COPYRIGHT 2014 STEEL JOIST INSTITUTE

REFERENCE MANUAL

AND

SPREADSHEET USERS

GUIDE

Joist Girder Moment Connections to

HSS Columns - Knife Plates

Version 1.0

Steel Joist Institute 234 W. Cheves Street Florence, SC 29501

Phone: (843) 407-4091 www.steeljoist.or

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Joist Girder Moment Connections to HSS Columns - Knife

Plates

The knife plate detail for a Joist Girder framing into an HSS column is shown in Figure 1. A detail of the knife plate is shown in Figure 2. If an insufficient amount of weld is available the knife plate can be extended farther into the Joist Girder top chord to obtain additional weld length, see Figure 3. If Joist Girders frame to the column from both sides, then the detail would be similar to Figure 1 with the cap plate extended on both sides of the HSS. See Figure 4.

The vertical reactions (both gravity and uplift) and the horizontal chord force are transferred to the column through the weld between the Joist Girder top chord and the knife plate and then through the column cap plate. For Joist Girders framing to both sides of the column the knife plate can also be used to transfer continuity forces from one Joist Girder to the other. The bottom chord force is transferred to the column through the stabilizer plates. If the Joist Girder is modeled as a truss the chord forces are obtained directly from the model; however, if the Joist Girder is modeled as a beam element the chord forces are determined by resolving the end moments into force couples. Numerous limit states must be examined. These limit states are discussed below.

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Figure 1: Joist Girder Framing to one side of the HSS

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Figure 2: Knife Plate Detail

Figure 3: Extended Joist Girder Top Chord

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Figure 4: Joist Girders Framing to both sides of the HSS

Design Requirements:

For brevity, this Manual is presented in LRFD format. ASD design procedures follow in a parallel nature. Before using the SPREADSHEET the user should perform a structural analysis to determine that the column has the available strength to resist the applied loads. The user should also have a working knowledge of the AISC connection design requirements.

Limits of Applicability- Single Joist Girders to HSS:

The AISC Specifications provide Limits of Applicability for the use of HSS connections. The following requirements must be met for the HSS. If they are not met for the member selected a different HSS must be selected. B/t or H/t 40 (B-3t)/t or (H-3t)/t 1.4SQRT (E/Fy)

Material Strength and HSS Thickness:

The strength of HSS connections not only depends on the yield strength and tensile strength of HSS, but it also depends on the design thickness of the shape and material type specified. For ASTM A500 and A501 the design thickness is 0.93

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times the nominal thickness. For ASTM A1065 and A1085 the design thickness may be taken as the nominal thickness. Shown in Table 1 are the common specifications for HSS.

American Manufacturing Standards for HSS

with Mechanical Properties of Common Grades

Product Specification Grade Fy, ksi Fu, ksi

Cold-formed HSS ASTM A500

B 46 62

C 50 62

Hot-formed HSS ASTM A501* B 50 70

Cold-formed HSS ASTM A1065 - 50 60

Cold-formed HSS ASTM A1085 - 50 65 *Not produced in North America

Table 1. Specifications for HSS

Other Specifications included in the SPREADSHEET are:

HSS with Mechanical Properties

Product Specification Grade Fy, ksi Fu, ksi

Hot-formed HSS ASTM A501 A 36 58

Hot-formed HSS ASTM A618 1 50 70

Hot-formed HSS ASTM A618 2 50 70

Hot-formed HSS ASTM A618 3 50 65

Cold-formed HSS ASTM A847 50 70

A. Knife Plate Connection:

The knife plate field weld is designed to resist the Joist Girder vertical reactions and the top chord axial forces. This design approach is used in the SPREADSHEET because the seat most likely will not fully bear on the cap plate due to roof pitch and seat fabrication tolerances. In many cases a gap will exist beneath the seat. Since the knife plate field weld has limited ductility transverse to its longitudinal axis the weld may crack, unless the Joist Girder seat has proper bearing. If the seat shimmed to provide good bearing one might be able to justify that only the top chord axial forces need to be resisted by the field weld; however, for uplift loads it is likely that the vertical reaction would only be resisted by the

field welds. The required strength of the weld connecting the top chord to the knife plate, and the required strength of the knife plate are determined from the vertical reaction, Ru and the axial force in the top chord of the Joist Girder(s), Pu = Mr/de. Mr is the required end moment of the Joist Girder and de is taken as the distance from the top of the Joist Girder to the half depth of the bottom chord leg. The Joist Girder Manufacturer has the responsibility to check the top chord angles for shear lag. The shear lag factor is calculated for the top chord based on the INPUT of the angle size and the Canadian Institute of Steel Construction Specification (CISC)*. Providing longer length fillet welds will reduce shear lag effects on the Joist Girders. *The AISC Specifications do not have a criterion for a single weld line.

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A 7/8 in. minimum thickness of the knife plate is recommended. The maximum thickness should not exceed 2.0 in. Cap plate extensions should not exceed 4 in.

When Joist Girders frame to both sides of a column, (Moment - Interior W Column), the continuity forces must be transferred through the knife plate. The effective net area of the knife plate for this condition is based on the Whitmore width.

A. TOP CHORD CONNECTION: 1. Shear lag Joist Girder Top Chord Case 2, AISC Manual Table D3.1

Joist Girder - Shear Lag

1x

U

where x =the distance from the weld line to the leg centroid.

= the length of the weld.

2. Weld Requirement between the Joist Girder Top Chord and the Knife Plate ( = 0.75)

Weld - Knife Plate to Joist Girder Top Chord The weld between the Joist Girder top chord and the knife plate is separated into two weld sizes and lengths in the SPREADSHEET. The weld length to resist the top chord axial forces is based on the total available weld length between the top chord and the knife plate.

The weld length for chord force, Ltc, equals one half of the HSS sidewall length plus the knife plate extension less the setback length.

Ltc = H/2 + Lkp - Stc (See SPREADSHEET for the variable designations).

Weld Design Strength = Ruh = (0.75)(0.707)(0.6)(FEXX)(wtc), kips/in. The weld length used to resist the vertical reaction is determined from a number of geometric parameters. To provide a symmetrical weld for the vertical shear, four limits are evaluated. Figure 5 illustrates these four geometric limits.

