steel beams analysis and deign

PART I I I

DETERMINING GIRDER AND BEAM SIZES FOR FLOORS & ROOFS

The architectural planning of any building requires many individual elements. During the pre-schematic and schematic design stages one important aspect to establish is the building height.During these stages of design preliminary structural information is required. This information willinclude: floor and roof system fire rating, floor slab depth, roof decking depth, floor beam depths, roofpurlin depth, floor and roof girder depths. Each of these items in combination with the mechanical andelectrical system requirements will establish the “ceiling sandwich” and the vertical proportions ofthe architectural design can be established.

Many times, during the early stages of planning and design, projects will be “designed” with very littleparticipation by the structural team. Without the early involvement by the structural engineerinaccurate assumptions for member depths and floor/roof systems could be made. The AmericanInstitute of Steel Construction has developed a series of tables to aid the architectural designer indetermining floor and roof system depths (Table sets A, B, C, and D). Each set of tables representsa distinct set of floor and roof system parameters. Three (3) different live load conditions for eachrange of beam and girder spans has been presented. The tables present nominal member depthranges for beam spans of 20 feet to 40 feet (example: W24 beam has a nominal depth of 24"), as wellas girder spans from 20 feet to 40 feet. Preliminary beam and girder depths can quickly bedetermined from the tables for square and rectangular bay sizes ranging from 20' x 20' to 40' x 40'.

The member sizes indicated in the tables represent a range of member depths for a particular span.It must be brought to the attention of the user that, as the member depth of any given beam orgirder becomes shallower an increase in member weight will occur. As a general “rule-of-thumb” a 25percent increase in member weight will occur with each size of depth reduction. As an example, if thereported range is W18 - W24 there will be an approximate 25 percent increase in weight for a W21member to meet the same design criteria as a W24. A W18 member will have an approximate 25percent increase in weight if used in place of a W21. Should a W18 member be used in place of a W24,the minimum increase in member weight will be approximately 60 percent.

As with any design problem there are many solutions. Each project will have a unique set of loadingand serviceability parameters. The design information and example have been prepared accuratelyand consistent with current structural design practice for several different load cases. All datacontained in this publication is, however, preliminary for general information and discussion only, andshall not be used or relied upon for any specific application without competent professionalexamination and verification of its suitability and applicability by a licensed professional structuralengineer.

PAGE 85 SYSTEMS

Des i gn Pa rame te r s and L im i t a t i on s

Many specific parameters and limitations go into the design of any structural member. Imposedloadings caused by earthquake, wind, snow, rain, construction methods, etc., vary across thecountry. Live loads are specified in the applicable building codes. Dead loads are much more variableand require special attention in their computation. Specific requirements for serviceability, strength,lateral stability of individual elements, and the lateral resistance of the building all contribute to thedesign of a safe and efficient building. The information presented in the tables to follow is intendedfor use in establishing preliminary floor and roof framing member depths only, without regard toearthquake loading or contributing to lateral resistance of the building.

Beam spans range from 20 feet to 40 feet in 5 foot increments. Girder spans range from 20 feet to40 feet in 5 foot increments for each of the beam span ranges noted. Therefore, girder depthsreported cover 25 different bay sizes for each of three load cases. Dead loads address the self-weight of the floor/roof framing system. Three (3) different slab conditions and one type of roofconstruction have been considered.

The following girder and floor beam sizing tables are based on the following parameters:

• AISC Load and Resistance Factor Design Specification, December 1, 1993

• Live and dead loads are uniformly distributed over a bay area

• Full live load has been applied to a full bay; no live load reduction has been taken intoaccount

• No analysis has been made for floor vibration/vibration suseptibility

• A construction live load of 20 psf has been applied for composite beam staged loadinganalysis

• Beam and girder depths represent designs for composite as well as non-compositemember design

• Live load deflection has been limited to 1⁄360 of the member span

• Shear connectors for composite action of the beams/girders have not been quantified

• All metal deck shall be composite type metal decking

• Normal weight (Nwt) concrete unit weight used in the designs is 145 pcf; Lightweight(Ltwt) concrete unit weight used in the designs is 110 pcf

• Beams and girders have been selected assuming that cambering will be considered bythe structural engineer of record for the placement of “level” floors

• Connection designs have not been considered

• 50 ksi steel yield and 3000 psi concrete strength

• Actual depths vary from the nominal depths tabulated. For actual mem ber depthsrefer to Part 1 of the AISC Manual of Steel Construction, latest edition.

