SCI Connections

Connection rules in cellular beams

P:\CMP\CMP703\21715^Connection rules in cellular beams.doc 3

A. DETAILED RULES FOR CONNECTION DESIGN IN CELLULAR BEAMS

Currently, software for the design of cellular beams does not consider the connection details and their effect on forces in the end web-post. This is because it is normally the responsibility of the fabricator to design the connections (which are unknown when the beam is designed).

It is good practice to ensure that the end web-post is at least half of the width of the internal web-post, but this may not be sufficient in all cases, depending on the form of the connection. Two alternative forms of connections are illustrated in Figure 1:

a. Beam to beam connections using a bolted cleat (or a welded fin plate).

b. Beam to column connections using a welded end plate.

In the first case, the flange is notched, which has the effect of:

• Increasing the instability of the web in compression.

• Reducing the longitudinal shear transfer into the beam.

• Reducing the Vierendeel bending resistance of the top Tee.

In the second case, the welded end plate has the effect of:

• Maintaining the Vierendeel bending resistance around the opening.

• Increasing the horizontal shear resistance of the end web-post.

• Developing a nominal moment which reduces the compression force in the top Tee.

Clearly, the difference between the behaviour of the end web-post in the two cases can be considerable and the end plate provides a more efficient connection. In Figure 1(a), the critical design checks are:

• The compression force in the web at the point where the flange is notched.

• The horizontal shear stress in the web-post.

For primary cellular beams, incoming secondary beams cause additional stresses in the web, depending on the form of the connections. The design cases, as illustrated in Figure 2, are:

a. Beam to beam connection using a notched secondary beam welded end plate.

b. Beam to beam connection using a welded fin plate.

The critical design condition for the primary beam is web-post buckling when the narrow web-post is subject to local forces from the connection and combined with the transfer of local forces due to the openings.



φ

θ

Δ − Δ

Δ

S Se o

(a) Cleated connection

τ H

Δ − Δ

S

o

e

τ H

θ = 45°

σ

(b) End plate connection

0.5 d

c

0.5 d

σ

oeff

eff

Ds

Δ

Δ

Δ

C

T C

V

Vhe Vh

T

d

C

T C

Vh

V

Vhe

T

d

dn

x b 0.5 ddθ

θd

Figure 1 Forces in end web-post for two connection types



(a) Cleated Connection with a Notched Beam For a notched beam, it may be assumed that insufficient composite action is developed at the centre of the first cell and so equilibrium of the first cell in Figure 1(a) leads to the following tensile force in the bottom Tee as given by:

ΔT = (0.5 do + se – xb) V/deff

and Vhe =ΔT

where do = opening diameter se = end web-post width xb = distance of line of bolts from the end of the beam deff = effective beam depth between centre of tees V = applied shear force

ΔT = tension force in bottom Tee at first cell

At the line of bolts, the horizontal shear stress in the end post is:

τH = ( ) y

e

he 6.0 pts

V≤

− φ

where: φ = bolt diameter

t = web thickness

The compressive stress σ acting in the notched web may be established by considering moment equilibrium about the centre-line of the opening. It is assumed that the shear force V is distributed equally between the Tees, and the equilibrium is satisfied by:

0.5V (0.5 do + se – xb) = σ t do × 0.5( do + dθ)

where dθ is the length of the notched web at angle θ

and dθ = on 5.0

cos

5.0d

dh−

−

θ

d is the beam depth dn is the depth of the notch c is the length of the notch

The critical angle is at the end of the notch and is given by:

tanθ = eff

eo )(2

d

csd −+

The compressive stress, Φ, acting on the web of the end-post is established from equilibrium of the notched web as:

( )( )( )( )

( ) θ

θσ

220

2n

2obeo

o cos2

cos22

ddd

dhxsd

tdhV

−−

−−+×

−=

σ = τ v × Factor



where τ v is the vertical shear stress acting on the perforated section

and Factor represents the local stress increase due to the notch.

