3.5 Reinforced Concrete Section Properties


 Bethanie Hudson
 11 months ago
 Views:
Transcription
1 CHAPER 3: Reinforced Concrete Slabs and Beams 3.5 Reinforced Concrete Section Properties Description his application calculates gross section moment of inertia neglecting reinforcement, moment of inertia of the cracked section transformed to concrete, and effective moment of inertia for beams, rectangular beams, or slabs, in accordance with Section of ACI 318. he user must enter the strengths of the concrete and the reinforcement, the unit weight of concrete, strength reduction factor for lightweight concrete, beam dimensions and slab thickness, maximum moments in the member at the stage deflection is computed, crosssectional areas of reinforcement and distances from the extreme compression fiber to the centroid of the tension and compression reinforcement. A summary of input and computed values is shown on pages Reference: ACI "Building Code Requirements for Reinforced Concrete." (Revised 199)
2 Input Notation Bending Moment Diagram for Beam with Uniformly Distributed Load Input Variables Enter flange width, flange thickness, beam web width and overall member thickness (for slabs enter the same width for the flange and the beam web). Flange width: b f 7 Overall thickness of member: Beam web width: Flange thickness: h 0 b w 10 h f 4.0 Enter maximum moments, effective depths and tension reinforcement areas (the first and third elements for the left and right negative moment sections, and the second for the positive moment section): Maximum moments in member at stage deflection is computed: M a [ ]
3 ension Reinforcement Distances from the extreme compression fiber to the centroid of the tension reinforcement: Crosssectional areas of tension reinforcement: d [ ] A s [ ] Compression Reinforcement (if used) Continuous top bars, or bottom bars lapped at supports, may be included as compression reinforcement in calculating cracked section properties. Enter 0 for each element of d' and A's where compression reinforcement is not used. Distances from the extreme compression fiber to the centroid of the compression reinforcement: d' [ ] Crosssectional areas of compression reinforcement: A' s [ ] Computed Variables fr modulus of rupture of concrete (ACI 318, ) Mcr cracking moment as defined in ACI 318, y distance from the tension reinforcement to the neutral axis of the cracked section yt distance from the neutral axis of the gross section to the top of the section yb distance from the neutral axis of the gross section to the bottom of the section kd distance from the extreme fiber in compression to the neutral axis of the cracked section Ig moment of inertia of gross concrete section about centroidal axis, neglecting reinforcement Icr moment of inertia of the cracked section transformed to concrete Ie effective moment of inertia for computation of deflection (ACI 318, ) Material Properties and Constants Enter concrete and reinforcement strengths, unit weight of concrete and the strength reduction factor for lightweight concrete: Specified compressive strength of concrete: Unit weight of concrete: Specified yield strength of nonprestressed reinforcement: Strength reduction factor for lightweight concrete applied to fr (0.75 for alllightweight and 0.85 for sandlightweight concrete (ACI 318, (b)): Modulus of elasticity of reinforcement (ACI 318, 8.5.): f' c 4 w c 145 f y 60 k v 1 E s 9000
4 Modulus of elasticity of concrete for unit weights between 90 pcf and 155 pcf (ACI 318, 8.5.1): E c w c f' c E c = 3644 ksi Modular ratio of elasticity: n E s = E c If preferred, the modular ratio of elasticity may be rounded to an even number at this point:
5 Calculations he specified yield strength of the reinforcement may not exceed 80 ksi in accordance with ACI 318, Section 9.4: f y 80, f y, 80 = 60 ksi f y f y Distance from the neutral axis of the gross section to the top of the section: y t 1 b w h + b f b w h f y t = in b w h + b f b w h f Distance from the neutral axis of the gross section to the bottom of the section: y b h y t = in y b Gross section moment of inertia: I g 1 b w h 3 + b f b w h f3 + b w h + 1 h y t b f b w h f h f y t I g = in 4 Neutral axis location for positive moment section Sum of moments about the neutral axis as functions of kd: 1) Neutral axis within the slab f1 (kd) b f kd n A s1 d kd + ( n 1) A' s1 kd 1 1 he neutral axis for flanged beams may be above the level of the top reinforcement. In that case the effective area of of top reinforcement will be underestimated by 1/n x A's, but the top reinforcement will be in tension and will have negligible effect on the location of kd. ) Neutral axis within the beam web f (kd) b w kd + b f b w h f kd h f n A s1 d kd + ( n 1) A' s1 kd 1 1
