INFORMATION_and_POOL_ETABS_MANUALS_English_E-TN-CBD-BS-5950-90-013 (Deflection limit).pdf

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1/6Deflection Check Locations Page 1 of 6

COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002

COMPOSITE BEAM DESIGN BS 5950-90

Technical Note

Beam Deflection Checks

This Technical Note describes how the program checks deflection when the

user selects the BS 5950-90 code.

Deflection Check Locations

For each design load combination specified for deflection calculations, the

program checks deflection at the following locations:

All design station locations defined by the user.

The point of maximum moment for the load combination.

The point load location for the load combination.

Deflection of a Composite Beam

Deflections are determined under serviceability load combinations specified

for deflection calculation in the program (BS 6.1.1, 2.4.1). The deflection is

calculated differently for propped (shored) and unpropped (unshored) con-

struction. The effect of partial composite connection is also taken into ac-

count. The program uses the following formula for calculating deflection:

= ( )

+ 1

I

IPCC1501

bare

effc . , for propped construction (BS 6.1.4)

= ( )

+ 1

I

IPCC1301

bare

effc . , for unpropped construction(BS 6.1.4

The preceding two formulas are the simplified version of those given in the

code:

= c+ 0.5 (1 Na/Np) (sc), for propped construction (BS 6.1.4)

= c+ 0.3 (1 Na/Np) (sc), for unpropped construction (BS 6.1.4)


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Composite Beam Design BS 5950-90 Beam Deflection Checks

Deflection of a Composite Beam Page 2 of 6

In the preceding expressions,

= Deflection of a composite beam at a station for a load combina-tion considering partial composite connection,

c = Deflection of a composite beam with full shear connection; cal-culation ofc is described in the next section,

s = Deflection of a composite beam with 0% shear connection; it isrelated to moment of inertia of bare steel section (steel shape

with cover plate, if present),

Na = Actual number of connectors provided between a point of zero

moment and a point of maximum moment,

Np = Number of shear connections required between a point of zeromoment and a point of maximum moment for full composite

connection,

PCC = Percent composite connection, used as a ratio,

Ibare = Moment of inertia of steel section, including cover plate if pres-

ent, and

Ieff = Effective moment of inertia of composite section.

Deflection of Composite Beam for Full Composite Connection

When calculating c, the behavior of a composite beam is taken as linearelastic (BS 6.1.4). The program calculates composite beam deflections using

a moment-area technique. An M/EI diagram is constructed by calculating

M/EIvalues at each output station along the length of the beam and then

connecting the M/EIvalues at those stations with straight-line segments.

In constructing the M/EIdiagram, Ieff is used for I, moment of inertia. For

simply supported or continuous composite beams, Ieff is taken as Ip, theequivalent moment of inertia for a cracked section in positive moment with

100% composite connection. For cantilever beams, Ieff is taken as In, the

equivalent moment of inertia for the cracked section in negative moment. The

program assumes that the moment of inertia does not vary along the length

of the beam.


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Deflections for the beam are calculated at each output station. The overall

deflected shape of the beam is drawn by connecting the computed values of

deflection at each output station with straight-line segments.

In this program's composite beam design, the reported deflection is the verti-

cal displacement relative to a line drawn between the deflected position of

the ends of the beam. For example, refer to the beam shown in Figure 1. Fig-

ure 1a shows the original undeformed beam and also shows an arbitrary point

along the beam labeled A. Figure 1b shows the beam in its deformed position

and illustrates the deflection that the Composite Beam Design postprocessor

reports for the beam at point A.

For cantilever overhangs, the program's Composite Beam Design postproces-

sor reports the displacement of the beam relative to the deformed position of

the supported end. If you use the Display menu > Show Deformed Shape

command to review the displacement at the end of the cantilever, the dis-

placement is reported relative to the undeformedposition of the end of the

cantilever. In that case, the rotation at the supported end of the cantilever

overhang is correctly taken into account. However, the displacements dis-

played are all based on the analysis section properties (non-composite mo-

ment of inertias).

A

A

Original position of beam

Line betweenposition of beamshown

Deflection reported byComposite Beampostprocess

b Deflected Sha e ofa

Figure 1: Deflection Results Reported by the Composite Beam DesignPostprocessor


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The program considers the effect of propped and unpropped construction

methods. For unpropped construction, the imposed load deflection is based on

the properties of the composite section, but the dead load deflection, result-

ing from the self weight of the steel beam and wet concrete, is based on the

properties of the bare steel section. For propped construction, all deflections

are based on the properties of the composite section (BS 6.1.1, 6.1.3.5).