The maximum value of σ is dependent on buckling of the web that is partially restrained by the connection of the beam to the slab. As an approximation, consider an effective length of the notched web as equal to the length of the notch, c. It follows that the slenderness of the web is:

λe = 3.46 c/t

The compressive strength of the end post, σc is determined using 8e from buckling curve c of EC3-1-1 or BS 5950-1, and it follows that for an acceptable design, σ ≤ σe. Instability may be ignored when c ≤ 8t and in this case, σ = py.

Cleated or fin-plate connections may be problematical when c ≥ 0.7 se or when se < 0.5 so.

Example : Cleated connection to a notched beam V = 300 kN for a typical 15 m span secondary beam at 3 m spacing.

d = 660 mm deff = 600 mm do = 450 mm se = 120 mm c = 150 mm dn = 30 mm t = 10 mm xb = 50 mm φ = 22 mm S 355 steel

( )VVVT 54.0

600

501504505.0h,e =

−+×==Δ

τ H = ( )

VV 42.01022150

100054.0=

×−

×

For V = 300 kN, τ H = 126 N/mm2 < 0.6 py = 213 N/mm2

Unity Factor in horizontal shear = 0.59

tanθ = ( )600

1501202450 −+ = 0.65 θ = 33o

Factor = ( )( )( )( ) 222

2

84.0450302660

84.04506605012024502

×−×−

×−−+

Factor = 0.8

τ v = ( )45066010

10300 3

−×

× = 143 N/mm2

σ = 0.8 × 143 = 114 N/mm2

λ = 3.46 × 150/10 = 52 σ pa = 270 N/mm2 for buckling curve C of BS 5950-1

Unity factor in web buckling = 114/270 = 0.42.



(b) Welded End Plate Connection A welded end plate permits rapid development of composite action in the slab so that equilibrium of the first cell in Figure 1(b) is given by:

ΔT = [V (0.5 do + se ) – )C (Ds + yt)]/deff

where: ΔC is the compression force developed in the slab over (0.5 do + xe) Ds is the depth of the slab yt is the depth of the elastic centroid of the top tee below the top flange and Vhe = ΔT

Allowing a nominal increase in the shear resistance of the end-post due to the thickness of the end plate, the horizontal shear stress is:

τH = ( ) y

ee

he 6.0 ptts

V≤

+

where te is the thickness of the end plate

The compressive stress, σ, acting on the web may be considered to be part of the Vierendeel bending check at the first cell. Conservatively, the previous analysis for a notched beam may be repeated by setting dn = 0. No buckling check is required because of the stabilising effect of the end plate and adjacent flange, in which case σ ≤ py.

In general, end plate connections may be shown to be acceptable when se ∃ 0.5 so, and no further checks on the end web-post are required.

(c) Secondary Beam-Primary Beam Connections at Web-Post

Connections of incoming secondary beams also affect the design of the web-post of the supporting primary beam. Two cases are illustrated in Figure 2. They may be treated in a similar manner by defining the position of centre of the connection below the top flange. For end plate connections in Figure 2(a), the horizontal distance between the bolts may be included (default of 90 mm).

The dispersion angle of the compression force, Pc, from the centre of the connection is taken as 45o. The effective width of the web-post in compression is then dependent on the projection to the centre-line of the web, as follows:

bwp = so for non-infilled openings bwp = 2 (d/2 – y conn) for infilled openings

or

where:

d = web depth so = width of web-post y conn = centre of connection below top flange The compressive stress in the web-post due to the force Pa is:



σp = Pc/(bwpt)

The slenderness of the web for web buckling under a concentrated load is defined as 0.7 × depth of web below the centre of the connection, as follows:

λc = 2.5 dwp/t

where:

dwp = d – y com

The thickness of the web is taken as the average of the top and bottom Tees unless the connection extends below the centre-centre line of the opening in which case the web thickness of the bottom Tee may be used.



(a) Welded end plate

Vh

Pc

wp

45°

End plate

dwp

d o

Dispersion

Vh

Pc

b wp

45°

d odwp

Fin plate

(b) Welded fin plate

s

s

o

o

y

y

conn

conn

b

60 mm min.