1) A length based on a 45 degree spread from the top of the HSS wall projected up to the top chord weld line.

2) Two times the distance from top chord setback to the center of the HSS wall. 3) Two times the length of the cap plate extension. 4) The leg length of the top chord.

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The least value of these four is used. The calculated effective weld length may be changed based on joist girder geometry at the discretion of the EOR/Specifying Professional.

Figure 5: Weld Length for Vertical Shear

Ruh = The Required Design Strength for the horizontal weld, kips/in. Ruv = The Required Design Strength for the vertical weld, kips/in. The Resultant Required Design Strength in the weld length for vertical shear, wtcr:

2 2

u uv uhR = R + R , kips / in.

3. Design Strength of the Knife Plate for Shear Yield ( = 1.0) Knife Plate - Shear Yield

Rn = (1.0)(0.6)(Fy)(tkp)(Lcp), kips where, Lcp = Rc + H + Lc

4. Design Strength of the Knife Plate for Shear Rupture ( = 0.75) Knife Plate - Shear Rupture

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Rn = (0.75)(0.6)(Fu)(t kp)(Lcp), kips, or

Rn = (0.75)(0.6)(Fu)(t kp)(Ltc), kips where, Lcp = Rc + H + Lc

5. Local Yielding of the Knife Plate at the HSS Walls ( = 0.9) Knife Plate - Yield (Local Yielding)

The vertical reactions are determined at the center line of HSS walls or at the center line of the wall reinforcing plate when present:

RL = Ph(Seat Depth + Column Cap Thickness)/H, kips RR = RL + Vertical Reaction, kips

The effective length, LL for yielding at the left side is taken as the minimum of:

a. Two times the cap plate thickness, or b. Two times the left cap plate extension beyond the HSS wall, or c. The HSS sidewall length divided by two.

Rn = FytkpLL , kips LL = minimum of: (2tcp, 2Lc, or H/2), in.

The effective length, LR for yielding at the right side is taken as the minimum of:

a. Two times the cap plate thickness, or b. Two times the right cap plate extension beyond the HSS wall, or c. The HSS sidewall length divided by two.

Rn = FytkpLR , kips LR = minimum of: (2tcp, 2Rc, or H/2), in.

6. Local Tensile Rupture of the Knife Plate at the HSS Walls ( = 0.75) Knife Plate - Tensile Rupture

For a CJP weld at the left side, Rn = (Fu)(tkp)(LL), kips

For a CJP weld at the right side, Rn = (Fu)(tkp)(LR), kips

For a PJP weld, Rn is based on the effective throat of the PJP weld:

Rn = (Fu)(tkp)(L)(Ecp)(2) , kips LL and LR are the same as for the local yielding check.

7. Buckling Strength of the Knife Plate ( = 0.9)

RL RR

Ph

Seat Depth

H

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Knife Plate - Left or Right Face Compression

Slenderness: kp

kp

2.1W 12KL / r =

t

, .kp kpwhere K = 2.1, L = W , in., r = t / 12 in

Pn = FcrAg, kips AISC E3-1 Ag = 2(tcp+tdes) tkp, in

2.

8. Weld Strength Knife Plate to Column Cap Plate ( = 0.75)

For CJP welds the strength is based on the base metal strength ( =1.0)

Rn = (1.0)(0.6)(Fy)(tkp)(Lcp), kips where, Lcp = Rc + H + Lc

For PJP welds the effective throat is taken as the minimum of the specified throat, Ecp or as (the thickness of the knife plate - 3/8)/2

Rn = (0.75)(0.6)FEXXE cp, kips/in.

9. Flexural Strength of the Cap Plate ( =0.9) Cap Plate - Horizontal Flexure Between Column Sidewalls

Rn = (0.9)FytcpL2cp/B, kips

10. Strength of the Cap Plate in Shear ( =1.0) Cap Plate - Shear Yielding

Rn = (1.0)(0.6)Fyt cpL cp, kips

11. Strength of the Weld Between the Cap Plate and the HSS Sidewall ( = 0.75) Shear Weld - Cap Plate to Column Sidewall

Weld Length, L = H - 4.5tnom, in. Minimum cap thickness, min. tcap = (0.6)(FEXX)(0.707)(w ccp)/[(0.6)(Fy)], in. Minimum wall thickness, min. tdes = (0.6)(FEXX)(0.707)(w ccp)/[(0.6)(Fu)], in.

Rn = (0.75)(0.707)(w ccp)(0.6)(70)(L)(2), kips

If the cap thickness, tcap is less than the minimum cap thickness, (min. tcap), Rn is reduced by the ratio of cap thickness divided by the minimum cap thickness. Likewise, if the wall thickness, tdes is less than the minimum wall thickness, (min.

tdes), Rn is reduced by the ratio of wall thickness divided by the minimum wall thickness.

12. Shear Strength of the HSS Column ( = 0.9)

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Column - Shear Yielding The AISC Specifications require that the nominal shear strength, Vn, of rectangular

HSS shall be determined using the provisions of AISC Section G5 ( = 0.9).

Vn = 0.6FyAwCv, kips AISC G2-1 where: Aw = 2htw, in.

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When w v y

h / t 1.10 k E / F Cv = 1.0 AISC G2-3

When v y w v y

1.10 k E / F < h / t 1.37 k E / F v y

v

w

1.10 k E / FC =

h / t AISC G2-4

When w v y

h / t >1.37 k E / F

vv 2

w y

1.51k EC =

h / t F

AISC G2-5

Note: There are no HSS that have w v y

h / t >1.37 k E / F

h = width resisting the shear force. If the corner radius is not known, h shall be taken as the corresponding outside dimension minus 3 times the thickness. t = design wall thickness, equals 0.93 times the nominal wall thickness for A500 and A501 material and equals the nominal wall thickness for A1065 and A1085 material. kv= 5

NOTE: If the HSS sidewalls do not have the available strength for shear it is generally more economical to select a column with thicker walls or one with longer walls.