6 Initialize vector kd: i 0 kd 0 i Guess value of kd': kd' h f kd' ( f1 (kd'), kd') kd' =.13 in kd 1 kd' h f, kd', ( f (kd'), kd') kd =.13 in 1 Subscript 1 refers to the positive moment section  the second element in a three element vector. Neutral axis locations for negative moment sections Sum of moments about the neutral axis as functions of kd: 1) Neutral axis within the slab (this case will govern for a very shallow beam web projection relative to the slab thickness) Left end negative moment section, f3 (kd) b w kd kd + h + b f b w f h n A s0 d kd + ( n 1) A' s0 kd 0 0 Right end negative moment section, f4 (kd) b w kd kd + h + b f b w f h n A s d kd + ( n 1) A' s kd Subscripts 0 and refer to the left and right end sections  the first and third elements in a three element vector. ) Neutral axis within the beam web Left end negative moment section, f5 (kd) b w kd n A s0 d kd + ( n 1) A' s0 kd 0 0 Right end negative moment section, f6 (kd) b w kd n A s d kd + ( n 1) A' s kd
7 Guess value of kd': kd for section at left end: kd' h 3 kd kd,, = 0 0 h h f ( f3 (kd'), kd') ( f5 (kd'), kd') 4.0 Guess value of kd': kd for section at right end: kd' h 3 kd kd,, h h f ( f4 (kd'), kd') ( f6 (kd'), kd') kd = in Cracked section moment of inertia for positive moment section: I cr1 n A s1 d kd + ( n 1) A' s1 kd + if kd h f 1 3 b f else 1 3 b w I cr1 = in 4 kd 3 1 kd b f b w h f b f b w h f kd 1 h f Cracked section moment of inertia for negative moment sections: Left end section, I cr b w kd 3 n A s0 d kd ( n 1) A' s0 kd kd > h h f b f b w kd h+ h 0 f I cr0 = in 4 Right end section, I cr b w kd 3 n A s d kd ( n 1) A' s kd kd > h h f b f b w kd h+ h f I cr = in 4
8 Note: Modulus of rupture (if available, the value of ft / 6.7 may be substituted for f'c and kv defined as 1, in accordance with ACI 318, Section (a)): f r k v 7.5 f' c k v = 1 f r = Cracking moment for positive moment section: M cr1 f r I g M cr1 = kip ft y b Cracking moments for negative moment sections: M cr0 f r I g M cr0 = kip ft y t M cr f r I g M cr = kip ft y t Effective moments of inertia (ACI 318, Eq. (97)), modified to limit Ie to Ig: i 0 I ei 3 M cri 3 M cri M cri > M ai, I g, I g + M ai 1 M ai I cri I e = in 4 Average of the moments of inertia at the negative and positive moment sections: Avg_I e 1 I e0 + I e + I e1 Avg_I e = in 4 he average effective moment of inertia may be used for computation of deflections given in ACI 318, Section
9 Summary Input Specified compressive strength of concrete: f' c = 4 Specified yield strength of nonprestressed reinforcement: f y = 60 ksi Unit weight of concrete: w c = 145 Modulus of elasticity of reinforcement: E s = 9000 Flange width: b f = 7 in Overall thickness of member: Strength reduction factor for lightweight concrete applied to fr (ACI 318, ): h = 0 k v = 1 Beam web width: b w = 10 Flange thickness: h f = 4 Maximum moments in member at stage deflection is computed: M a = [ ] ft Depths from the extreme compression fiber to the centroid of the tension reinforcement: d = [ ] Crosssectional areas of tension reinforcement: A s = [ ] Depths from the extreme compression fiber to the centroid of the compression reinforcement: d' = [ ] Crosssectional areas of compression reinforcement: A' s = [ ]
10 Computed Variables Modulus of elasticity of concrete: E c = 3644 ksi Distance from the neutral axis to the top of the gross section: Gross moment of inertia neglecting reinforcement: Cracked section moments of inertia: y t = in I g = in I cr = in Effective moments of inertia: I e = in 4 Modular ratio of elasticity: n = Distance from the neutral axis to the top of the gross section: y b = in Note 1st row of the Icr and Ie vectors is the leftend negative moment section, nd row is the midspan positive moment section, and the third row is rightend negative moment section. Average effective moment of inertia for computation of deflections: Avg_I e = in 4
This procedure covers the determination of the moment of inertia about the neutral axis.
