NCCI Initial Sizing of Vertical Bracing

NCCI: Initial sizing of vertical bracing for a multi-storey building for design as a braced, non-sway frame

SN028a-EN-EU


Presents a simple procedure for the selection of bracing member sizes in order to ensure that the frame is a non-sway frame and that first order analysis may be used for the structure, without any amplification of horizontal loads.

Contents

1. Introduction 2

2. Scope 3

3. Design procedure 3

Appendix A Background and parametric study 5

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NCCI: Initial sizing of vertical bracing for a multi-storey building for design as a braced, non-sway frameCr

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1. Introduction Vertical bracing is designed to resist wind load plus equivalent horizontal forces given by 5.3 of EN 1993-1-1. First order frame analysis can be used for braced frames, provided that the vertical bracing provides sufficient stiffness. For first order analysis to be applicable, EN 1993-1-1 5.2.1 requires that cr 10 for the whole frame, and therefore for each storey of a multi-storey building.

Simple guidance is given in Sections 2 and 3 for the selection of bracing members so that sufficient stiffness is provided for such analysis to be valid. This allows the designer to avoid the complexities of second order analysis, or of allowing for second order effects by amplification of first order effects.

The bracing arrangements considered by this study are presented in Figure 1.1.

H

H

H

H

H

1

4

3

2

5

b

H H

H

FEd

H

(a) (b)

(c) (d)

b

b

b

b

At each floor level, Hi = 0,025 VEd,i where VEd,i is the total design load applied at that floor level

Figure 1.1 Practical arrangements for multi-storey bracing: (a) cross bracing, only tension in diagonal participation; (b) diagonal bracing; (c) horizontal K bracing; (d) vertical K bracing

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2. Scope The design procedure presented below was derived for buildings with the following limitations:

Height not exceeding 30 m Angle of bracing members between 15o and 50o to the horizontal. The bracing arrangements shown in Figure 1.1. Note that the procedure does not depend on the steel grade.

3. Design procedure Select one of the bracing arrangements shown in Figure 1.1 Check that, in the columns and beams of the system to be braced, the axial stresses

calculated on the gross cross-section due to resistance of the horizontally applied loads of 2,5% of vertical applied loads alone do not exceed 30 N/mm2. If the stresses are higher in the columns, either larger sections must be chosen, or the spacing of the columns, b in Figure 1.1, must be increased (but not exceeding 12m). If the stresses in the beams are larger, either a larger section must be chosen or the bracing arrangement must be changed.

Size the bracing, by conventional design methods, to resist horizontal applied loads of 2,5% of vertical applied loads, ensuring that axial stresses on the gross cross-section of the bracing do not exceed the values given in Table 3.1. For intermediate floors, either the stress limits in Table 3.1 for the top floor should be used or a higher stress may be found by linear interpolation between the stress limits according to the height of the bottom of the storey considered.

If the externally applied horizontal loads plus the equivalent horizontal forces from imperfections plus any other sway effects calculated by first-order analysis exceed 2,5% of the vertical loads, check the resistance of the bracing to these loads. The stress limitations in Table 3.1 should not be applied when checking this load combination.

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Table 3.1 Limiting stress on the gross cross-section of the bracing members a building of a maximum height of 30 m, storey height 3m, with 5 m b 12 m and with a maximum axial stress on the gross cross-section of the columns and beams of 30 N/mm2 due to horizontal load = 0,025V

Stress limit on the gross cross-section of the bracing member due to horizontal forces equal to 0,025V Angle of bracing to

the horizontal Top storey Top storey Bottom storey (degrees)

of 30 m building of 20 m building of building

65 N / mm2 80 N / mm2 100 N / mm2 15 < 20 70 N / mm2 95 N / mm2 135 N / mm2 20 < 30 55 N / mm2 110 N / mm2 195 N / mm2 30 < 40 75 N / mm2 130 N / mm2 225 N / mm2 40 50

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Appendix A Background and parametric study For a given storey, the criterion for non-sway may be expressed as follows:

10EdH,Ed

Edcr >

=

hVH

where

HEd is the (total) design value of the horizontal reaction at the bottom of the storey to the horizontal loads and fictitious horizontal loads

VEd is the total design vertical load on the structure at the bottom of the storey

H,Ed is the horizontal displacement at the top of the storey, relative to the bottom of the storey (due to the horizontal loads)

h is the storey height

Traditionally, bracing has been sized to resist horizontal forces of 2,5% of vertical forces, without any direct consideration of frame flexibility. The resulting structures have proved satisfactory. The analysis presented in Appendix A therefore takes this percentage as a starting point and investigates the limitations on overall bracing and frame design to ensure that cr 10,0. H,Ed is caused both by the shear deflection of the braced panels and by the curvature of building acting as a vertical cantilever.