13. Weld Strength Between the Cap Plate and Column Face or Bearing Plate ( =0.75) Weld - Cap Plate to Column Face or Bearing Plate The effective length, L, of weld is taken as the minimum of: [B - 4.5tnom, or 5(tcp) + tkp]

Rn = 1.5 (wccp)(L)(0.6)(FEXX)(0.707), kips

14. HSS Wall Yielding due to the Knife Plate Forces ( = 1.0) Column - HSS Wall Local Yielding

tkp

tcp

tdes

Yield and Crippling Area

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Rn = Fytdes[5tcp + tkp], when (5tcp + tkp) < B AISC K1-14a

Rn = FyBtdes when [5tcp +tkp] B AISC K1-14b

15. HSS Wall Crippling due to the Knife Plate Forces ( = 1.0) Column - HSS Wall Local Crippling

1.5

p2 bn y cp kp

p

t6l tR =1.6t 1+ EF ,when 5t + t < B

B t t AISC K1-15

For a single wall: Rn/2

If local yielding or local crippling values are exceeded, the thickness of the cap plate can often be increased to solve the problem. Alternatively a bearing plate can be added to the face of the column under the cap plate. When a bearing plate is used the SPREADSHEET only uses the strength of the bearing plate for compressive and tensile loads. This is due to the fact that the cap plate would not be welded to the HSS wall behind the bearing plate.

16. Tension Strength of the Knife Plate ( = 0.9) Knife Plate Continuity Force Yielding If the column is supporting Joist Girders from each side, the knife plate may also be subjected to tension stresses.

Rn = Fy A, kips A = (tkp)(Effective Plate Depth)

The effective plate depth is taken as the minimum of the height to the weld line (seat depth) or the depth based on the Whitmore width: {Wkp, or MIN[Left (Ltc), right (Ltc)]tan30

0}

The following limit states are examined when Bearing Plates are used:

17. Local Yielding of the Bearing Plate ( = 1.0) Bearing Plate - Local Yielding

If [5tcp +tkp] < B: Rn = (5tcp + tkp)Fytbp, kips

If [5tcp +tkp] > B: Rn = BFytbp, kips

18. Local Crippling of the Bearing Plate ( = 0.75) Bearing Plate - Local Crippling

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,

1.5

kp bp y cp2

n bp

cp bp

t t EF tR =1.6t 1+6 kips

B t t

19. Shear Yielding of the Bearing Plate ( = 1.0) Bearing Plate - Shear Yield

Rn = (2)(0.6)FytbpLbp, kips

20. Weld between the Bearing Plate and the Column Face ( = 0.75) Weld - Bearing Plate to Column

Rn = 2ELbp(0.6)FEXX, kips B. Bottom Chord, Stabilizer and HSS Wall Checks:

Bottom Chord Connection:

The bottom chord of the Joist Girder must be attached to the stabilizer plate to resist the same force as the top plate. In addition the stabilizer plate must transfer this same force to the column. Stabilizer plates are normally sized based on a 3/4 in. thickness of plate. Using a 3/4 in. plate allows the plate to fit between the bottom chord angles allowing fillet welds to be made to the heels and toes of the chord angles. For economy the stabilizer plates can usually be connected to the column using only fillet welds. If moment reversal exists the stabilizer plate must be welded to the column web to also resist a tensile force. The Specifying Professional must specify that the Joist Girder bottom chords be a minimum thickness to accommodate the required weld size. As is required for the top chord, the Joist Girder Manufacturer has the responsibility to check the bottom chord angles for shear lag. Case 2 from Table D3.1 is applicable for this check. For reference, the shear lag factor is calculated for the bottom chord based on the INPUT of the angle size. Shear lag factors greater than 0.92 do not have an effect on the Joist Girders. Providing longer length fillet welds will reduce shear lag effects. Stabilizer Checks:

1. Determine the weld between the bottom chord and the stabilizer ( = 0.75) Weld - Joist Girder Bottom Chord to Stabilizer Plate There are four welds:

Rn = (4)(1.392)D = kips/ in.

Required length = Pu/Rn, in.

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The weld length must be two times the bottom chord leg height to avoid a shear lag reduction for the stabilizer.

2. Stabilizer yielding ( =0.90). Stabilizer Plate Yielding

Pu Rn AISC D2-1

Rn = tshsFy, kips Where: ts = stabilizer thickness, hs = stabilizer effective width based on the Whitmore width (AISC Manual Section 9-3). If the bottom chord weld starts at the end of the stabilizer the Whitmore width equals (2)(tan30o)(Weld Length) + the bottom chord leg height.

3. Stabilizer block shear rupture strength ( = 0.75). AISC J4.3 Stabilizer Plate - Block Shear Rupture Strength

(a) Block shear plane 1: Rn = 0.60FuAnv + UbsFuAnt 0.60FyAgv + UbsFuAnt, kips Anv = net area subject to shear, in.

2 Ant = net area subject to tension, in.

2 Ubs = 1.0 (b) Block shear plane 2: Checked as in (a)

4. Weld strength between the stabilizer and the column

Weld - Stabilizer Plate to HSS Wall There are two welds:

Rn = (2)(1.392)D = kips/ in.

Required length = Pu/Rn, in. The SPREADSHEET uses the Joist Girder bottom chord forces to determine the weld requirements. Some designers prefer to provide enough weld to develop the full strength of the stabilizer. The directional weld strength increase is not allowed as indicated in AISC Equations K4-1, K4-2 and K4-3.

5. Joist Girder bottom chord shear lag factor Joist Girder - Shear Lag Case 2 AISC Table D3.1

1x

U

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HSS Wall Checks:

1. Strength of the HSS wall for the limit state of wall plastification ( =1.0) HSS - Plastification The stabilizer plate strength is limited by the yielding of the HSS wall due to the stabilizer pushing or pulling against the wall. This limit state is referred to as HSS Plastification. The strength is determined using AISC Eq.K1-12.