327 Sample Problems Problem 16.1 The moment of inertia about the neutral axis for the Tbeam shown is most nearly (A) 36 in 4 (C) 236 in 4 (B) 136 in 4 (D) 736 in 4 This procedure covers the determination
More information3.4 Reinforced Concrete Beams  Size Selection
CHAPER 3: Reinforced Concrete Slabs and Beams 3.4 Reinforced Concrete Beams  Size Selection Description his application calculates the spacing for shear reinforcement of a concrete beam supporting a uniformly
More informationServiceability Deflection calculation
Chp6:Lecture Goals Serviceability Deflection calculation Deflection example Structural Design Profession is concerned with: Limit States Philosophy: Strength Limit State (safetyfracture, fatigue, overturning
More information4.3 Moment Magnification
CHAPTER 4: Reinforced Concrete Columns 4.3 Moment Magnification Description An ordinary or first order frame analysis does not include either the effects of the lateral sidesway deflections of the column
More informationFlexure: Behavior and Nominal Strength of Beam Sections
4 5000 4000 (increased d ) (increased f (increased A s or f y ) c or b) Flexure: Behavior and Nominal Strength of Beam Sections Moment (kipin.) 3000 2000 1000 0 0 (basic) (A s 0.5A s ) 0.0005 0.001 0.0015
More informationAppendix J. Example of Proposed Changes
Appendix J Example of Proposed Changes J.1 Introduction The proposed changes are illustrated with reference to a 200ft, single span, Washington DOT WF bridge girder with debonded strands and no skew.
More informationSPECIFIC VERIFICATION Chapter 5
As = 736624/(0.5*413.69) = 3562 mm 2 (ADAPT 3569 mm 2, B29, C6) Data Block 27  Compressive Stresses The initial compressive strength, f ci, is the strength entered in the Material/Concrete input screen.
More informationSERVICEABILITY OF BEAMS AND ONEWAY SLABS
CHAPTER REINFORCED CONCRETE Reinforced Concrete Design A Fundamental Approach  Fifth Edition Fifth Edition SERVICEABILITY OF BEAMS AND ONEWAY SLABS A. J. Clark School of Engineering Department of Civil
More informationORIGIN 0. PTC_CE_BSD_7.2_us_mp.mcdx. Mathcad Enabled Content Copyright 2011 Knovel Corp.
PC_CE_BSD_7._us_mp.mcdx Copyright 011 Knovel Corp. Building Structural Design homas P. Magner, P.E. 011 Parametric echnology Corp. Chapter 7: Reinforced Concrete Column and Wall Footings 7. Pile Footings
More informationε t increases from the compressioncontrolled Figure 9.15: Adjusted interaction diagram
CHAPTER NINE COLUMNS 4 b. The modified axial strength in compression is reduced to account for accidental eccentricity. The magnitude of axial force evaluated in step (a) is multiplied by 0.80 in case
More informationLecture04 Design of RC Members for Shear and Torsion
Lecture04 Design of RC Members for Shear and Torsion By: Prof. Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk www.drqaisarali.com 1 Topics Addressed Design of
More informationLecture05 Serviceability Requirements & Development of Reinforcement
Lecture05 Serviceability Requirements & Development of Reinforcement By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk www.drqaisarali.com 1 Section 1: Deflections
More informationMECHANICS OF MATERIALS Sample Problem 4.2
Sample Problem 4. SOLUTON: Based on the cross section geometry, calculate the location of the section centroid and moment of inertia. ya ( + Y Ad ) A A castiron machine part is acted upon by a knm couple.
More information5. What is the moment of inertia about the x  x axis of the rectangular beam shown?
