Steel Designer''''s Manual Part 11 doc

Mode 2 Bolt failure and yielding of the flange The potential resistance of the column flange or end-plate in tension is given by thefollowing expression: where SPtis the total tension ca

Q 'Q QQ

0 is the prying force

yielding of the flange (Mode 2) and bolt failure (Mode 3) These modes are shown

diagrammatically in Fig 26.28 The equations for calculating the potential resistancefor each of these modes of failure are given below

Mode 1 Complete flange yielding

The potential resistance of either the column flange or end-plate, Pr, can be mined from the following expression:

deter-where Mpis the plastic moment capacity of the equivalent tee-stub representing the

column flange or end-plate

m is the distance from the bolt centre to a line located 20% into either the

column root or end-plate weld

Mode 2 Bolt failure and yielding of the flange

The potential resistance of the column flange or end-plate in tension is given by thefollowing expression:

where SPtis the total tension capacity of all the bolts in the group

n is the effective edge distance.

of this method, Zoetemijer, addresses the problem of prying action in a backgroundpublication.12In this publication Zoetemijer develops the following three expres-sions for the equivalent effective length of an unstiffened column flange taking intoaccount different levels of prying action:

For prying force = 0.0 Leff= ( p + 5.5m + 4n)

For maximum prying force Leff= ( p + 4m)

For an intermediate value Leff= ( p + 4m + 1.25n)

where p is the bolt pitch

Zoetemijer explains that the first expression has an inadequate margin of safetyagainst bolt failure while the margin of safety in the second is too high He there-fore suggests using the third equation, which allows for approximately 33% pryingaction This approach simplifies the calculations by omitting complicated expres-sions for determining prying action

BS 5950: Part 1 allows two approaches for calculating the tension capacity of abolt in the presence of prying forces The simple method given in clause 6.3.4.2places certain restrictions on the centre-to-centre bolt spacing and on the capacity

of the connected part to reduce prying action A reduced bolt capacity is also used

by including a 0.8 factor in the expression for calculating the nominal tension

capac-ity ( pnom) of the bolt One advantage of this approach is that it obviates the need tocalculate prying forces directly In the more exact approach given in clause 6.3.4.3

bolt tension capacities ( pt) are allowed provided the connection is not subject toprying action or the prying forces are included in the design method As explainedabove the design method described here allows for prying action without the need

to calculate prying forces directly and therefore the enhanced bolt capacities of themore exact method can be used

web bearing and buckling and include the following:

• Column web in bearing

• Column web buckling

• Beam flange in compression

Column web in compression

In many designs it is common for the column web to be loaded to such an extentthat it governs the design of the connection However, this can be avoided either bychoosing a heavier column or by strengthening the web with one of the compres-sion stiffeners shown in section 26.3.2.4

The resistance of an unstiffened column web subject to compressive forces, Pc, isgiven by the smaller of the expressions for column web bearing and column webbuckling

Column web bearing

The resistance of the column web to bearing is based on an area of web calculated

by assuming the compression force from the beam’s flange is dispersed over a lengthshown in Fig 26.29 From this the resistance of the column web to crushing is given

by the following expression:

where b1 is the stiff bearing length based on a 45° dispersion through the end-plate

from the edge of the welds

n except at the end of a member n = 5

k is obtained as follows:

– for a rolled I- or H-section k = Tc+ r – for a welded I- or H-section k = Tc

Tcis the column flange thickness

r is the root radius

tc is the thickness of the column web

pywis the design strength of the column web

Pbw=(b1+nk)¥tc ¥pyw

j4

Column web buckling

The resistance of the column web to buckling is based on bearing capacity of thecolumn web and is given by the following expression in clause 4.5.3.1 of BS 5950:Part 1:

where b1, n, k and t are defined above

d is the depth of the web

Pbwis the bearing capacity of the unstiffened web at the web-to-flange connection given in the section above

Beam flange in compression

The factor 1.4 in front of this expression accounts for two effects Firstly, it accountsfor the spread of compression into the beam’s web and secondly it accounts for possible strain-hardening of the steel in the beam flange.