2F t t2ly pbR sin = + 4 1- Q

tn fB Bp

1-B

, kips AISC K1-12

tp = the stabilizer thickness (t st), in. lb = the stabilizer width (W st), in. B = the HSS wall dimension, in. t = the HSS design wall thickness, in.

sin=1.0 For HSS (connecting surface) in tension Qf = 1

For HSS (connecting surface) in compression, for longitudinal plate and longitudinal through plate connections:

f

2Q = 1- U AISC K1-17

P Mro ro

U= + , F A F Sc g c

AISC K1-6

The AISC Specification states that, Pro and Mro refer to required strengths in the HSS, where Pro and Mro are determined on the side of the joint that has the lower compression stress. The compressive stress used in the SPREADSHEET is calculated from the axial load, the bending from the Joist Girder moment, and the bending from the eccentric load on the stiffened seat.

Pro = Pu for LRFD; Pa for ASD. Mro = Mu for LRFD; Ma for ASD. Fc = Fy for LRFD, 0.6Fy for ASD

Note on Interior HSS Columns: Where Joist Girders frame to both sides of a column, all loads in a given load combination are conservatively considered additive, regardless of their sign for the calculation of the utilization ratio in Eq. K1-6. The stress is always assumed compressive. If the left and right bottom chord connections overlap the connection is treated as a cross-connection, and an additional sidewall crippling check is performed for load

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combinations when both bottom chord forces are compressive. The equation is identical to that for web compression buckling of wide flange members per AISC Eq. J10-8.

In many cases the walls will not have sufficient strength for the compressive or tensile forces delivered by the stabilizer. The strength can be increased by:

Increasing the HSS wall thickness.

Increasing the width of the stabilizer plate. When increasing the width of the stabilizer plate the length of the stabilizer may need to be increased (Whitmore width).

Adding a reinforcing side plate to the column face as shown in Figure 1.

Using a Through Plate (AISC Eq. K1-13) which doubles the strength.

The limit states of Sidewall Local Yielding and Sidewall Local Crippling technically apply; however, unless reinforcing plates are added to the HSS wall they will never control. See Wall Reinforcing below. Wall Reinforcing:

1. Strength of the reinforcing plate in flexure ( = 0.9) Reinforcing Plate - Thickness The reinforcing plate is analyzed as a simple beam with a span of B - tdes

Mr = PbcL/4 kip-in.

2M = F Z = F W t kip - inpl y y eff min

Mrt = in.

min F Wy eff

, .

The SPREADSHEET rounds tmin up to the nearest 1/8 in.; however the designer should select a plate with an available thickness.

2. Strength of the reinforcing plate in shear ( = 1.0) Reinforcing Plate - Shear Yield

Rn = (2)(0.6)FyWeff tmin kips AISC G2-1

3. Strength of flare bevel groove welds of the reinforcing plate to HSS

Flare - Bevel Groove Weld ( =0.8):

Effective throat = 5/8tdes, in. AISC Table J2.2

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Rn = (2)(0.6)(70)(5/8)(tdes)(Weff), kips

4. HSS Base Metal Strength ( = 0.90) HSS - Base Metal Strength

Rn = 2(Fy)(tdes)(Weff) kips

5. Local yielding strength of HSS sidewalls ( =1.0) Local Yielding of Chord Sidewalls

AISC local yielding of chord side walls, when = 1.0 and branch is in compression, for T- or Y-connections.

P sin = 2F t 5k +ly bn , kips AISC K2-9 where: lb = the reinforcing plate height = Wst, in. k = 1.5tdes, in.

6. Local crippling strength of HSS sidewalls ( = 0.75) Local crippling of Sidewalls

AISC local crippling of chord side walls, when = 1.0 and branch is in compression, for Plate-to Rectangular HSS.

2 bn y f

3lR =1.6t 1+ EF Q kips AISC K1-10

H- 3t,

lb = Weff, in.

f

UQ =1.3 - 0.4 1.3 - 0.4U

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COMMENTS ON SUMMARY RESULTS for MOMENT CONNECTION

TOP CHORD CONNECTION

Cell F74: A NG is shown if the setback is greater than one half of the HSS sidewall length minus 2 in. or if the setback is less than the negative value of one half of the HSS sidewall length minus the weld length between the Joist Girder top chord and the knife plate (Stc > H/2 2 in., or < -H/2 - Lcp). The 2 in. length is to ensure that the top chord extends over the column by a minimum of 2 in. Cell F75: A NG is shown if twice the top chord weld size plus 1/8 in. is greater than the gap between the Joist Girder chords, or if the concentrated weld length for the vertical shear plus 1/8 in. is greater than the gap (2wtc or wtc1) + 1/8 > gap. Cell F76: A NG is shown if the knife plate thickness is greater than the gap, or if the knife plate thickness is less than the gap minus 1/8 in. (tkp > gap, or tkp < (gap - 1/8 in.). Cell F77: A NG is shown if the knife plate extension is less than the right or left cap plate extension, or if Joist Girder weld length is less than the top chord leg angle size (Lkp < Rc or Ltc < Btc). Cell F78: A NG is shown if the right knife plate extension is less than the right cap plate extension, or if Joist Girder weld length is less than the bearing plate thickness plus the cap plate weld plus in. (Rc < tbp + wccp + in.) Cell F79: A NG is shown if the left knife plate extension is less than the left cap plate extension, or if Joist Girder weld length is less than the bearing plate thickness plus the cap plate weld plus in. (Lc < tbp + wccp + in.). Cell F80: A NG is shown if the PJP weld, Ecp, between the knife plate and the column cap plate violates the values shown in AISC Table J2.3.

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EXAMPLE:

Given: HSS: Material A500 Joist Girder Data (Factored Loads): 12X12X1/2 in. M = 183 kip-ft. = 2196 kip-in. (tension in top chord) Fy = 46 ksi Pv = 100 kips. Fu = 58 ksi Ph = 64.6 kips tdes =0.465 Joist Girder Depth = 36 in. A = 20.9 in2 Chord Angles 4x4x1/4 S = 76.2 in3 gap = 1.375 in Cap Plate t = 1.5 in. Knife Plate: 1.25x7.5x16.5 in. (Fy = 50 ksi) Stabilizer Plate: 3/4x8x10 in. All other plates A36 The cap plate is detailed to project 3 in. from the right face of the column and 1 in. from the left face. The 4 in. projection is the maximum that should be used, as a greater projection will cause the Joist Girder manufacturer to provide a seat height greater than 7.5 inches to have the vertical reaction centered over the column wall. Check Limits of Applicability for the HSS 12X12X1/2 in. B/t or H/t 40, 12/0.465 = 25.8 40 ok (B-3t)/t or (H-3t)/t 1.4SQRT (E/Fy), [12-(3)(0.465)]/0.465 = 10.6 1.4SQRT(29000/46) 10.6 35.2 ok. A. TOP CHORD CONNECTION: 1. Shear lag Joist Girder Top Chord

Joist Girder - Shear Lag

1 09

1 1 0 878 5

x .U .