1 of 5 Continuing Education Course #274 What Every Engineer Should Know About Structures Part D  Bending Strength Of Materials NOTE: The following question was revised on 15 August 2018 1. The moment
More informationDr. Hazim Dwairi. Example: Continuous beam deflection
Example: Continuous beam deflection Analyze the shortterm and ultimate longterm deflections of endspan of multispan beam shown below. Ignore comp steel Beam spacing = 3000 mm b eff = 9000/4 = 2250
More informationColumn Design. Columns Axial Load and Bending
Column Design MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE VI Dr. Jason E. Charalambides = = Columns Axial Load and Bending We tend to have this image of columns that we envision
More informationUNIT III DEFLECTION OF BEAMS 1. What are the methods for finding out the slope and deflection at a section? The important methods used for finding out the slope and deflection at a section in a loaded
More informationInteraction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements
Interaction Diagram Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Interaction Diagram  Dumbbell Concrete Shear Wall Unsymmetrical Boundary Elements Investigate the capacity for the irregular
More informationPart 1 is to be completed without notes, beam tables or a calculator. DO NOT turn Part 2 over until you have completed and turned in Part 1.
NAME CM 3505 Fall 06 Test 2 Part 1 is to be completed without notes, beam tables or a calculator. Part 2 is to be completed after turning in Part 1. DO NOT turn Part 2 over until you have completed and
More informationA.2 AASHTO Type IV, LRFD Specifications
A.2 AASHTO Type IV, LRFD Specifications A.2.1 INTRODUCTION A.2.2 DESIGN PARAMETERS 1'5.0" Detailed example showing sample calculations for design of typical Interior AASHTO Type IV prestressed concrete
More informationPUNCHING SHEAR CALCULATIONS 1 ACI 318; ADAPTPT
Structural Concrete Software System TN191_PT7_punching_shear_aci_4 011505 PUNCHING SHEAR CALCULATIONS 1 ACI 318; ADAPTPT 1. OVERVIEW Punching shear calculation applies to columnsupported slabs, classified
More informationPURE BENDING. If a simply supported beam carries two point loads of 10 kn as shown in the following figure, pure bending occurs at segment BC.
BENDING STRESS The effect of a bending moment applied to a crosssection of a beam is to induce a state of stress across that section. These stresses are known as bending stresses and they act normally
More informationDesign of Reinforced Concrete Beam for Shear
Lecture 06 Design of Reinforced Concrete Beam for Shear By: Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk Topics Addressed Shear Stresses in Rectangular Beams Diagonal Tension
More informationProperties of Sections
ARCH 314 Structures I Test Primer Questions Dr.Ing. Peter von Buelow Properties of Sections 1. Select all that apply to the characteristics of the Center of Gravity: A) 1. The point about which the body
More informationLecture03 Design of Reinforced Concrete Members for Flexure and Axial Loads
Lecture03 Design of Reinforced Concrete Members for Flexure and Axial Loads By: Prof. Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk www.drqaisarali.com Prof.
More informationDesign of Reinforced Concrete Beam for Shear
Lecture 06 Design of Reinforced Concrete Beam for Shear By: Prof Dr. Qaisar Ali Civil Engineering Department UET Peshawar drqaisarali@uetpeshawar.edu.pk 1 Topics Addressed Shear Stresses in Rectangular
More informationLecture 7 TwoWay Slabs
Lecture 7 TwoWay Slabs Twoway slabs have tension reinforcing spanning in BOTH directions, and may take the general form of one of the following: Types of TwoWay Slab Systems Lecture 7 Page 1 of 13 The
More information= 50 ksi. The maximum beam deflection Δ max is not = R B. = 30 kips. Notes for Strength of Materials, ET 200