This simple check is usually sufficient to determine the crushing capacity of thebeam’s flange However, where high moments are present or moment is combinedwith axial load, method 2 is more appropriate

Beam flange in compression – Method 2

In this approach the potential resistance of the beam flange is given by the ing expression:

follow-Pc= 1.2 ¥ pyb¥ Ac

where Acis the area in compression shown in Fig 26.30

It should be noted that in this approach the factor 1.4 is reduced to 1.2 since thecontribution of the web is now taken into account directly It should also be noted

that the centre of compression is now at the centroid of the area Ac, and the arm of the bolts is reduced accordingly Changing the position of the centre of com-pression will also affect the moment, and an iterative calculation procedure becomesnecessary

lever-Fig 26.30 Area of beam flange and web in compression

shear force will be zero However, in the case of a two sided connection subject

to moments acting in the same sense the resultant shears will be additive For any connection the resulting shear force can be obtained from the following expression:

where Mb1and Mb2are the moments in connections 1 and 2 (hogging positive)

Z1 and Z2are the lever-arms for connections 1 and 2 It is usually assumedthat the moment can be represented by equal and opposite forces in the

beam’s tension and compression flanges In this case Z1and Z2 are equal

to the distances between the centroids of the beam flanges for connections

1 and 2 respectively

The resistance of an unstiffened column web panel in shear is given by the ing expression:

follow-Pv= 0.6 ¥ pyc¥ tc¥ Dc

where pycis the design strength of the column

tcis the thickness of the column web

Dc is the depth of the column sectionWebs of most UC sections will fail in panel shear before they fail in either bearing or buckling and therefore most single sided connections are likely to fail in shear The strength of a column web can be increased either by choos-ing a heavier column section or by using one of the shear stiffeners shown in Fig 26.13c

Z

M Z

vp

There is often a high shear stress in the column web, particularly in single sidedconnections, and stiffening is required Diagonal or supplementary web plates can

be used (see Fig 26.31c) Wherever possible the angle of diagonal stiffeners should

be between 30° and 60° However, if the depth of the column is considerably lessthan the depth of the beam ‘K’ stiffening may be used

In general the type of strengthening must be chosen so that it does not clash withother components at the connections

Fig 26.31c Commonly used method of shear stiffening

Fig 26.31a Tension stiffeners

Fig 26.31b Compression stiffeners

tions regarding the structural behaviour of the steel frame When choosing and portioning connections the engineer should always consider the basic requirementssuch as the stiffness/flexibility of the connection, strength and the required rota-tional capacity The design philosophy presented in this chapter together with thedetailed design checks provide the engineer with a basic set of tools that can beused to design connections which are better able to meet the design assumptions.

pro-To aid the designer further this chapter concludes with a set of worked examplesfor simple connections

References to Chapter 26

1 The Steel Construction Institute/The British Constructional Steelwork

Associ-ation LTD (2002) Joints in Steel Construction: Simple Connections, PublicAssoci-ation

No 212 SCI, BCSA

2 The Steel Construction Institute/The British Constructional Steelwork

Associ-ation LTD (1995) Joints in Steel Construction: Moment Connections, PublicAssoci-ation

No 207 SCI, BCSA

3 British Standards Institution (1993) DD ENV1993-1-1: 1992 Eurocode 3: Design

of steel structures Part 1.1 General rules and rules for buildings, BSI, London.

4 British Standards Institution (2000) BS 5950: Structural use of steelwork in ing Part 1: Code of practice for design – Rolled and welded sections BSI, London.

build-5 The British Constructional Steelwork Association & the Steel Construction

Institute (1994) National Structural Steelwork Specification for building struction, Publication No 203/94, BCSA, SCI, London.

con-6 Hogan T J & Thomas I R (1994) Design of structural connections, 4th edn,

Australian Institute of Steel Construction

The splice is between a 305 ¥ 305 ¥ 97 UC upper column and a 356

¥ 356 ¥ 153 UC lower column Both columns are grade S275 steel.

The factored forces and moments acting on the splice are:

2no 305 ¥ 27 ¥ 305 mm Bolts

M24, Grade 8.8

Check 2 – The presence of tension due to axial load and moment

The basic requirement is to check for the presence of tension in the

splice due to axial load and moment.

tension does not occur and the splice need only be detailed to

trans-mit axial compression in direct bearing.

net tension does occur and the flange cover plates and their

fasten-ers should be designed for the tension.

Tension is present in the splice and the flange cover plates, and their

fasteners should be designed to resist the net tension.

33 33

.

Check 3 – Tension capacity of the cover plate

The basic requirement is that the net tension capacity of the cover

plate must be greater than or equal to the applied net tension.

The tension capacity of the cover plate is given by the following

expression:

F t = p y A fp

where p y is the tensile strength of the plate

A fp is the effective area of the cover plate

Net area of the flange plate is greater than the gross area of the

section therefore take the net area equal to the gross area.