.

where x =the distance from the weld line to the leg centroid = 1.09 in.

= the length of the weld = 8.5 in.

2. Weld Requirement between the Joist Girder Top Chord and the Knife Plate ( = 0.75)

Weld- Knife Plate to Joist Girder Top Chord

Effective length for vertical shear = 4.0 in. (4 in. chords) Effective weld length for chord force = Ltc = H/2 + Lkp - Stc = 6 + 3 - 0.5 = 8.5 in.

Design Strength (chord force) = Rn = (0.75)(0.707)(0.6)(70)(0.3125) = 6.96 kips/in.

Design Strength (shear) = Rn = (0.75)(0.707)(0.6)(70)(0.625) = 13.92 kips/in. Horizontal Weld, Ruh = Pu/Ltc = 64.6/[(2)(8.5)] = 3.80 kips/in. Vertical Weld, Ruv = Ru/4 = 100/[(2)(4)] = 12.5 kips/in.

Resultant weld: 2 2 2 2

u uv uhR = R + R = 12 50 + 3 80 =13.06 kips / in.. .

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JG Horizontal Ratio: Ruh/Rn = 3.8/6.96 = 0.546 ok

JG Vertical Ratio Ruv/Rn = 13.06/13.92 = 0.938 ok Use 5/8 in. fillet welds in reinforced area. Note the stabilizer plate must be 1.25 in. thick.

3. Design Strength of the Knife Plate for Shear Yield ( = 1.0) Knife Plate - Shear Yield

Rn = (0.6)(Fy)(tkp)(Lcp), Lcp = Rc + H + Lc, Lcp = 3.0 + 12 + 1.0 = 16 in. Rn = (0.6)(50)(1.25)(16) = 600.0 kips

Rn = (1.0)(600) = 600.0 kips

Shear Yielding = Ru/Rn = 64.6/600 = 0.108 ok

4. Design Strength of the Knife Plate for Shear Rupture ( = 0.75) Knife Plate - Shear Rupture

Rn = (0.6)(Fu)(tkp)(Lcp) = (0.6)(65)(1.25)(16.5) = 804.4 kips, or Rn = (0.75)(0.6)(Fu)(t kp)(Ltc) = (0.6)(65)(1.25)(8.5) = 414.4 kips where, Lcp = Rc + H + Lc = 3.0 + 12 + 1.5 = 16.5 in.

Rn = (0.75)(414.4) = 310.8 kips

Shear Rupture = Ru/Rn = 64.6/310.8 = 0.208 ok

5. Local Yielding of the Knife Plate at the HSS Walls ( = 0.9) Knife Plate - Yield (Local Yielding)

Determine vertical reactions on center line of HSS walls:

Thickness of cap plate = 1.5 in.

RL = (64.6)(7.5 + 1.5)/(12.0 0.465) = 50.39 kips RR = 50.4 + 100 = 150.39 kips Left Face Effective Length, L (no reinforcing plate): L = MIN(2tcp, 2Lc, H/2) = MIN( 3.0, 2.0, 6.0) = 2.0 in. Rn = FytkpL = (50)(1.25)(2.0) = 125.0 kips

Rn = (0.9)(125) = 112.5 kips

Ru/Rn = 50.39/112.5 = 0.448 ok Right Face Effective Length, L (no reinforcing plate):

RL RR

64.6 kips

7.5"

21

L = MIN(2tcp, 2Rc, H/2) = MIN( 3.0, 6.0, 6.0) = 3.0 in. Rn = FytkpL = (50)(1.25)(3.0) = 187.5 kips

Rn = (0.9)(187.5) = 168.8 kips

Ru/Rn = 150.39/187.5 = 0.891 ok

6. Local Tensile Rupture of the Knife Plate at the HSS Walls ( = 0.75) Knife Plate - Tensile Rupture

For CJP weld for left face: Rn = (Fu)(tkp)(Lc) = (65)(1.25)(2.0) = 162.5 kips

Rn = (0.75)(162.5) = 121.9 kips

Shear Yielding controls, Ru/Rn = 0.448 ok For CJP weld for right face: Rn = (Fu)(tkp)(Rc) = (65)(1.25)(3.0) = 243.8kips

Rn = (0.75)(243.8) = 182.8 kips

Shear Yielding controls: Ru/Rn = 0.891 ok

7. Buckling Strength of the Knife Plate ( = 0.9) Knife Plate - Right Face Compression

Slenderness: kp

kp

2.1w 12 2.1 7.5 12KL / r = = = 43.65

t 1.25

Ag = (2tcp+tdes)tkp = [(2)(1.5) +0.465]1.25 = 4.33 in2.

Using the AISC Column Equations with =0.9, Rn = Pn = 169.6 kips

Ru/Rn = 100.0/169.6 = 0.590 ok 8. Weld Strength Knife Plate to Column Cap Plate

Since a CJP weld was specified no calculation is required. If a PJP weld was specified for the 1.25 in. thick knife plate the Effective Throat of the weld would be, E = MIN[Ecp, (tkp - 3/8)/2 ] = 0.4375 in. The required force is determined from the square root of the sum of the squares of the applied forces.

Weld Strength: Rn = (0.75)(0.6)FEXXE = (0.75)(0.6)(70)(0.4375) = 13.78 kips/in. Horizontal Force = 64.6/(2Lc) = 64.6/[(2)(16.5)] = 1.875 kips/in Vertical Force = 150.39/[(2- welds)(2)(Minimum of tcp, Rc - tbp,H/2)] Vertical Force = 150.39/[(2)(2)(1.5)] = 25.065 kips/in. Resultant Force = 25.14 kips/in

Ru/Rn = 25.14/13.78 = 1.82 ng, thus a CJP is required.