Notes for Strength of Materials, ET 00 Steel Six Easy Steps Steel beam design is about selecting the lightest steel beam that will support the load without exceeding the bending strength or shear strength
More informationtwenty one concrete construction: shear & deflection ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture
ARCHITECTURAL STRUCTURES: FORM, BEHAVIOR, AND DESIGN DR. ANNE NICHOLS SUMMER 2014 lecture twenty one concrete construction: Copyright Kirk Martini shear & deflection Concrete Shear 1 Shear in Concrete
More informationSway Column Example. PCA Notes on ACI 318
Sway Column Example PCA Notes on ACI 318 ASDIP Concrete is available for purchase online at www.asdipsoft.com Example 11.2 Slenderness Effects for Columns in a Sway Frame Design columns C1 and C2 in the
More informationLecture Example. Steel Deck (info from Vulcraft Steel Roof and Floor Deck Manual)
1 / 8 Geometry beam span L 40 ft Steel Wide Flange Beam: beam spacing s beam 10 ft F y 50 ksi construction live load LL construc 20 psf row 148 live load LL 150 psf unit weight of concrete UW conc 145
More informationIntroduction to Structural Member Properties
Introduction to Structural Member Properties Structural Member Properties Moment of Inertia (I): a mathematical property of a crosssection (measured in inches 4 or in 4 ) that gives important information
More informationDEFLECTION CALCULATIONS (from Nilson and Nawy)
DEFLECTION CALCULATIONS (from Nilson and Nawy) The deflection of a uniformly loaded flat plate, flat slab, or twoway slab supported by beams on column lines can be calculated by an equivalent method that
More informationMoment Redistribution
TIME SAVING DESIGN AID Page 1 of 23 A 3span continuous beam has centertocenter span lengths of 30 ft0 in. The beam is 20 in. by 28 in. and all columns are 20 in. by 20 in. In this example, the beam
More informationAppendix K Design Examples
Appendix K Design Examples Example 1 * TwoSpan IGirder Bridge Continuous for Live Loads AASHTO Type IV I girder Zero Skew (a) Bridge Deck The bridge deck reinforcement using A615 rebars is shown below.
More informationSoftware Verification
PROGRAM NAME: SAFE 014 EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 161 depicts a plot of the uncracked and cracked conditions, 1 State 1, and, State,
More informationDesign 1 Calculations
Design 1 Calculations The following calculations are based on the method employed by Java Module A and are consistent with ACI31899. The values in Fig. 1 below were taken from the Design 1 Example found
More informationChapter 8. Shear and Diagonal Tension
Chapter 8. and Diagonal Tension 8.1. READING ASSIGNMENT Text Chapter 4; Sections 4.14.5 Code Chapter 11; Sections 11.1.1, 11.3, 11.5.1, 11.5.3, 11.5.4, 11.5.5.1, and 11.5.6 8.2. INTRODUCTION OF SHEAR
More informationhost structure (S.F.D.)
TABLE 00.4 FBC Typical Mansard Beam [AAF] Allowable Span of Mansard Screen Enclosure SelfMating Beams in accordance with requirements of Table 00.4 (and the 005 Aluminum Design Manual) using 6005T5 alloy:
More informationPROPOSED SATSANG HALL TECHNICAL REPORT
PROPOSED SATSANG HALL  VERTICAL STRIP V1 1  ADAPT CORPORATION STRUCTURAL CONCRETE SOFTWARE SYSTEM 1733 Woodside Road, Suite
More informationAnalytical Model for Estimating LongTerm Deflections of TwoWay Reinforced Concrete Slabs *
Analytical Model for Estimating LongTerm Deflections of TwoWay Reinforced Concrete Slabs * Dr. Bayan Salim AlNu'man Civil Engineering Department, College of Engineering AlMustansiriya University, Baghdad,
More informationDerivation of minimum steel ratio: based on service applied stresses
MATEC Web of Conferences, () DOI:./ matecconf/ Derivation of minimum steel ratio: based on service applied stresses Humam AL Sebai,*, Salah Al Toubat University of Sharjah, Sharjah city, UAE Abstract.
More informationThis Technical Note describes how the program checks column capacity or designs reinforced concrete columns when the ACI code is selected.