Figure 2 Connection of secondary beams to web-post

The compressive strength of the web-post, σc, for this slenderness is defined using buckling curve c of BS 5950-1 or EC3-1-1. The combined effect of compression and web-post buckling due to shear is included by reducing the Unity Factor for web-post buckling according to:

UFweb-post + σp/σc ≤ 1.0



This maximum Unity Factor is then used to check against the results of Cellbeam 5 for web-post buckling. The horizontal shear resistance is largely unaffected by combined shear and compression.

If this check is not satisfied, the compressive strength of the web-post may be increased locally by one of the following measures:

• Half or full infills adjacent to the connection.

• Ring stiffener in the adjacent openings.

• Vertical stiffener extending at least d/2 from the top flange.

• Deeper end plate extending at least d/2 from the top flange.

Generally, one of these measures will be required and, for scheme design, it is suggested that UFweb-post ≤ 0.7 for design at the secondary beam connections.



B. SIMPLIFIED RULES FOR CONNECTION DESIGN IN CELLULAR BEAMS Maximum available factored loads for limiting conditions

Notes:1. The tables below have been developed from a parametric assessment of the SCI design proposals for notched connections2. It is assumed that the opening is of maximum diameter for the given beam depth 3. It is assumed that the internal spacing of the openings is limited to the minimum permissable4. The web has been assumed to be a nominal thickness of 12.5mm (This should represent a conservative value)5. The elastic neutral axis has been assumed to be 2/3 depth of the flange (This should represent a conservative estimate)6. The limiting scenario is assumed when notch depth and length are maximum for an end post length of S0/27. Table 1 represents the Westok proposals, Table 2 represents proposals for stricter limits on notch dimensions

Table 1 - For S0/2, 2c or 3dnS275 S355

Depth Opening S0Max Load

(kN) Shear UF Buckling UF Max Load (kN) Shear UF Buckling UF

200 160 230 180 0.99 0.77 230 0.98 0.75300 240 345 270 0.94 0.99 345 0.92 0.99400 320 460 305 0.78 0.98 395 0.77 0.99500 400 575 345 0.69 0.99 440 0.68 0.99600 480 690 380 0.63 0.99 485 0.61 0.99700 560 805 410 0.58 0.99 520 0.56 0.99800 640 920 435 0.53 0.99 545 0.51 0.99900 720 1035 455 0.49 0.99 565 0.47 0.991000 800 1150 465 0.45 0.99 570 0.42 0.991100 880 1265 475 0.42 0.99 575 0.39 0.991200 960 1380 475 0.38 0.99 570 0.36 0.991300 1040 1495 475 0.35 0.99 555 0.32 0.991400 1120 1610 470 0.32 0.99 545 0.29 0.991500 1200 1725 460 0.29 0.99 525 0.26 0.99

Table 2 - For S0/2, 3c or 4dnS275 S355

Depth Opening S0Max Load

(kN) Shear UF Buckling UF Max Load (kN) Shear UF Buckling UF

200 160 230 180 0.99 0.43 230 0.98 0.43300 240 345 285 0.99 0.58 370 0.99 0.57400 320 460 390 0.99 0.66 505 0.99 0.66500 400 575 495 0.99 0.73 645 0.99 0.74600 480 690 600 0.99 0.78 780 0.99 0.79700 560 805 705 0.99 0.84 920 0.99 0.85800 640 920 810 0.99 0.88 1060 0.99 0.9900 720 1035 920 0.99 0.93 1190 0.99 0.941000 800 1150 1020 0.99 0.97 1325 0.99 0.991100 880 1265 1100 0.97 0.99 1390 0.94 0.991200 960 1380 1150 0.92 0.99 1435 0.89 0.991300 1040 1495 1190 0.88 0.99 1485 0.84 0.991400 1120 1610 1220 0.84 0.99 1515 0.8 0.991500 1200 1725 1245 0.8 0.99 1535 0.75 0.99

SCI Connections

Documents

Transcript of SCI Connections