9. Flexural Strength of the Cap Plate ( =0.9) Cap Plate - Horizontal Flexure between Column Sidewalls

22

Rn = FytcpL

2cp/B = 36)(1.5)(16)

2/12 = 1152.0 kips

Rn = (0.9)(1152.0) = 1036.8 kips

Rn/Rn = 64.6/1036.8 = 0.062

10. Strength of the Cap Plate in Shear ( =1.0) Cap Plate - Shear Yielding

Rn = (0.6)FytcpLcp = (0.6)(36)(1.5)(16) = 518.4 kips

Rn = (1.0)(518.4) = 518.4 kips

11. Strength of the Weld Between the Cap Plate and the HSS Sidewall ( = 0.75) Shear Weld - Cap Plate to Column Sidewall

Weld Length, L = H - 4.5tnom = 12 - (4.5)(0.5) = 9.75 in. Min. tcap = (0.6)(FEXX)(0.707)(wccp)/[(0.6)(Fu) = (0.6)(70)(0.707)(0.3125)/[(0.6)(58) = 0.266 in. Min. tdes = (0.6)(FEXX)(0.707)(wccp)/[(0.6)(Fu) = (0.6)(70)(0.707)(0.3125)/[(0.6)(58) = 0.266 in. Rn = (0.707)(wccp)(0.6)(70)(L)(2) = (0.707)(0.3125)(0.6)(70)(9.75)(2) = 180.9 kips

Rn = (0.75)(180.9) = 135.7 kips

Rn/Rn = 64.6/135.7 = 0.476 ok

12. Shear Strength of the HSS Column ( = 0.9) Column - Shear Yielding

h/tdes = (12.0 - 3tdes)/tdes = 10.60/0.465 = 22.8 Aw = 2htdes = (2)[(12.0 - (3)(0.465)](0.465) = 9.86 in

2

When des v yh / t 1.10 k E / F =1.10 (5)29000 / 46 = 61.8 Cv = 1.0 Vn = 0.6FyAwCv =(0.6)(46)(9.86)(1.0) = 272.1 kips

Vn = (0.9)(272.1) = 245 kips

Ru/Vn = 64.6/245 = 0.264 ok

13. Weld Strength Between the Cap Plate and Column Wall or Bearing Plate ( =0.75) Weld - Cap Plate to Column Face or Bearing Plate

Effective Length = L = MIN (B - 4.5tnom, 5(tcp) + tkp) = MIN[12 - 4.5(0.500) = 9.75 in., (5)(1.5) + 1.25 = 8.75 in,] = 8.75 in. Rn = 1.5 (wccp)(L)(0.6)(E70)(0.707) = (1.5)(0.3125)(8.75)(0.6)(70)(0.707) = 121.8 kips

Rn = (0.75)(121.8) = 91.4 kips

Ru/Rn = 50.4/91.4 = 0.552 ok

14. HSS Wall Yielding due to the Knife Plate Forces ( = 1.0) Column - HSS Wall Local Yielding

23

Rn = Fytdes[5tcp + tkp], when (5tcp + tkp) < B AISC K1-14a Rn = FyBtdes when [5tcp +tkp] B AISC K1-14b (5tcp + tkp) = 5(1.5) + 1.25 = 8.75 < 12

Rn = (1.0)(46)(0.465)(8.75) = 187.2 kips

Ru/Rn = 50.39/187.2 = 0.269 ok

15. HSS Wall Crippling due to the Knife Plate Forces ( = 1.0) Column - HSS Wall Local Crippling

. . .

. . .

1.5

p2 bn y cp kp

p

1.52

n

t6l tR =1.6t 1+ EF ,when 5t + t < B

B t t

6 125 0465 15R = 1.6 0465 1+ 29000 46 = 725.8 kips

12 15 0465

For one wall: Rn = 397.5 kips, Rn = (0.75)(397.5) = 298.2 kips

Ru/Rn = 150.39/298.2 = 0.504 Yielding controls.

B. Bottom Chord, Stabilizer and HSS Wall Checks:

1. Strength of the HSS wall for the limit state of wall plastification ( =1.0) HSS - Plastification:

The strength is determined using AISC Eq.K1-12, =1.0.

tkp

tcp

tdes

Yield and Crippling Area

24

des

2F t t2ly pbR sin = + 4 1- Q , kips AISC K1-12

tn fB Bp

1-B

BHbcM = Top Chord Force d - +R - t

ro u2 2

4 12 0.465 = 64.6 36 - +100 - = 27

2 2 2

f

73 kip - in.

P Mro ro 100 2773

U= + = + = 0.895 AISC K1- 6F A F S 46 20.9 46 76.2c g c

22Q = 1-U = 1- 0.895 = 0.446 AISC K1-12

246 0.465 2

R =0.75n

1-12

8 0.75+ 4 1- 0.446 R = 32.47kips

n12 12

Since Rn 64.6 kips wall reinforcement is necessary. Add a wall reinforcing plate tminx8x12 in.

Use flare bevel welds to the HSS wall

1. Strength of the reinforcing plate in flexure ( = 0.9) Reinforcing Plate - Thickness The reinforcing plate is analyzed as a simple beam with a span of B - tdes = 12.0 - 0.465 = 11.54 in. Mr = PbcL/4 = 64.6(11.54)/4 = 186.4 kip-in.

20.9 36 8 t2 2minM = F Z = F W t = = 64.8t kip - in

pl y y eff min min4

M 186.3rt = = = 1.70 in.min 64.8 64.8

, .

Rounded up tmin = 1.75 in.

Use tplate = 1.75 in.