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA DECEMBER 2001 CONCRETE FRAME DESIGN ACI31899 Technical Note This Technical Note describes how the program checks column capacity or designs reinforced
More informationKarbala University College of Engineering Department of Civil Eng. Lecturer: Dr. Jawad T. Abodi
Chapter 05 Structural Steel Design According to the AISC Manual 13 th Edition Analysis and Design of Beams By Dr. Jawad Talib AlNasrawi University of Karbala Department of Civil Engineering 71 Introduction
More informationChapter 8: Bending and Shear Stresses in Beams
Chapter 8: Bending and Shear Stresses in Beams Introduction One of the earliest studies concerned with the strength and deflection of beams was conducted by Galileo Galilei. Galileo was the first to discuss
More informationHomework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. Fall 2004
Homework No. 1 MAE/CE 459/559 John A. Gilbert, Ph.D. 1. A beam is loaded as shown. The dimensions of the cross section appear in the insert. the figure. Draw a complete free body diagram showing an equivalent
More information7 TRANSVERSE SHEAR transverse shear stress longitudinal shear stresses
7 TRANSVERSE SHEAR Before we develop a relationship that describes the shearstress distribution over the cross section of a beam, we will make some preliminary remarks regarding the way shear acts within
More informationNAME: Given Formulae: Law of Cosines: Law of Sines:
NME: Given Formulae: Law of Cosines: EXM 3 PST PROBLEMS (LESSONS 21 TO 28) 100 points Thursday, November 16, 2017, 7pm to 9:30, Room 200 You are allowed to use a calculator and drawing equipment, only.
More informationPurpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on Exam 3.
ES230 STRENGTH OF MTERILS Exam 3 Study Guide Exam 3: Wednesday, March 8 th inclass Updated 3/3/17 Purpose of this Guide: To thoroughly prepare students for the exact types of problems that will be on
More informationGeneration of Biaxial Interaction Surfaces
COPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA AUGUST 2002 CONCRETE FRAE DESIGN BS 811097 Technical Note This Technical Note describes how the program checks column capacity or designs reinforced
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationFailure in Flexure. Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas
Introduction to Steel Design, Tensile Steel Members Modes of Failure & Effective Areas MORGAN STATE UNIVERSITY SCHOOL OF ARCHITECTURE AND PLANNING LECTURE VIII Dr. Jason E. Charalambides Failure in Flexure!
More informationSoftware Verification
EXAMPLE 16 racked Slab Analysis RAKED ANALYSIS METHOD The moment curvature diagram shown in Figure 161 depicts a plot of the uncracked and cracked conditions, Ψ 1 State 1, and, Ψ State, for a reinforced
More informationSeismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design
Seismic Pushover Analysis Using AASHTO Guide Specifications for LRFD Seismic Bridge Design Elmer E. Marx, Alaska Department of Transportation and Public Facilities Michael Keever, California Department
More informationPrestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension
Prestressed concrete = Precompression concrete Precompression stresses is applied at the place when tensile stress occur Concrete weak in tension but strong in compression Steel tendon is first stressed
More informationDesign of Reinforced Concrete Structures (II)
Design of Reinforced Concrete Structures (II) Discussion Eng. Mohammed R. Kuheil Review The thickness of oneway ribbed slabs After finding the value of total load (Dead and live loads), the elements are
More informationFigure 1: Representative strip. = = 3.70 m. min. per unit length of the selected strip: Own weight of slab = = 0.
Example (8.1): Using the ACI Code approximate structural analysis, design for a warehouse, a continuous oneway solid slab supported on beams 4.0 m apart as shown in Figure 1. Assume that the beam webs
More information1/29/2010 Page 2 of 65 1/29/2010 Page 3 of 65 1/29/2010 Page 4 of 65 Project Information 1/29/2010 Page 5 of 65 Muckleshoot Indian Tribe Project Number 09118 West Detention Vault West Vault City of Auburn
More informationA Simply supported beam with a concentrated load at midspan: Loading Stages
A Simply supported beam with a concentrated load at midspan: Loading Stages P L/2 L PL/4 MOMNT F b < 1 lastic F b = 2 lastic F b = 3 lastoplastic 4 F b = Plastic hinge Plastic Dr. M.. Haque, P.. (LRFD:
More informationReinforced Concrete Structures
Reinforced Concrete Structures MIM 232E Dr. Haluk Sesigür I.T.U. Faculty of Architecture Structural and Earthquake Engineering WG Ultimate Strength Theory Design of Singly Reinforced Rectangular Beams
More informationCHAPTER 3 VERIFICATION OF PROPOSED EQUATIONS FOR THE EFFECTIVE MOMENT OF INERTIA OF STEEL JOIST  CONCRETE SLAB SYSTEMS
CHAPTER 3 VERIFICATION OF PROPOSED EQUATIONS FOR THE EFFECTIVE MOMENT OF INERTIA OF STEEL JOIST  CONCRETE SLAB SYSTEMS 3.1 Overview The proposed equations in the AISC Guide (Murray et al. 1997) for the
More information9.5 Compression Members
9.5 Compression Members This section covers the following topics. Introduction Analysis Development of Interaction Diagram Effect of Prestressing Force 9.5.1 Introduction Prestressing is meaningful when
More informationCHAPTER 6: ULTIMATE LIMIT STATE
CHAPTER 6: ULTIMATE LIMIT STATE 6.1 GENERAL It shall be in accordance with JSCE Standard Specification (Design), 6.1. The collapse mechanism in statically indeterminate structures shall not be considered.