A fp = 3050 mm 2

3.4.3

Check 4 – Shear capacity of bolt group connecting flange cover plate

to column flange The basic requirement is that the shear capacity of the bolt group

must be greater than or equal to the applied tensile force.

The shear capacity of the bolt group is given by the following

expression:

Shear capacity of bolt group = Reduction factor ¥ SPs

where P s is the shear capacity of a single bolt

The reduction factor is a factor to allow for the effects of packing.

Shear strength of bolts

a Top bolts

The shear capacity of the top bolts is limited by the bearing

capac-ity of the flange plate The bearing capaccapac-ity is given by the smaller

of the following two expressions:

The reduction factor is an empirical factor which allows for the

effects of bending in the bolt due to thick packing

Reduced shear capacity of bolt = 0.79 ¥ 132.4

= 104.6 kN < P bs (110.4 kN ) Shear capacity of joint

132 4

Check 5 – Bearing capacity of flange cover plate connected to column

flange

The basic check is that the bearing capacity of the flange cover plates

( SP bs ) must be greater than the applied tensile force (F t ).

457 x 152 x 52 UB 120

The connection is between a 610 ¥ 229 ¥ 101 UB (S275) supporting

beam and a 457 ¥ 152 ¥ 52 UB (S275) supported beam.

The end reaction of the simply supported beam due to factored loads

is 110 kN.

Refer to Table 26.8 for design checks.

Check 2 – Capacity of bolt group connecting the fin plate to the web

of supported beam

The basic requirement is that the bearing capacity per bolt (P bs ) must

be greater than the resultant force on the outermost bolt due to direct

shear and moment (F s )

P bs ≥ F s

For a single line of bolts the resultant shear is given by:

where F sv is the vertical force on the bolt due to shear.

F sm is the force on the outmost bolt due to the moment

a is the eccentricity of the vertical force

Z bg is the elastic section modulus of the bolt group.

=

n

sv v

=

F s =(F sv 2+F sm 2)1 2 /

Bearing capacity connected plate (fin plate)

The bearing capacity of the connected plate is given by the

follow-ing expressions:

P bs = k bs dt p p bs

6.3.3.3 but

Bearing capacity connected part (beam web)

The bearing capacity of the connected part is given by the following

expression:

P bs = k bs dt p p bs

6.3.3.3 but

.

For the beam web

The bearing capacity of the beam web is smaller than the bearing

capacity of the fin plate.

69.9 kN > 44 kN Therefore the bearing capacity of the bolt group is adequate.

69 9

69 9

.

Check 3a – plain end beams – strength of beam at net section

This check is not necessary because the beam is notched.

Check 3b – Shear and bending capacity of the supported beam

For shear

The basic requirement is that the shear capacity of the beam must

be greater than the applied shear.

P v ≥ F v

For shear there are three checks to consider These are:

• shear of the gross section

• shear of the net section

• block shear

Shear of the gross section

The shear capacity of the gross section is given by:

Shear of the net section

The shear capacity of the net section is given by:

Shear and bending interaction at the notch

The basic requirement is that the moment capacity at the notch in

the presence of shear must be greater than the moment from the

product of the end reaction and the distance to the end of the notch.

t 1 is the gap

c is the notch length

Check for low shear

102 6

3 6

.

M cn≥F t v( 1+c)

Check 3c – Supported beam – local stability of notched beam

The beam is restrained against lateral torsional buckling, therefore

no account need be taken of notch stability provided for one flange

notched the following requirement is satisfied:

c = 120 mm

D = 449.8 mm

t w = 7.6 mm

120 mm < 346.8 mm

Check 3d – Unrestrained supported beam overall stability of notched beam

The notched beam is restrained therefore the overall stability of the

beam need not be checked.

Check 4 – Shear and bending capacity of fin plate connected to

supported beam

For shear

The basic requirement is that the shear capacity of the fin plate must

be greater than the shear force.

P v ≥ F v

For shear the following checks must be made:

• shear at the gross section

• shear at the net section

• block shear

Shear (gross section)

4.2.3

Shear (net section)

The effect of bolt holes need not be allowed for in the shear area

v net v h

,

,

.

0 9 3200 2880

0 6 275 2880 1000

475 2

2

2

/

The shear capacity of the net section is given by:

For bending

The basic requirement is that the moment capacity of the fin plate

must be greater than the applied moment

Check 5 – Lateral torsional buckling resistance of long fin-plate

For long fin-plates

a = 50 mm

t = 10 mm

t/0.15 = 66 mm

50 mm < 66 mm

Therefore this is a short fin plate and does not need to be checked

for lateral torsional buckling.

