Groove Weld Shear Resistance (Check 8.12)

V.r_812 0.67 φ.w * h.d * δ' * F.ud * :

V.r_812 kN 534

V.f_812 V.doubler V.yst 2 / + :

Square groove weld shear resistance, S16-14 §13.13.2.1(a)

V.f_812 kN 70

Demand —»

V.f_812 kN 70

V.f_812 V.r_812 check OK

UR8.12 V.f_812 V.r_812 UR :

Resistance —»

V.r_812 kN 534

UR8.12 0.13

Interface Between Web Doubler and Stiffener

Fillet Weld Resistance, Weld #5 (check 8.13)

V.r_813 0.67 φ.w * A.w_s5 * X.u * 1 0.5 θ.813 sin (1.5^* + (* :

A.w_s5 12 sqrt / s.5 * L.s 2 c * - (* :

A.w_s5 mm 2^1005

where:

One side weld

θ.813 0 deg * :

V.f_813 P.doubler :

V.f_813 kN 59

Design force for one side weld

Fillet weld resistance, S16-14 §13.13.2.2

UR8.13 V.f_813 V.r_813 UR :

Demand —»

V.f_813 kN 59

V.f_813 V.r_813 check OK

Resistance —»

V.r_813 kN 221

UR8.13 0.27

Interface Between Column Web and Stiffener Recheck

Fillet Weld Resistance, Weld #4 (Check 8.14)

V.r_814 0.67 φ.w * A.w_s14 * X.u * 1 0.5 θ.814 sin (1.5^* + (* :

A.w_s14 12 sqrt / s.4 * L.s 2 c * - (* :

A.w_s4 mm 2^2009

where:

Weld # 4 area (one side only)

LS.4 P.doubler :

LS.4 kN 59

Load in weld #4 - interface between column web and stiffener

θ.814 0.5 P.sh_tab * 1.2 * LS.4 / atan :

θ.814 ° 0

R.sf_814 LS.4 2^0.5 P.sh_tab * 1.2 * (2^+ sqrt :

R.sf_814 kN 59

Fillet weld resistance, S16-14 §13.13.2.2

UR8.14 R.sf_814 V.r_814 UR :

Demand —»

R.sf_814 kN 59