25

2. Strength of the reinforcing plate in shear ( = 1.0) Reinforcing Plate - Shear Yield

Rn = (2)(0.6)FyWefftplate = (1.0)(2)(0.6)(36)(8)(1.75) = 604.8 kips 64.6 kips ok

3. Strength of flare bevel groove welds of the reinforcing plate to HSS

Flare - Bevel Grove Weld ( = 0.8) Effective throat = 5/8tdes, in. Rn = (2)(0.6)(70)(5/8)(tdes)(Weff) = (2)(0.6)(70)(5/8)(0.465)(8) = 195.3 kips

Rn = (0.8)(195.3) = 156.2 kips 64.6 kips ok

4. HSS Base Metal Strength ( = 0.90) HSS - Base Metal Strength

Rn = 2(Fy)(tdes)(Weff) = (0.9)(2)(46)(0.465)(8) = 308 kips 64.6 kips ok

5. Local yielding strength of HSS sidewalls ( =1.0) HSS - Sidewall Local Yielding

AISC local yielding of chord side walls, when = 1.0 and branch is in compression, for T- or Y-connections.

. . . P sin = 2F t 5k +ly bn 2 46 0 465 5 1 5 0 465 8 491 kips Pn = 491 kips 64.6 kips ok.

6. Local crippling strength of HSS sidewalls ( = 0.75) HSS - Sidewall Local Crippling

AISC local crippling of chord side walls, when = 1.0 and branch is in compression, for Plate-to Rectangular HSS.

2 bn y f

2

3lR = 1.6t 1+ EF Q

H - 3t

3 8.0 = 1.6 0.465 1+ 29000 46 0.905 = 1,179 kips

12 - 3 0.465

lb = Weff = 8.0

fU

Q =1.3 - 0.4 1.3 - 0.4 0.987 = 0.905

From the previous calculation:

26

.

P Mro ro

U= + 0 987F A F Sc g c

Rn = 884 kips > 64.6 kips ok.

Bottom Chord Checks: 1. Determine the weld between the bottom chord and the stabilizer

Weld - Joist Girder Bottom Chord to Stabilizer Plate

Try 3/16 in. fillet welds: Rn = (4)(1.392)(3) = 16.7 kips/ in. Required length = 64.6/16.7 = 3.9 in. The welds must be 8 in. long (2 times the bottom chord leg height) to avoid a shear lag reduction for the stabilizer. Use 4-3/16 in. fillet welds 8 in. long

Rn = 16.7(8) = 133.6 kips

The Specifying Professional must request that the Joist Girder bottom chords be a minimum of 1/4 in. thickness to accommodate the required weld size.

2. Check stabilizer yielding ( =0.90) Stabilizer Plate - Yielding

Rn = tshsFy, kips Where: ts = stabilizer thickness, hs = stabilizer effective width (Whitmore width). Check the Whitmore width for stabilizer: Assuming the bottom chord weld starts at the end of the stabilizer the Whitmore length equals (2)(tan30o)(8) = 9.24 in. plus the bottom chord leg length. Thus the Whitmore width = 9.24 + 4 = 13.24 in. > 8 in. ok Effective width = 8.0 in.

Rn = (0.9)(3/4)(8)(36) = 194.4 kips > 64.6 kips ok

3. Check stabilizer block shear rupture strength ( = 0.75) Stabilizer Plate - Block Shear Rupture Strength These calculations are shown only as an example. They are not applicable for the load case given since the bottom chord is in compression.

Block shear plane 1:

27

Rn = 0.60FuAnv + UbsFuAnt 0.60FyAgv + UbsFuAnt, kips Anv = Agv = (2)(8)(0.75) = 12 in.

2 Ant = (4)(0.75) = 3.0 in.

2 Rn = (0.60)(58)(12) + (1.0)(58)(3.0) (0.6)(36)(12) + (1.0)(58)(3.0) = 542 433 kips, Rn =433 kips Block shear plane 2: Anv = Agv = (8)(0.75) = 6.0 in

2

Ant = [Angle leg length + (Wst - Angle leg length)/2]tst =[4 + (8 - 4)/2](0.75) = 4.5 in2

Rn = (0.60)(58)(6.0)+(1.0)(58)(4.5) (0.6)(36)(6.0)+(1.0)(58)(4.5) = 470 391 kips, Rn =391 kips

Rn = (0.75)(391) = 294 64.6 kips ok 4. Determine the weld between the stabilizer and the column

Weld - Stabilizer Plate to Column

The weld force per inch equals 64.6/16 = 4.04 kips/in.

Try 1/4 in. fillet welds: Rn = (1.392)(4) = 5.57 kips/ in. > 4.04 kips ok Use 2-1/4 in. fillet welds 8 in. long

5. Joist Girder bottom chord shear lag factor Joist Girder - Shear Lag Case 2 AISC Table D3.1

1 08

1 1 0 868

x .U .

28

PROGRAM USAGE GUIDE Joist Girder Connections to HSS Columns- Knife Plates

SPREADSHEET Philosophy:

The SPREADSHEET is structured to allow the user to input all data rather than forcing

computer generated values. This allows the user to select values or to use office

standards. This is especially useful when a multitude of designs are being considered

so that calculations can be provided for lumping common values.

SPREADSHEET Description: The SPREADSHEET has seven sheet tabs consisting of General Information,

Formatting, Sidewall HSS Column Diagram, Moment Sidewall HSS Column, Interior

HSS Column Diagram, Moment Interior HSS Column, and AISC Database v14.

General Information List of design references, explanation of LFRD and

ASD color coding.

Formatting Information on the printing formatting setup for the

SPREADSHEET.

Sidewall HSS Column Diagram A diagram of the connection being

designed for a Joist Girder to a sidewall HSS column (with nomenclature).

Moment-Sidewall HSS Column Design input and output sheet for the

moment connection for a Joist Girder to a sidewall HSS column.

Interior HSS Column Diagram A diagram of the connection being

designed for Joist Girder to an interior HSS column (with nomenclature).

Moment-Interior HSS Column Design Input and Output sheet for the

moment connection for two Joist Girders to an interior HSS column.

AISC Database v14 AISC shape data for use in the connection design.

The actual design input and output sheets have been formatted to print all required

information for the design calculations of the connections.

SPREADSHEET Usage:

Before using the SPREADSHEET you should have in your possession: 1. The Steel Joist Institutes Technical Digest 11, Design of Lateral Load Resisting

Frames Using Steel Joists and Joist Girders. 2. ANSI/AISC 360 -10, Specification for Structural Steel Buildings. 3. The Steel Joist Institutes Standard Specification for Joist Girders, 2010. 4. Frame analysis results, such as Joist Girder end reactions, connection moments,

and column axial loads.