PAGE 86SYSTEMS

Selec t ion Example for Girder and F loor Beam S iz ing Tables

Known Design Criteria:

• Dead load includes system self weight (slab + steel)• Superimposed dead load = 25 psf (partitions + MEP)• Loads are uniformly distributed over bay area• Live Load = 100 psf• Dead Load = 25 psf (partitions + MEP)• Self Wt. considered on the table formulation• 4 1⁄4" Lightweight (Ltwt) concrete topping• 2" metal decking (composite)• Fy = 50 ksi• Floor system requiring a 3 hour fire rating (floor assembly, unprotected metal deck)• Bay size 30 feet x 35 feet (Girder span x Beam span)

Solution:Beam depth selection:

Enter Table C, Beam Sizes, second row for 100 psf live loading.Under Beam Span: B1 (ft), fourth column for a 35 foot member span. Read the range of member sizes to be W21 - W24. This indicates that the beam depth could be as shallow as 21" (nominal) for the W21 beam or as deep as 24" (nominal) for the W24 beam.

Girder depth selection:Enter Table C35, Girder Sizes / Beam Span 35 feet, second row for 100 psf live loading.

Under girder span selection: G1 (ft), third column for a 30 foot girder span. Read the range of member sizes to be W24 - W30. This indicates that the beam depth could be as shallow as 24" (nominal) for the W24 beam or as deep as 30" (nominal) for the W30 beam. An intermediate depth of 27" (nominal) for a W27 could also be selected.

Summary:35 foot beam span: W21 - W24 (Note that actual depths will vary).30 foot girder span: W24 - W30 (Note that actual depths will vary).Member cambers may be required (Consult a structural engineer for specifics).

PAGE 87 SYSTEMS

SYSTEMS

Tab l e s A t o A40

Design Critieria Floor Diagram

• Dead load includes system self weight (slab + steel)

• Superimposed dead load = 25 psf (partitions + MEP)

• Loads are uniformly distributed over bay area

• 3 1⁄4" Lightweight concrete topping• 2" Composite metal decking• 50 ksi steel yield• 3000 psi concrete strength• 2 Hour Fire Rating

TABLE A20Girder Sizes

Girder Span: G1 (ft)

Live Load, psf 20 25 30 35 40 Classification

50 Office

100 Assembly

150 Storage

W16 - W18 W18 - W21 W21 - W24 W24 - W27 W24 - W27

W18 - W21 W21 - W24 W24 - W27 W24 - W30 W27 - W30

W21 - W24 W21 - W24 W24 - W27 W24 - W30 W30 - W33

Beam Span20 feet

TABLE A

Beam Sizes

Beam Span: B1 (ft)


50 W10 - W16 W14 - W16 W16 - W21 W18 - W21 W21 - W27 Office

100 W12 - W16 W14 - W18 W16 - W24 W18 - W24 W21 - W27 Assembly

150 W14 - W18 W18 - W21 W18 - W24 W21 - W27 W24 - W30 Storage

SYSTEMS




50 Office

100 Assembly

150 Storage

Beam Span25 feet

W16 - W18 W16 - W18 W18 - W24 W21 - W27 W24 - W30

W18 - W21 W21 - W24 W21 - W27 W24 - W30 W27 - W33

W21 - W24 W21 - W24 W24 - W27 W30 - W33 W30 - W33




50 Office

100 Assembly

150 Storage

Beam Span30 feet

W16 - W21 W18 - W21 W18 - W24 W24 - W30 W27 - W30

W18 - W21 W21 - W24 W21 - W27 W27 - W30 W30 - W33

W21 - W24 W21 - W24 W24 - W27 W30 - W33 W33 - W36




50 Office

100 Assembly

150 Storage

Beam Span35 feet

W18 - W21 W21 - W24 W24 - W27 W24 - W27 W27 - W30

W21 - W24 W24 - W27 W24 - W30 W24 - W30 W30 - W33

W14 - W18 W18 - W21 W18 - W24 W21 - W27 W27 - W30




50 Office

100 Assembly

150 Storage

Beam Span40 feet

W21 - W24 W21 - W24 W24 - W27 W24 - W27 W27 - W33

W24 - W27 W24 - W27 W24 - W27 W27 - W30 W30 - W33

W21 - W24 W24 - W27 W30 - W36 W33 - W36W24 - W27

SYSTEMS

TABLE B25Girder Sizes



50 Office

100 Assembly

150 Storage

Beam Span25 feet

W16 - W18 W21 - W24 W24 - W27 W27 - W30 W27 - W33

W16 - W21 W18 - W24 W21 - W30 W27 - W30 W30 - W33

W18 - W24 W21 - W24 W24 - W27 W27 - W30 W30 - W36




50 Office

100 Assembly

150 Storage

Beam Span30 feet

W16 - W21 W18 - W24 W21 - W24 W24 - W27 W27 - W30

W18 - W24 W21 - W27 W21 - W24 W24 - W30 W24 - W33

W18 - W24 W24 - W30 W27 - W33 W27 - W33 W30 - W36




50 Office

100 Assembly

150 Storage

Beam Span35 feet

W18 - W24 W21 - W24 W21 - W27 W24 - W30 W27 - W33

W21 - W24 W21 - W24 W24 - W27 W27 - W30 W30 - W36

W21 - W24 W24 - W27 W27 - W33 W30 - W36 W33 - W36




50 Office

100 Assembly

150 Storage

Beam Span40 feet

W21 - W24 W21 - W24 W24 - W27 W27 - W30 W27 - W36

W24 - W27 W24 - W30 W27 - W30 W27 - W36 W33 - W36

W24 - W27 W24 - W30 W27 - W33 W30 - W36 W33 - W40

SYSTEMS

Tab l e s C t o C40

Design Critieria Floor Diagram

• Dead load includes system self weight (slab + steel)

