Deflection Limit State
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A Beginner's Guide to the Steel Construction Manual, 13th ed. (old)
Chapter 8 Bending Members © 2006, 2007, 2008 T. Bartlett Quimby
Introduction
Section 8.4.2 Flexure Flexural Limit State Behavior Determining Applicable Limit States Flexural Yielding Limit State Lateral Torsional Buckling Limit State Flange Local Buckling Limit State
Shear Shear Behavior Shear Strength Limit State
Deflection Deflection Behavior Deflection Limit State
Misc. Limit States Web Local Yielding Web Crippling
Beam Design
Deflection Limit State Last Revised: 11/04/2014
In the absence of more specific criteria, criteria for structures with brittle finishes (as found in code documents for years) is frequently used. This simplistic criteria puts a limit of the span divided by 360 on the incremental deflection due to live (or transient) load only and a limit of the span divided by 240 on deflection under total load. These limit states are mathematic expressed as: LL < L/360 TL < L/240 These limits were originally developed for members with "brittle" finishes, such as plaster. Plaster is not commonly used as a finishing material anymore. The goal of the limits was to minimize the possibility of damage to the finish and provide reasonable comfort for the building occupants. The criteria has persisted in practice. Other criteria has been used that more explicitly addresses the use of the beam under consideration. For example, the Timber Construction Manual [ref. 12], page 66 suggests the values given in Table 8.4.2.1 and 8.4.2.2. Other references give different, but similar, criteria. Table 8.4.2.1 AITC Recommended Deflection Limits Used with Permission
Applied Load Only
Applied Load + Dead Load
Roof Beams
Industrial
L/180
L/120
Without plaster ceiling
L/240
L/180
With plaster ceiling
L/360
L/240
Use Classification
Commercial and institutional
Selecting Sections Cover Plates Transverse Stiffeners for Shear Bearing Plates Transverse Stiffeners for Concentrated Loads Continuous Beams
Floor Beams
L/360
L/240
Highway bridge stringers
L/200 to L/300
Railway bridge stringers
L/300 to L/400
Ordinary usagea
aOrdinary usage classification for floors is intended for construction in which walking comfort and minimized plaster cracking are the main considerations. These recommended deflection limits may not eliminate all objections to vibrations such as in long spans approaching the maximum limits or for some office and institutional applications where increased floor stiffness is desired. For these usages, the deflections limits of table 8.4.2.2 have been found to provide additional stiffness.
Table 8.4.2.2 AITC Deflection Limits for Uses Where Increased Floor Stiffness is Desired
Chapter Summary
Example Problems Homework Problems References
Report Errors or Make Suggestions Purchase Hard Copy Make Donation
Used with Permission
Use Classification
Applied Load Only
Applied Load + Dead Loada
Floor Beams Commercial, Office & Institutional Floor Joists, spans to 26 ftb LL < 60 psf
L/480
L/360
60 psf < LL < 80 psf
L/480
L/360
LL > 80 psf
L/420
L/300
LL < 60 psf
L/480
L/360
60 psf < LL < 80 psf
L/420
L/300
LL > 80 psf
L/360
L/240
Girders, spans to 36 ftb
aThe AITC includes a modifier on DL depending on whether or not the timber is seasoned. bFor girder spans greater than 36 ft and joist spans greater than 26 ft, special design considerations may be required such as more restrictive deflection limits and vibration considerations that include the total mass of the floor.
The span length, L, in the limit equations above is taken as the distance between center of supports. For cantilever beams, a value equal to twice the actual cantilever length is generally used for the L in determining the deflection limits. Ponding In roof systems that are essentially flat, provisions must be made to support
Figure 8.4.2.1 Frozen Scupper
ponding water. Ponding is a progressive event. The more water on the roof, the more deflection you get, which means that even more water can be retained, which leads to more deflection, etc... If the beam is stiff enough, then ponding can be minimized. The best solution to the ponding problem is architectural. It is strongly recommended that sufficient slope be given to roof systems (a minimum of 1/4" per foot) to prevent ponding. Appropriate drainage must also be provided. Roofs in cold regions that use scuppers to drain a roof located behind a parapet may become plugged with ice, resulting in unintentional ponding, leading to disastrous results. Figure 8.4.2.1 shows such a frozen scupper. Scuppers must also be made large enough to allow water to escape during a deluge and to minimize blockage by debris. Tolerances of Attached Elements or NonStructural Elements Below Often times, nonstructural elements have specific deflection tolerances that are more restrictive than the general criteria given above. These tolerances generally are expressed in terms as a maximum deflection value and must be considered in design. For example, a floor girder spanning 36 ft may deflect up to 1.2 inches under a live load only deflection limit of L/360. Any nonstructural partition under the beam must be able to accommodate this deflection. However, if it cannot, then the amount of live load deflection that can be accommodated becomes the new deflection criteria for this beam. Vibrations Certain vibrations have been found to be objectionable in most occupancy classifications. Vibrations are often lumped together with deflection since both are stiffness related. Vibrations are a function of
stiffness and mass. The frequency of the vibrations is of more concern than the amplitude. The treatment of vibrations is beyond the current scope of this text. Selection of Criteria The choice of deflection criteria is a project dependent. Other criteria may be encountered that have been developed for special structures and/or situations. These may be considered as needed. For the problems in this text, the equations listed at the start of this section will be used unless otherwise specified. <<< Previous Section <<< >>> Next Section >>>
