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Building Design and Construction Handbook - Merritt - Ventech!

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5.56 SECTION FIVE<br />

TABLE 5.4 Values of K for Curved Beams<br />

Section<br />

R<br />

c<br />

1.2<br />

1.4<br />

1.6<br />

1.8<br />

2.0<br />

3.0<br />

4.0<br />

6.0<br />

8.0<br />

10.0<br />

1.2<br />

1.4<br />

1.6<br />

1.8<br />

2.0<br />

3.0<br />

4.0<br />

6.0<br />

8.0<br />

10.0<br />

1.2<br />

1.4<br />

1.6<br />

1.8<br />

2.0<br />

3.0<br />

4.0<br />

6.0<br />

8.0<br />

10.0<br />

K<br />

Inside face Outside face y o<br />

3.41<br />

2.40<br />

1.96<br />

1.75<br />

1.62<br />

1.33<br />

1.23<br />

1.14<br />

1.10<br />

1.08<br />

3.28<br />

2.31<br />

1.89<br />

1.70<br />

1.57<br />

1.31<br />

1.21<br />

1.13<br />

1.10<br />

1.07<br />

2.89<br />

2.13<br />

1.79<br />

1.63<br />

1.52<br />

1.30<br />

1.20<br />

1.12<br />

1.09<br />

1.07<br />

0.54<br />

0.60<br />

0.65<br />

0.68<br />

0.71<br />

0.79<br />

0.84<br />

0.89<br />

0.91<br />

0.93<br />

0.58<br />

0.64<br />

0.68<br />

0.71<br />

0.73<br />

0.81<br />

0.85<br />

0.90<br />

0.92<br />

0.93<br />

0.57<br />

0.63<br />

0.67<br />

0.70<br />

0.73<br />

0.81<br />

0.85<br />

0.90<br />

0.92<br />

0.94<br />

0.224R<br />

0.141R<br />

0.108R<br />

0.0847R<br />

0.069R<br />

0.030R<br />

0.016R<br />

0.0070R<br />

0.0039R<br />

0.0025R<br />

0.269R<br />

0.182R<br />

0.134R<br />

0.104R<br />

0.083R<br />

0.038R<br />

0.020R<br />

0.0087R<br />

0.0049R<br />

0.0031R<br />

0.305R<br />

0.204R<br />

0.149R<br />

0.112R<br />

0.090R<br />

0.041R<br />

0.0217R<br />

0.0093R<br />

0.0052R<br />

0.0033R<br />

where I � moment of inertia of modified section about its centroidal axis<br />

R � radius of curvature of centroidal axis<br />

c � distance from centroidal axis to center of the more sharply curved flange<br />

Because of the high stress factor, it is advisable to stiffen or brace curved I-beam<br />

flanges.<br />

The maximum radial stress will occur at the junction of web <strong>and</strong> flange of I<br />

beams. If the moment is negative, that is, if the loads tend to flatten out the beam,<br />

the radial stress is tensile, <strong>and</strong> there is a tendency for the more sharply curved<br />

flange to pull away from the web. An approximate value of this maximum stress<br />

is<br />

Aƒ M<br />

ƒr �� (5.82)<br />

Atcr�<br />

w g

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