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Engr. Nimfa Maren S. Tabucal1stSemester 2015-2016 1NMST/1st Sem 2015-2016

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5.1 Introduction

5.2 Yield Moment and Plastic Moment

5.3 Classification of Shapes

5.4 Bending Strength

5.5 Shear Strength

5.6 Deflection Limit

5.7 Design

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Beams are structural member designed tocarry transverse loads along its longitudinalaxis

Loads are transferred to points supportingthe beam

Classified based on their supports, location,

and function

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Classification of beam according to support:

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Simple Beam

Overhanging Beam

Continuous Beam

Cantilever Beam

Fixed Ended Beam

Propped Beam

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Classification of beam based on function:

Floor beam

Roof beam

Floor joistGirder

Stringer

Purlins

Rafter and Girt

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Assumptions:

1. Moments are applied in plane of symmetry ofcross section.

2. No axial load present.

3. No deformation on the transverse section ofelement after load application

4. Linear stress-strain diagram

5. Material of beam has same stress-strain

characteristics in compression as in tension.

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Where: A Total Cross-sectional Area

a Distance between centroids

of two-half areas

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Based on plate local buckling

AISC classifies shapes according to the ff:

Compact Section

Noncompact SectionSlender-Element Section

Depends on width-to-thickness ratio,

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Compact Section

- sections which can develop a fully plasticstress distribution

- flange is continuously connected to web

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Noncompact Section

- sections which can develop yield stress incompression before local buckling occurs

- will not resist inelastic local buckling

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Procedure:

1. Determine the classification of shape: Compact

Noncompact

Slender2. If compact, check for the ff:

Yielding

Lateral Torsional Buckling (LTB)

3. If noncompact, check for the ff: LTB

Flange Local Buckling (FLB)

Web Local Buckling (WLB)

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Factors

Yielding Strength

(LRFD)

(ASD)

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Lateral Torsional Buckling LTB

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Lateral Torsional Buckling LTB

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Lateral Torsional Buckling LTB

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Lateral Torsional Buckling LTB

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Flange Local Buckling

No FLB

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Determine the required flexural strength of

W18x50, ASTM A992 beam shown below. The beam issimply supported and is braced at both ends and atcenter point. Consider LRFD.

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Yielding

Flange Local Buckling

Compact Flange

Non Compact Flange

Slender Flange

yyyypn SFZFMM 6.1

yyyypn SFZFMM 6.1

pfrf

pf

yyppn

SFMMM

7.0

ycrn SFM 269.0

EFcr

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Determine the required flexural strength of

W12x58, ASTM A992 beam shown below. Uniformloads are applied at the beams weak axis. The beam issimply supported and is braced at both ends only.Consider LRFD.

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Shear Limit State for Beams

Shear yielding of web

- excessive deformation

Shear buckling of web

- buckling of slender webs prior toyielding

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(LRFD)

(ASD)

(LRFD)

(ASD)

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Nominal Shear Strength

applies for members with unstiffened andstiffened webs

For singly or doubly symmetric membersand channels subject to shear in plane ofweb

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Nominal Shear Strength

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Methods

Double Integration

Moment-Area

Conjugate-Beam Energy Methods

Unit Load Method

Slope-Deflection Method Three-moment Equation

Matrix Analysis

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Fixed End Moments

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Select a standard hot-rolled shape of

A992 steel for a simply supported beam. Thebeam has continuous lateral support and mustsupport a uniform service live load of 4.5kips/ft applied to its strong axis. Themaximum permissible live load deflection isL/240.