It is assumed that the component of stress in the columns and beams due to participation with the bracing is 30 N/mm2 at every storey.

The horizontal deflection then depends on the spacing of the columns, h, the angle and the stress in the bracing members. Thus, the criterion for first order analysis may be expressed as a limit to the stress in the bracing, for a given angle of the bracing members to the horizontal. The deformation of a braced panel under horizontal loading is shown diagrammatically in Figure A.1.

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h

b

d

H

1

d

h

Figure A.1 A braced panel subject to horizontal load

In the above braced panel, the deflection of the top of the left hand column, relative to the bottom of the column, is given by:

321EdH, ++= where:

1 is the horizontal deflection at the top right hand column, due to the strains in the diagonal bracing member and in the right hand column due to applied loads H = 0,025V

tan

costan

costan

coscd

cd

hd

Eh

Edhd +=+=+=

2 is the horizontal deflection from the strain in the beam due to applied loads H = 0,025V

bE

b bb ==

3 is the horizontal displacement between the top and the bottom of the columns of each storey due to the bending deformation of the frame acting as a vertical cantilever resisting the applied loads H = 0,025V

For the bottom storey, 3 = 0 (giving the total deflection = 1 + 2)

hbL

Eh

bL

22tfctf

c3 == For the top storey,

where:

d, c and b are the axial strains on the gross cross-sections of the diagonals, the columns and the beams respectively due to the applied horizontal load H = 0,025V

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is the angle of the diagonal from the horizontal d is the length of the diagonal h is the storey height b is the spacing of the columns in the braced bay as shown in Figure 1.1 Ltf is the height of the top floor ( = overall building height 1 storey height) E is the modulus of elasticity ( = 210 000 N/mm2)

d, c and b are the axial stresses on the gross cross-sections of the diagonals, the columns and the beams respectively due to the applied horizontal load, H = 2,5%V

The calculation of this effect for the top storey means that value is conservative for lower storeys.

A parametric study was carried out to determine the limitations on column and bracing stresses to ensure that cr is greater than 10 for HEd = 0,025VEd. It had the following scope: All grades of steel. Angle of bracing members is between 15 o and 50o to the horizontal. Height of building 30 m for a typical loading of 8,0 kN/m2. Storey height 3m. Spacing of the columns in the braced bay is in the range of 5 m to 12 m. Stresses in the columns from horizontal forces do not exceed 30 N/mm2. It was based on the following assumptions:

Horizontal forces are 2,5% of the vertical forces. Elastic analyses of a pin jointed frame. The angle of the bracing and the storey height is the same in all storeys. Partial factors on resistance are M0 = 1,0 and M1 = 1,0. The limit on the axial stress on the gross cross-section of the bracing is given in Table 3.1 for the building height, column spacing and axial stresses on the gross cross-sections of beams and columns.

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Quality Record RESOURCE TITLE NCCI: Initial sizing of vertical bracing for a multistorey building for

design as a braced, non-sway frame

Reference(s)

ORIGINAL DOCUMENT

Name Company Date

Created by Alena Ticha SCI

Technical content checked by Charles King SCI 6/7/06

Editorial content checked by

Technical content endorsed by the following STEEL Partners:

1. UK G W Owens SCI 10/7/06

2. France A Bureau CTICM 12/7/06

3. Sweden B Uppfeldt SBI 10/7/06

4. Germany C Mller RWTH 10/7/06

5. Spain J Chica Labein 19/7/06

Resource approved by Technical Coordinator

G W Owens SCI 16/01/07

TRANSLATED DOCUMENT

This Translation made and checked by:

Translated resource approved by:

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1. IntroductionFigure1.1 Practical arrangements for multi storey bracing: (a) cross bracing, only tension in diagonal participation; (b) diagonal bracing; (c) horizontal Kbracing; (d) vertical Kbracing

2. Scope3. Design procedureTable3.1 Limiting stress on the gross cross-section of the bracing members a building of a maximum height of 30 m, storey height 3m, with 5 m b 12 m and with a maximum axial stress on the gross cross-section of the columns and beams of 30 N/mm2 due to horizontal load = 0,025V

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NCCI Initial Sizing of Vertical Bracing