Steel Designer''''s Manual Part 15 potx

SiMPLY SUPPOATED BEAMSat the ends of the beam — Wn;/11,AW The value of the maximum bending moment — C.. but the maximum shear force in any span of tM continuous beam = V/J.IAW The value

Table 2a Symbols used in EN 10025

Supply condition at manufacturer’s discretion

Examples: S235JRG1, S355K2G4

Table 2b Symbols used in EN 10155

Supply condition at manufacturer’s discretion

Examples: S235J0WP, S355K2G2W

Table 2c Symbols used in EN 10113

Examples: S460QL, S620QL1

CA NT/LEVERS

M _T()_2] Mmax = w( 4)

dmax Jf(i+ i7)

1 N B For ant/—clockwise moments

the deflect/on is upwards.

fCU/hLk

SIMPLY SUPPORTED BEAMS

SIMPLY SUPPORT(O BEAMS

z_

when x= a/i—

_IA

SIMPLY SUPPORTED BEAMS

Pot central deflection

derived from the formula

in the adjacent diagram.

PL3

°;nax.

RA-R8-P J/nax.

-— Pb/L Po/L

always occurs within

00774 L of tfie centre of the beo,n When ba,

centre 48E1L L (LII

This value is a/ways with/n

S % of the maximum value.

I JB dp

SiMPLY SUPPOATED BEAMS

at the ends of the beam — W(n;/)11,AW

The value of the maximum bending moment — C WL

The value of the deflection at the centre of the span — k.

SIMPLY SUPPORTED BEAMS

_ Shear diagram when MA "M8

the deections are reversed 2nd degree_parabola W Complement of parabola.

SIMPLY SUPPORTED BEAMS

NIA

When r is the sinp/esupport reaction

BUILT—/N BEAMS parabolic total /oao W

JRa '!4 W/2

bending moment diagram

A

RB

A =R8 = W/2

is ha/f the bending

•:.:i•• O o.& , 4;.' •O4•4•.

EfIiiiitiIII n CONTINUOUS BEAM }d L/n#-+-L/n4L/n+-L/-#L1-+-44

L

L - When n >10, consider the load nitorrrdy oYstiibuted

-The load on the outside stringers is carried c'/rect/y by the supports

The continuous beam Is assumed to be horizontal at each support The reaction at the supports for each s,oan = W/2 but the maximum

shear force in any span of tM continuous beam = V/J.IAW

The value of the fixing moment at each support = — B WL The value of the maximum positive moment for each span = C W4

The value of the maximum deflection for each span —0'0O26

= —

-— WL3 dmax -

PROPPED CAN T/L(VERS

Where and r3 are the simple

support reactions for the beam (MA being considered positive)

w /

84 'C 01.

PROPPED CANT/LEVERS W/2

PROPPED CANILEVEPS

p p p p

D E F19 L/4tL/4tL/44L/

If AArea of free B.MDiagram

dmax occurs at point corresponding

to Xon M diagram, the area A being equal to the area 0

Area SXx Vmax =

EQUAL SPAN CONTINUOUS BEAMS

UNIFORMLY DISTRIBUTED LOADS

EQUAL SPAN CONTINUOUS BEAMS

CENTRAL POINT LOADS Moment coefficient x Wx L

Reaction = coefficient x W

where W is the Load on one span only and L is one span

1W

EQUAL SPAN CONTINUOUS BEAMS

POINT LOADS AT THIRD POINTS OP SPANS

Moment = coefficient A' Wx L React/on = coef/cIenf x W

where Wis the total boo' on one span only a L is one span

Influence lines for bending moments — two-span beam

Influence line for React/on at A and S.Fenvelopefor span AB

Influence lines for reactions and shear forces — three-span beam

Influence lines for reactions and shear forces — four-span beam

2468/O/2/4/6/82022242t5283032343638/ 3 5 7 9 II /3 /5 /7 /9 2/ 232527293/ 33353739

I

O) iOOO 00 00

W0,-J-Jo) '4W140, O)0.4-JO 14-'(4-J

U,U,1.(4 (0(40114-4 '4.400)01 (2—'0140) (4141414 14010-.J 01(41)010 14WW—'Ui

SECOND MOMENTS OF AREA (cm4)

SECOND MOMENTS OF AREA (cm4)

OF RECTANGULAR PLATES

aboutaxis x—x

d rnni

SECOND MOMENTS OF AREA (cm4)

200000231525266200

304175

345600390625439400

492075548800609725

675000

74477581920089842598260010718751166400126632513718001482975

1 600000

1723025185220019876752129600227812524334002595575276480029412253125000

3333344367576007323391467112500136533163767194400228633266667

308700

354933405567

460800

5208335858676561007317338129679000009930331092267119790013101331429167155520016884331829067197730021333332297367246960026502332839467303750032445333460767368640039216334166667

41667554587200091542114333140625170667

204708

243000285792333333385875443667506958576000651042732333820125914667101620811250001241292136533314973751637667178645819440002110542228633324716252666667

2871 708308700033127923549333379687540556674325958460800049020425208333

5000066550

86400

109850137200168750

204800245650291600342950400000463050532400608350691200781250878800984150

1097600121945013500001489550163840017968501965200214375023328002532650274360029659503200000344605037044003975350

425920045562504866800

5191150

5529600

58824506250000

6666788733115200146467182933

225000

273067

327533388800

457267533333

617400

709867811133

921600

10416671171733131220014634671625933180000019860672184533239580026202672858333311040033768673658133395460042666674594733493920053004675678933607500064890676921533737280078432678333333