Check 6 – Supporting beam welds

The basic requirement is that the leg length of fillet weld must be

greater than or equal to 0.8 times the thickness of the fin plate.

Check 7 – Supporting beam – local capacity (with one supported beam)

The basic requirement is that the local shear capacity of the

sup-porting beam web should be greater than the end reaction.

P v ≥ F v

The following two modes of failure should be considered:

• Local shear failure of the supporting beam web

• Punching shear capacity

Local shear failure (beam web)

The local shear failure is given by the following expression:

l is the depth of fin plate

t w is web thickness of supporting beam

503 7

.

Punching shear capacity

The punching shear capacity of the supporting web is satisfactory provided that

where t f is the fin plate thickness

t w is the thickness of the web of the supporting beam

U s is the ultimate tensile strength of the supporting beam = 410 N/mm 2

p y is the design strength of the fin plate

Check 8 – Structural integrity – connecting elements

The basic requirement is that the tension capacity of the fin plate

must be greater than the tie force.

Tension capacity of fin plate ≥ Tie force

Tie force

Note that in certain cases the tie force will be greater than 75 kN and

it may be necessary to check for a tying force equal to the end

reac-tion of the supported beam.

Tension capacity of fin plate

The following two checks should be considered:

• capacity of gross section

• capacity of net section

Capacity of the gross section

The tension capacity of the gross section is given by:

Capacity of net section

The tension capacity of the net section is given by:

The tension capacity of the fin plate is 880 kN.

880 kN > 75 kN Therefore the tension capacity of the fin plate is adequate.

1026 9

Check 9 – Structural integrity – supported beam

For tension

The basic requirement is that the tension capacity of the supported

beam web must be greater than the tie force.

Tension capacity of the beam web ≥ Tie force

For tension the following checks should be considered:

• net tension capacity

• local tension capacity

• bearing capacity

Net tension capacity

The net tension capacity of the beam’s web is given by the following

expression:

For the notched section

where A g is the gross area of the notched beam

A e=K A e( g-n D t h )

Local tension capacity

This is tension failure through a group of bolt holes at a free edge.

This consists of tension failure at the row of bolt holes accompanied

by shear failure along a line from the end bolts to the free edge.

The tension capacity is given by the following expression:

where A v is the shear area and is given by

p is the bolt pitch

t is the web thickness

429.1 kN > 75 kN

Therefore the local tension capacity of the web is adequate.

Bearing

The basic requirement is that the bearing capacity of the beam web

must be greater than the tie force.

bearing capacity of the beam web ≥ tie force

P t=2 0 6( p A y v)+ (n-1) (p-D t p h) y

Refer to Table 26.3 for design checks.

Check 2 – Shear capacity of bolt group connecting cleats to web of

supported beam Basic check is:

P ≥ F /2

a is the eccentricity of bolt group

Z bg is the elastic modulus of the bolt group

where p is the bolt pitch

\ resultant shear on the outermost bolt is

F s /2 = 29.6 kN

The shear resistance of a single bolt in double shear is given by:

where p s is the bolt shear strength

P s > F s /2 \ the shear capacity of the bolt group is adequate.

4 46 25

Check 3 – Shear and bearing capacity of cleat connected to

sup-ported beam

Shear

The basic check for shear is that the shear capacity of the leg of the

angle cleat (P v ) must be greater than half the end reaction

For shear the following three checks must be made:

• shear capacity of the gross section

• shear capacity of the net section

• block shear

Shear capacity of the gross section

The shear capacity of the gross section is given by the following

expression:

P v = 0.6 p y A v

where p y is the design strength of the angle 4.2.3

A v is the shear area of the angle For an 8 mm thick angle

p y = 275 N/mm 2

4.2.3 where A is the gross area for a 90 ¥ 90 ¥ 8 angle 300 mm long

Shear capacity of the net section

The effect of bolt holes on the shear capacity of the section need not

be considered provided that:

where A v,net is the net shear area after deducting bolt holes 6.2.3

K e is the effective net area coefficient

A v,net = 0.9A - nDht

where n is the number of bolt holes

D h is the diameter of the hole

t is the thickness of cleat

\ A v,net = 0.9 ¥ 2400 - 4 ¥ 22 ¥ 8 mm 2

= 1456 mm 2

1456 < 1530

Therefore the effect of bolt holes must be taken into account.

The shear capacity of the net section is given by the following

.

≥0 85