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User's Manual_Shear

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User's Manual_Shear

    SHEAR DESIGNAASHTO LRFD 2007 EDITION

Issue Date Subject of issue / Revision

    1 06/05/2008 First Issue

     Issue : 1 Nom Date Visa Written by : TEODOR DOBRINESCU Checked by : S.MONTENS / T.DUCLOS A.CHEIKH MHAMED Approved by : Y. GAUTHIER

    SHEAR DESIGN

    ACCORDING TO

    AASHTO LRFD 2007 EDITION

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    SHEAR DESIGNAASHTO LRFD 2007 EDITION

    TABLE OF CONTENTS

    ?0 : INTRODUCTION & NOTATION ............................................. 3 0.1 INTRODUCTION ....................................................................................................................................................... 4 0.2 NOTATIONS............................................................................................................................................................. 6

    ?1 : SHEAR DESIGN ........................................................................ 8 1.1 FLOWCHART ........................................................................................................................................................... 9 1.2 AASHTO LRFD 2007 EXTRACT ............................................................................................................................ 10 1.3 VALIDATION BY MANUAL CALCULATION ................................................................................................................ 14 1.4 SPREADSHEETS LIMITS ......................................................................................................................................... 16 1.5 INTERFACE PRESENTATION .................................................................................................................................... 18

    ?2 CONCLUSION ........................................................................... 22

    ?3 BIBLIOGRAPHY ....................................................................... 24

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SHEAR DESIGNAASHTO LRFD 2007 EDITION

?0 : Introduction & Notation

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    SHEAR DESIGNAASHTO LRFD 2007 EDITION

    0.1 Introduction

    The present user’s manual treats the spreadsheet used to design at shear composite sections at the ultimate limit state.

    The code used as base for the spreadsheets’ development was the 2007 edition of the American code AASHTO LRFD.

    The spreadsheets can be used to find the necessary transverse reinforcement for a composite flanged beam. In order to accomplish that computation the user has to enter the INPUT data (geometrical, material characteristics, sectional force effects, etc).

    The design procedures follow a sectional model, which is appropriate for the design of typical bridge girders, slabs, and other regions of components where the assumptions of traditional engineering beam theory are valid. This theory assumes that the response at a particular section depends only on the calculated values of the sectional force effects, i.e., moment, shear, axial load, and torsion, and does not consider the specific details of how the force effects were introduced in the member. The general section of a flanged beam is shown below:

    CcNeutral

     Axis

    bvShearderesistancehdvarea(bv*dv)

    Aps

    AsT

     Figure 1 Schematic view of a flanged section as defined in the spreadsheet

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    SHEAR DESIGNAASHTO LRFD 2007 EDITION

    The design method used distinguishes three components of the shear resistance of a concrete member that is:

    ; Vc a component that relies on the tensile stress in the concrete

    ; Vs a component that relies on the tensile stresses in the transverse reinforcement

    ; Vp the vertical component of the prestressing force

    The shear failure mechanisms can be generally classified in two branches:

    ; Fracture through diagonal

    tension

    ; Failure through diagonal

    compression

The first of these can be addressed by using stirrups or other reinforcement to “sow” the crack

    The failure by compression means that the concrete in the web of the beam crushes prior to yield of the transverse reinforcement. Due to the brittle compression failure mechanism, the approach of the model used, intended to ensure that the effective shear concrete (bv*av) is enough to ensure a fracture by steel yielding and not concrete crushing.

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    0.2 Notations

    AASHTO EXCEL Description Symbol Notation

    average stress in the prestressing steel ffps ps

    specified tensile strength of prestressing steel f fpu pu

    0,70 * fpu f fpo po

    specified minimum yielding stress for tensioned steel f fy y

    specified compressive strength of concrete for use in design f’f_c c

    modulus of elasticity for bar EEs s

    area of unbonded prestressing steel EEp p

    modulus of elasticity for concrete EEc c

    total area of prestressing steel AAps ps

    area of mild steel tension reinforcement AAs s

    area of transverse reinforcement within distance s A Av v

    number of stirrups’ legs in the section N?legs no

    stirrups' diameter D diam

    spacing of transverse reinforcement (stirrups) s s

    minimum web width measured parallel to the neutral axis, between the resultants of the tensile bv bv and compressive forces due to flexure

    width of web b bw w

    overall depth hh

    distance from extreme compression fiber to the centroid of the tensile force in the tensile d de ereinforcement

    segmental post tensioned concrete box girder bridge (S.PT.C.B.G.B) type type

    the shortest dimension of the cross section; ONLY for S.PT.C.B.G.B shortshort

    crack spacing parameter 5.8.3.4.2 [1] sxsx

    maximum aggregate size ag ag

    crack spacing parameter 5.8.3.4.2 4 -[1] sxe sxe

    angle of inclination of transverse reinforcement to longitudinal axis α alpha

    factored moment at the section M Mu u

    factored shear force at section VVu u

    factored axial force at section (positive if traction) N Nu u

    component in the direction of the applied shear of the effective prestressing force; positive if VVp p resisting the applied shear

    resistance factor for moment resistance φ phif f

    resistance factor for shear resistance φ phiv v

    resistance factor for axial resistance φ phic c

    nominal flexural resistance MMn n

    effective shear depth d dv v

    shear stress on the concrete v v

    maximum spacing of transverse reinforcement ssmax max min minimum transverse reinforcement AAvmin v

    axial strain at middepth (dv/2) of the member εepsx x

    ratio of shear stress in the concrete and its compressive strength v/f’c v/f_c

    angle between cracks and longitudinal reinforcement θ theta

    factor indicating the ability of diagonally cracked concrete to transmit tension β beta

    nominal shear resistance provided by tensile stresses in the concrete V Vc cmin shear resistance provided by the minimum transverse reinforcement VVs_min s

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    shear necessary shear resistance of steel based on 5.8.3.3 1 [1] Vs_nec_v Vs,neclong necessary shear resistance of steel based on 5.8.3.5 1 [1] VVs_nec_f s,nec

    necessary shear resistance of transverse reinforcement VVs_nec s,nec

    necessary transverse reinforcement area AAv_nec v,nec

    required stirrups' minimal diameter D Dmin min

Table 1 Notations used

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?1 : Shear Design

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    1.1 Flowchart

    Here is presented the flowchart of the algorithm:

     Remark: There is no VBA code implemented, therefore

    the OUTPUT data changes automatically with

     any change in the INPUT data.

    Figure 2 Flowchart for calculating sections with bonded tendons

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    1.2 AASHTO LRFD

    2007 extract

    Here below is an extract of the code used as base for the sheet:

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