More informationSTEEL BUILDINGS IN EUROPE. MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite Beams
STEEL BUILDINGS IN EUROPE MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite Beams MultiStorey Steel Buildings Part 10: Technical Software Specification for Composite
More informationSERVICEABILITY LIMIT STATE DESIGN
CHAPTER 11 SERVICEABILITY LIMIT STATE DESIGN Article 49. Cracking Limit State 49.1 General considerations In the case of verifications relating to Cracking Limit State, the effects of actions comprise
More informationMade by SMH Date Aug Checked by NRB Date Dec Revised by MEB Date April 2006
Job No. OSM 4 Sheet 1 of 8 Rev B Telephone: (0144) 45 Fax: (0144) 944 Made b SMH Date Aug 001 Checked b NRB Date Dec 001 Revised b MEB Date April 00 DESIGN EXAMPLE 9  BEAM WITH UNRESTRAINED COMPRESSION
More informationTORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES)
Page1 TORSION INCLUDING WARPING OF OPEN SECTIONS (I, C, Z, T AND L SHAPES) Restrained warping for the torsion of thinwall open sections is not included in most commonly used frame analysis programs. Almost
More informationThe plastic moment capacity of a composite crosssection is calculated in the program on the following basis (BS 4.4.2):
COMPUTERS AND STRUCTURES, INC., BERKELEY, CALIFORNIA SEPTEMBER 2002 COMPOSITE BEAM DESIGN BS 595090 Technical Note Composite Plastic Moment Capacity for Positive Bending This Technical Note describes
More informationRoadway Grade = m, amsl HWM = Roadway grade dictates elevation of superstructure and not minimum free board requirement.
Example on Design of Slab Bridge Design Data and Specifications Chapter 5 SUPERSTRUCTURES Superstructure consists of 10m slab, 36m box girder and 10m Tgirder all simply supported. Only the design of Slab
More informationComposite bridge design (EN19942) Bridge modelling and structural analysis
EUROCODES Bridges: Background and applications Dissemination of information for training Vienna, 46 October 2010 1 Composite bridge design (EN19942) Bridge modelling and structural analysis Laurence
More informationSamantha Ramirez, MSE
Samantha Ramirez, MSE Centroids The centroid of an area refers to the point that defines the geometric center for the area. In cases where the area has an axis of symmetry, the centroid will lie along
More informationCHAPTER 4. Stresses in Beams
CHAPTER 4 Stresses in Beams Problem 1. A rolled steel joint (RSJ) of section has top and bottom flanges 150 mm 5 mm and web of size 00 mm 1 mm. t is used as a simply supported beam over a span of 4 m
More informationTherefore, for all members designed according to ACI 318 Code, f s =f y at failure, and the nominal strength is given by:
5.11. Underreinforced Beams (Read Sect. 3.4b oour text) We want the reinforced concrete beams to fail in tension because is not a sudden failure. Therefore, following Figure 5.3, you have to make sure
More informationExternal Work. When a force F undergoes a displacement dx in the same direction i as the force, the work done is
Structure Analysis I Chapter 9 Deflection Energy Method External Work Energy Method When a force F undergoes a displacement dx in the same direction i as the force, the work done is du e = F dx If the
More informationExperimental Lab. Principles of Superposition
Experimental Lab Principles of Superposition Objective: The objective of this lab is to demonstrate and validate the principle of superposition using both an experimental lab and theory. For this lab you
More informationSimplified procedures for calculation of instantaneous and longterm deflections of reinforced concrete beams
Simplified procedures for calculation of instantaneous and longterm deflections of reinforced concrete beams José Milton de Araújo 1 Department of Materials and Construction, University of Rio Grande