Typically, the composite beams are simply supported. For those simply sup-

ported composite beams, there is no scope for moment redistribution. Also

the effect of pattern loading and shakedown effects can be neglected. The

program does not consider moment redistribution, shakedown and pattern

loading for calculation of deflection. Those factors may be important for con-

tinuous beams, and the user should consider those effects independently (BS

6.1.1, 6.1.3, 6.1.3.2, 6.1.3.3).

For simply supported composite beams, the code recommends the use of Ig,

the gross moment of inertia of the equivalent uncracked section, instead ofIp,

the moment of inertia of the equivalent cracked section, for calculation of de-

flection (BS 6.1.2, 6.1.3.5, 4.2.1). The user should be aware of that there

might be a slight difference between Ip for 100% PCC and Ig.

Effective Moment of Inertia, IeffThe program uses the effective moment of inertia of composite section, Ieff,

for deflection calculation. For simply supported or continuous compositebeams, Ieff is taken as Ip, the equivalent moment of inertia for cracked section

in positive moment with 100% composite connection. For cantilever beams,

Ieff is taken as In, the equivalent moment of inertia for cracked section in

negative moment.

For calculation ofIp, the width of the concrete slab and ribs (if ribs run paral-

lel to the beam) is scaled down by a factor of Ec/Es to make the section

equivalent to the steel section in terms of stiffness. Also, the concrete depth

that is in tension under elastic moment distribution is neglected. If the steel

section is large, the elastic neutral axis lies in the web of the steel section. In

such cases, Ip becomes the same as Ig, the equivalent moment of inertia for

gross uncracked section. If the concrete section becomes very large, the

elastic neutral axis lies in concrete, and in that case, Ip may become slightly

smaller than Ig. The effect of the short term and long term modular ratio is


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Deflection Limits Page 5 of 6

considered for calculation ifIp (BS 4.1). See Technical Note Transformed Sec-

tion Moment of Inertia Composite Beam Design BS 5950-90 for details.

For calculating In, the concrete is neglected. If there is a cover plate, it is con-

sidered. In becomes the moment of inertia for bare steel (Ibare), and it also

becomes Ip for 0% composite connection.

Deflection Limits

The deflection limit for total load and live load is taken as follows:

TL,limit =240

L

LL,limit

=360

L

These are the default deflection limits for total load and live load, represec-

tively, in the program. The user can change those limits (BS 2.4.2; BS 5950-1

2.5.1, Table 5). Note that camber is subtracted from the total load deflection

before the total load deflection is compared to the total load deflection limit.

See Technical Note Camber Calculation Composite Beam Design BS 5950-90

for details about camber.

Deflection ChecksFor each service load combination, two deflections are calculatedone for liveload and the other for total loadfor every point. The maximum of the totalload deflection within the span, TL, is compared with its allowable limit,TL,limit. Similarly, the maximum of the live load deflection within the span, LL,is compared with its allowable limit. LL,limit. The following ratios are calculated.

itlimTL,

camberTL

and

itlim,LL

LL

,

where,

TL = Maximum total load deflection for a load combination,
http://e-tn-cbd-bs-5950-90-017.pdf/http://e-tn-cbd-bs-5950-90-017.pdf/http://e-tn-cbd-bs-5950-90-014.pdf/http://e-tn-cbd-bs-5950-90-014.pdf/http://e-tn-cbd-bs-5950-90-017.pdf/http://e-tn-cbd-bs-5950-90-017.pdf/


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Deflection Checks Page 6 of 6

LL = Maximum live load deflection for a load combination,

TL, limit = Maximum allowed total load deflection,

LL, limit = Maximum allowed live load deflection, and

camber = Camber of the beam.

The maximum of the total load deflection ratio and the maximum of the live

load deflection ratios considering all of the service load combinations are re-

ported by the program.

Note that camber is subtracted from the total load deflection before the total

load deflection is compared to the total load deflection limit. See Technical

Note Camber Calculation Composite Beam Design BS 5950-90 for details

about camber.
http://e-tn-cbd-bs-5950-90-014.pdf/http://e-tn-cbd-bs-5950-90-014.pdf/

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INFORMATION_and_POOL_ETABS_MANUALS_English_E-TN-CBD-BS-5950-90-013 (Deflection limit).pdf