First read the General Information Tab and the Formatting Tab.

29

Print out the diagrams: Sidewall HSS Column Diagram and the Interior HSS Column

Diagram. These will assist you with input requirements. For proper printing of the

SPREADSHEET you may have to reset the margins.

Joist Girder Data:

Typically at the early stage of the design the actual Joist Girder design is not known by

the user. The user can either estimate the Joist Girder chords, weights and seat sizes,

or they can contact a SJI member company for the information. If the Joist Girder data

is unknown the following information can be estimated:

The chord sizes can be estimated as described in Chapter 2 of the SJI Technical Digest 11.

The Joist Girder weight can be estimated using the SJI tabulated values in the published catalog, or by multiplying the chord weight by 2.5. See the PRELIMINARY SIZING EXAMPLE.

The seat size can be estimated using the standards set forth by SJI Standard Code of practice suggested sizes based on Joist Girder weight.

Knife Plate Preliminary Sizing:

The initial thickness of the knife plate, W tp, should be taken as 7/8 in. The maximum

thickness should not exceed 2.0 in.

Stabilizer Plate Preliminary Sizing:

An initial thickness of the stabilizer plate, t st, is based on the 1 in. standard gap between

the Joist Girder chord angles. Typically a 3/4 in. thickness is used to allow tolerance for

field erection and still allow for fillet welds from the chord angles to the plate.

The width of the stabilizer plate (W st) is estimated by dividing the required axial force by

the thickness of the stabilizer plate and Fy (LRFD) or 0.6Fy (ASD). The stabilizer width

must be a minimum of the chord angle leg size plus the weld shelf dimensions.

Minimum Weld Shelf Dimensions

Field Weld Size, in. Minimum Shelf Dimension, in

3/16 7/16

1/4 1/2

5/16 9/16

3/8 5/8

7/16 11/16

1/2 3/4

Table 1 Minimum Weld Shelf Dimensions

30

INPUT:

Use the Tabs to select a Moment- Sidewall HSS Column Design, or a Moment-

Interior HSS Column Design. If an interior column only has one side with a moment

connection, use the Moment-Sidewall HSS Column Tab.

All yellow filled cells are required input.

There are two pull down Tabs, one used to select whether you want an LRFD or an

ASD Design and the second to choose the size of the HSS column for the design.

The CLEAR buttons can be used to clear all of the input cells in the group. There is

one button for connection input and one for the loading input. This CLEAR button does

not clear the project information, i.e., project name, number or engineer.

COLUMN DATA:

The ASTM designation for the HSS being used must be specified since it affects the

material thickness of the HSS. Column data is automatically obtained from a file of the

AISC HSS-Shapes after using the drop down tab, or by typing in the column size.

JOIST GIRDER TOP CHORD WELD:

The user of the SPREADSHEET has the option to increase or decrease the length of

weld (Ltcr) used in the SPREADSHEET. An INPUT value of zero should be entered in

Cell J19 if the user accepts the SPREADSHEET calculated value.

JOIST GIRDER DATA:

For preliminary design, if the Joist Girder properties are not known, the chord sizes can

be estimated as described in Chapter 2 of the SJI Technical Digest 11. If you have

conducted your analysis using the SJI Virtual Joist Girder Tables, you can also obtain

the Joist Girder weight from your analysis.

JOIST GIRDER & COLUMN DESIGN LOAD DATA: Fill in the values indicated in the Table. Values must be consistent with the type of

design you have selected, i.e. LRFD or ASD. Up to six load cases are permitted per

design. The column axial load is the total axial load on the column and must include the

reaction(s) of the Joist Girder(s).

REMARKS INDICATED ON THE INPUT DATA: (1) Includes Joist Girder end reactions:

The Column Axial Load, Pu (LRFD) or Pa (ASD), is to include the end reaction(s) of the Joist Girder(s). DESIGN REVIEW:

31

Examine the SUMMARY RESULTS for MOMENT CONNECTION to determine if the design criteria are satisfied, or if undo conservatism exists relative to any of the input data. The DETAILED RESULTS for MOMENT CONNECTION provides minimum design criteria, the nominal strength, and the Design Strength (LRFD) or the Allowable Strength (ASD) for the input data. These values can be studied to determine input refinements. You can then make any necessary input changes. PRELIMINARY SIZING EXAMPLE: For a 48G8N18F Joist Girder spanning 40 ft., with an end moment of 500 kip-ft. and an

end reaction of 100 kips estimate the chord size.

Assume a stabilizer width (W st) of 6 in. , Pchord = (12)(500)/(48-3) = 133 kips

From TD 11 Table 2-1 (LRFD), Fy = 50 ksi, = 0.90).

The table yields a chord angle size of 3 x 3 x 5/16.

Estimate the Joist Girder weight: From the SJI Catalog 47 plf.

From the chord size, the Joist Girder weight = (2.5)(3.4)(4.21) = 36 plf

So conservatively assume the Joist Girder weight = 47 plf

Preliminary Stabilizer Plate size: t st = 3/4 in. for a 1 in. gap between chords W st = (133)/[(0.75)(0.9)(36)] [3.5+(2)(9/16)] = 5.47 4.63, Use a 6 in. plate

Angle Size Unbraced Length Area

L = 5 ft. in.2

2L 4 x 4 x 3/4 406 10.9

2L 4 x 4 x 5/8 345 9.21

2L 4 x 4 x 1/2 281 7.49

2L 4 x 4 x 7/16 249 6.61

2L 4 x 4 x 3/8 211 5.71

2L 4 x 4 x 5/16 143 4.80

2L 4 x 4 x 1/4 92 3.87

2L 3-1/2 x 3-1/2 x 1/2 231 6.53

2L 3-1/2 x 3-1/2 x 7/16 205 5.77

2L 3-1/2 x 3-1/2 x 3/8 178 5.50

2L 3-1/2 x 3-1/2 x 5/16 139 4.21

2L 3-1/2 x 3-1/2 x 1/4 92 3.41