• Superimposed dead load = 25 psf (partitions + MEP)

• Loads are uniformly distributed over bay area

• 4 1⁄4" Lightweight concrete topping• 2" Composite metal decking• 50 ksi steel yield• 3000 psi concrete strength• 3 Hour Fire Rating

TABLE CBeam Sizes

Beam Span: B1 (ft)


50 Office

100 Assembly

150 Storage

W10 - W16 W14 - W16 W16 - W21 W18 - W21 W21 - W27

W12 - W16 W14 - W18 W16 - W24 W21 - W24 W21 - W27

W14 - W16 W16 - W21 W18 - W24 W21 - W27 W24 - W30

TABLE C20Girder Sizes



50 Office

100 Assembly

150 Storage

W16 - W18 W18 - W21 W21 - W24 W21 - W24 W24 - W30

W16 - W18 W18 - W21 W21 - W24 W24 - W27 W24 - W30

W16 - W21 W18 - W21 W21 - W24 W24 - W27 W27 - W33

Beam Span20 feet

SYSTEMS




50 Office

100 Assembly

150 Storage

Beam Span25 feet

W16 - W18 W16 - W21 W21 - W24 W21 - W27 W24 - W27

W18 - W21 W18 - W24 W21 - W24 W24 - W30 W24 - W30

W18 - W21 W21 - W24 W24 - W30 W27 - W33 W30 - W36




50 Office

100 Assembly

150 Storage

Beam Span30 feet

W18 - W21 W18 - W24 W21 - W24 W24 - W27 W27 - W30

W18 - W21 W21 - W24 W21 - W30 W24 - W33 W27 - W36

W21 - W24 W24 - W30 W24 - W33 W27 - W33 W30 - W36




50 Office

100 Assembly

150 Storage

Beam Span35 feet

W18 - W24 W21 - W24 W24 - W27 W24 - W30 W27 - W30

W21 - W24 W21 - W27 W24 - W30 W27 - W33 W30 - W36

W24 - W27 W24 - W30 W27 - W30 W27 - W33 W30 - W36




50 Office

100 Assembly

150 Storage

Beam Span40 feet

W21 - W24 W21 - W24 W24 - W30 W27 - W30 W30 - W33

W24 - W27 W24 - W30 W24 - W30 W27 - W33 W30 - W36

W27 - W30 W27 - W30 W27 - W33 W30 - W36 W33 - W40

SYSTEMS

TABLE D25Girder Sizes


Live Load, psf 20 25 30 35 40

20

30

40

Beam Span25 feet

W16 - W18 W16 - W21 W21 - W24 W21 - W24 W24 - W27

W18 - W21 W18 - W21 W21 - W24 W21 - W27 W24 - W30

W18 - W21 W18 - W24 W21 - W24 W24 - W30 W27 - W33



Live Load, psf 20 25 30 35 40

20

30

40

Beam Span30 feet

W18 - W21 W18 - W24 W21 - W24 W24 - W27 W24 - W30

W18 - W21 W21 - W24 W21 - W30 W24 - W30 W27 - W33

W18 - W21 W21 - W27 W24 - W30 W27 - W30 W27 - W33



Live Load, psf 20 25 30 35 40

20

30

40

Beam Span35 feet

W18 - W24 W21 - W24 W24 - W27 W24 - W30 W27 - W30

W21 - W24 W21 - W24 W24 - W30 W24 - W30 W30 - W33

W21 - W24 W21 - W24 W24 - W30 W27 - W33 W30 - W36

SYSTEMS



Live Load, psf 20 25 30 35 40

20

30

40

Beam Span40 feet

W21 - W24 W21 - W24 W24 - W27 W27 - W30 W27 - W33

W21 - W24 W24 - W27 W24 - W30 W27 - W33 W30 - W33

W24 - W24 W24 - W30 W27 - W30 W27 - W33 W30 - W36

SYSTEMS

10 20 40 60 80 100

Space Frames

Joists "DLH / SLH" Series

Trusses - Fabricated

Plate Girders -Fabricated Beams

Long Spans

Girders (See Tables)

Beams (See Tables)

Noncomposite Slab

Composite Slab

Floor Framing

LH Series

K Series

Joists

Girders (See Tables)

Beams (See Tables)

6" Metal Deck

3" Metal Deck

1 1/2" Metal Deck

Roof Framing

Representative Span Ranges ofDifferent Structural Steel Components

Component Span Range, feet

TABLE E

Span Ranges

steel beams analysis and deign

Documents

structural member

member weight

member sizes

w18 member

design information

floor beam depths

range of member depths

w24 beam