83333110917144000183083228667281250341333409417

486000

57158366666777175088733310139171152000130208314646671640250182933320324172250000248258327306672994750327533335729173888000422108345726674943250533333357434176174000662558370986677593750811133386519179216000980408310416667

00)010)01 —(0-401 ONJOWNJ -J.NJ.0 0)000(0)

NJ(0—40( 0O0NJ (11U1(00 000(0(0 NJ—0(0 0NJ(0.O 0)00—JO 00)0)00

GEOMETRICAL PROPER TIES OF PLANE SECTIONS

I

).V

4=O•8204d2O4l42o'

n s/des

Regular Figure

4 = n rZ tanO4.ns/n2e

centre

ttX ZZyy Zyy=——

ZW=O1009r3

Zyy OO4r U,- ,V—ec

e,,=os,,r

TxX'Xyy=0007Sr4 Zuu=OO12r4

GEOMETRICAL PROPERTIES OF PLANE SECTIONS

PLASTIC MODULUS OF RECTANGLES

w per unit length

Extract: 'Kleinlogel, Rahmenformeln' 11 AuflageBerlin— Verlag von Wilhelm Ernst &Sohn.

k 1 L

N =2k +3

wL2MM

w per unit length

IIIIIfIIIIII

\zfr

I,4

wL2 k(8+15#)+cS(6—) Constants: *X_

VE=j L_ VA= -VE HA=HE='1Y2

S Notethat X, —X and Marerespectively half the values of MA (ME),MB(=M)

and M from the previous set of formu1 where the whole span was loaded

M +X1+mX2

NLMZ M2JV H4A1i.

AHA '4-'MA

Pa(B + 3b1k) Constant: =

VE= VA=P-VE HA=HE=

Extract: 'Kleinlogel, Rahmenfornieln' 11.AuflageBerlin— Verlag von Wilhelm Ernst &Sohn

MB=-MD=Pa M=O HA=-HR=-P VA=-VE=-

Explanatory notes on section dimensions and properties,

bolts and welds

1 General

The symbols used in this section are generally the same as those in BS 5950-1: 2000.[1]

1.1 Material, section dimensions and tolerances

The structural sections referred to in this design guide are of weldable structural steels conforming to the relevant British Standards given in the table below:

Product

Technical delivery requirements

Dimensions Tolerances Non-alloy steels Fine grain steels

universal columns

Castellated universal beams

– – Castellated universal

columns

ASB (asymmetric beams) Generally BS EN 10025 [2] , See note a) Generally

Slimdek ® beam but see note b) BS EN 10034 [5] ,

but also see note b) Hot finished BS EN 10210-1 [9] BS EN 10210-2 [9] BS EN 10210-2 [9]

hollow sections

Cold formed BS EN 10219-1 [10] BS EN 10219-2 [10] BS EN 10219-2 [10]

hollow sections

Notes:

For full details of the British Standards, see the reference list at the end of the Explanatory Notes.

a) See Corus publication [11]

b) For further details consult Corus.

Table – Structural steel products

1.2 Dimensional units

The dimensions of sections are given in millimetres (mm).

1.3 Property units

Generally, the centimetre (cm) is used for the calculated properties but for surface

areas and for the warping constant (H), the metre (m) and the decimetre (dm)

respectively are used.

Note: 1 dm = 0.1 m = 100 mm

1 dm6 = 1 ¥ 10-6m6 = 1 ¥ 1012mm6

1.4 Mass and force units

The units used are the kilogram (kg), the newton (N) and the metre per second2

(m/s2) so that 1 N = 1 kg ¥ 1 m/s2 For convenience, a standard value of the ation due to gravity has been generally accepted as 9.80665 m/s2 Thus, the force exerted by 1 kg under the action of gravity is 9.80665 N and the force exerted by

2.2 Ratios for local buckling

The ratios of the flange outstand to thickness (b/T) and the web depth to thickness (d/t) are given for I, H and channel sections The ratios of the outside diameter to thickness (D/t) are given for circular hollow sections The ratios d/t and b/t are also

given for square and rectangular hollow sections All the ratios for local buckling have been calculated using the dimensional notation given in Figure 5 of

BS 5950-1: 2000 and are for use when element and section class are being checked

to the limits given in Tables 11 and 12 of BS 5950-1: 2000.

2.3 Dimensions for detailing

The dimensions C, N and n have the meanings given in the figures at the heads of

the tables and have been calculated according to the formulae below The formulae

for N and C make allowance for rolling tolerances, whereas the formulae for n make

no such allowance.

2.3.1 Universal beams, universal columns and bearing piles

2.3.2 Joists

Note: Flanges of BS 4-1 joists have an 8° taper.

2.3.3 Parallel flange channels

(rounded up to the nearest 2 mm above) (taken to the next higher multiple of 2 mm)

C = t + 2 mm (rounded up to the nearest mm)

2 2

mm (rounded to the nearest 2 mm above)

(rounded to the nearest 2 mm above)

mm (rounded to the nearest mm)

2 2

mm (rounded to the nearest 2 mm above)

(rounded to the nearest 2 mm above)

mm (rounded to the nearest mm)

2.3.4 Castellated sections

The depth of the castellated section Dc, is given by:

where D is the actual depth of the original section

Ds is the serial depth of the original section, except that Ds= 381 mm for

signifi-3.2 Sections other than hollow sections

3.2.1 Second moment of area (I)

The second moment of area of the section, often referred to as moment of inertia, has been calculated taking into account all tapers, radii and fillets of the sections.

3.2.2 Radius of gyration (r)

The radius of gyration is a parameter used in buckling calculation and is derived as follows:

where A is the cross-sectional area.

For castellated sections, the radius of gyration given is calculated at the net section