Chapter 8 Bending Members © 2006, 2007, 2008 T. Bartlett Quimby
Introduction
Section 8.4.2 Flexure Flexural Limit State Behavior Determining Applicable Limit States Flexural Yielding Limit State Lateral Torsional Buckling Limit State Flange Local Buckling Limit State
Shear Shear Behavior Shear Strength Limit State
Deflection Deflection Behavior Deflection Limit State
Misc. Limit States Web Local Yielding Web Crippling
Beam Design
Deflection Limit State Last Revised: 11/04/2014
In the absence of more specific criteria, criteria for structures with brittle finishes (as found in code documents for years) is frequently used. This simplistic criteria puts a limit of the span divided by 360 on the incremental deflection due to live (or transient) load only and a limit of the span divided by 240 on deflection under total load. These limit states are mathematic expressed as: LL < L/360 TL < L/240 These limits were originally developed for members with "brittle" finishes, such as plaster. Plaster is not commonly used as a finishing material anymore. The goal of the limits was to minimize the possibility of damage to the finish and provide reasonable comfort for the building occupants. The criteria has persisted in practice. Other criteria has been used that more explicitly addresses the use of the beam under consideration. For example, the Timber Construction Manual [ref. 12], page 66 suggests the values given in Table 8.4.2.1 and 8.4.2.2. Other references give different, but similar, criteria. Table 8.4.2.1 AITC Recommended Deflection Limits Used with Permission
Applied Load Only
Applied Load + Dead Load
Roof Beams
Industrial
L/180
L/120
Without plaster ceiling
L/240
L/180
With plaster ceiling
L/360
L/240
Use Classification
Commercial and institutional
Selecting Sections Cover Plates Transverse Stiffeners for Shear Bearing Plates Transverse Stiffeners for Concentrated Loads Continuous Beams
Floor Beams
L/360
L/240
Highway bridge stringers
L/200 to L/300
Railway bridge stringers
L/300 to L/400
Ordinary usagea
aOrdinary usage classification for floors is intended for construction in which walking comfort and minimized plaster cracking are the main considerations. These recommended deflection limits may not eliminate all objections to vibrations such as in long spans approaching the maximum limits or for some office and institutional applications where increased floor stiffness is desired. For these usages, the deflections limits of table 8.4.2.2 have been found to provide additional stiffness.
Table 8.4.2.2 AITC Deflection Limits for Uses Where Increased Floor Stiffness is Desired
Chapter Summary
Example Problems Homework Problems References
Report Errors or Make Suggestions Purchase Hard Copy Make Donation
Used with Permission
Use Classification
Applied Load Only
Applied Load + Dead Loada
Floor Beams Commercial, Office & Institutional Floor Joists, spans to 26 ftb LL < 60 psf
L/480
L/360
60 psf < LL < 80 psf
L/480
L/360
LL > 80 psf
L/420
L/300
LL < 60 psf
L/480
L/360
60 psf < LL < 80 psf
L/420
L/300
LL > 80 psf
L/360
L/240
Girders, spans to 36 ftb
aThe AITC includes a modifier on DL depending on whether or not the timber is seasoned. bFor girder spans greater than 36 ft and joist spans greater than 26 ft, special design considerations may be required such as more restrictive deflection limits and vibration considerations that include the total mass of the floor.
The span length, L, in the limit equations above is taken as the distance between center of supports. For cantilever beams, a value equal to twice the actual cantilever length is generally used for the L in determining the deflection limits. Ponding In roof systems that are essentially flat, provisions must be made to support
Figure 8.4.2.1 Frozen Scupper
ponding water. Ponding is a progressive event. The more water on the roof, the more deflection you get, which means that even more water can be retained, which leads to more deflection, etc... If the beam is stiff enough, then ponding can be minimized. The best solution to the ponding problem is architectural. It is strongly recommended that sufficient slope be given to roof systems (a minimum of 1/4" per foot) to prevent ponding. Appropriate drainage must also be provided. Roofs in cold regions that use scuppers to drain a roof located behind a parapet may become plugged with ice, resulting in unintentional ponding, leading to disastrous results. Figure 8.4.2.1 shows such a frozen scupper. Scuppers must also be made large enough to allow water to escape during a deluge and to minimize blockage by debris. Tolerances of Attached Elements or NonStructural Elements Below Often times, nonstructural elements have specific deflection tolerances that are more restrictive than the general criteria given above. These tolerances generally are expressed in terms as a maximum deflection value and must be considered in design. For example, a floor girder spanning 36 ft may deflect up to 1.2 inches under a live load only deflection limit of L/360. Any nonstructural partition under the beam must be able to accommodate this deflection. However, if it cannot, then the amount of live load deflection that can be accommodated becomes the new deflection criteria for this beam. Vibrations Certain vibrations have been found to be objectionable in most occupancy classifications. Vibrations are often lumped together with deflection since both are stiffness related. Vibrations are a function of
stiffness and mass. The frequency of the vibrations is of more concern than the amplitude. The treatment of vibrations is beyond the current scope of this text. Selection of Criteria The choice of deflection criteria is a project dependent. Other criteria may be encountered that have been developed for special structures and/or situations. These may be considered as needed. For the problems in this text, the equations listed at the start of this section will be used unless otherwise specified. <<< Previous Section <<< >>> Next Section >>>
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