More informationFinal Report. Predicting of the stiffness of cracked reinforced concrete structure. Author: Yongzhen Li
Predicting of the stiffness of cracked reinforced concrete structure Final Report Predicting of the Stiffness of Cracked Reinforced Concrete Structures Author: 1531344 Delft University of Technology Faculty
More informationCOLUMNS: BUCKLING (DIFFERENT ENDS)
COLUMNS: BUCKLING (DIFFERENT ENDS) Buckling of Long Straight Columns Example 4 Slide No. 1 A simple pinconnected truss is loaded and supported as shown in Fig. 1. All members of the truss are WT10 43
More informationCIVIL DEPARTMENT MECHANICS OF STRUCTURES ASSIGNMENT NO 1. Brach: CE YEAR:
MECHANICS OF STRUCTURES ASSIGNMENT NO 1 SEMESTER: V 1) Find the least moment of Inertia about the centroidal axes XX and YY of an unequal angle section 125 mm 75 mm 10 mm as shown in figure 2) Determine
More informationSabah Shawkat Cabinet of Structural Engineering Walls carrying vertical loads should be designed as columns. Basically walls are designed in
Sabah Shawkat Cabinet of Structural Engineering 17 3.6 Shear walls Walls carrying vertical loads should be designed as columns. Basically walls are designed in the same manner as columns, but there are
More informationChapter. Materials. 1.1 Notations Used in This Chapter
Chapter 1 Materials 1.1 Notations Used in This Chapter A Area of concrete crosssection C s Constant depending on the type of curing C t Creep coefficient (C t = ε sp /ε i ) C u Ultimate creep coefficient
More informationERRATA for PE Civil Structural Practice Exam ISBN Copyright 2014 (July 2016 Second Printing) Errata posted
Errata posted 8162017 Revisions are shown in red. Question 521, p. 47: Question 521 should read as follows: 521. The W10 22 steel eam (Fy = 50 ksi) shown in the figure is only raced at the center of
More informationNOVEL FLOWCHART TO COMPUTE MOMENT MAGNIFICATION FOR LONG R/C COLUMNS
NOVEL FLOWCHART TO COMPUTE MOMENT MAGNIFICATION FOR LONG R/C COLUMNS Abdul Kareem M. B. AlShammaa and Ehsan Ali AlZubaidi 2 Department of Urban Planning Faculty of Physical Planning University of Kufa
More informationREVIEW FOR EXAM II. Dr. Ibrahim A. Assakkaf SPRING 2002
REVIEW FOR EXM II. J. Clark School of Engineering Department of Civil and Environmental Engineering b Dr. Ibrahim. ssakkaf SPRING 00 ENES 0 Mechanics of Materials Department of Civil and Environmental
More informationMechanics of Solids notes
Mechanics of Solids notes 1 UNIT II Pure Bending Loading restrictions: As we are aware of the fact internal reactions developed on any crosssection of a beam may consists of a resultant normal force,
More informationKarbala University College of Engineering Department of Civil Eng. Lecturer: Dr. Jawad T. Abodi
Chapter 04 Structural Steel Design According to the AISC Manual 13 th Edition Analysis and Design of Compression Members By Dr. Jawad Talib AlNasrawi University of Karbala Department of Civil Engineering
More informationTwoWay Flat Plate Concrete Floor System Analysis and Design
TwoWay Flat Plate Concrete Floor System Analysis and Design Version: Aug10017 TwoWay Flat Plate Concrete Floor System Analysis and Design The concrete floor slab system shown below is for an intermediate
More informationPreferred practice on semiintegral abutment layout falls in the following order:
GENERAL INFORMATION: This section of the chapter establishes the practices and requirements necessary for the design and detailing of semiintegral abutments. For general requirements and guidelines on
More informationDISTRIBUTION OF STRESS IN GROUNDSUPPORTED SLABS
Structural Concrete Software System TN207_sog_stresses_10 122005 DISTRIBUTION OF STRESS IN GROUNDSUPPORTED SLABS Bijan O Aalami 1 This Technical Note describes the distribution of stress in groundsupported
More informationLecture 15 Strain and stress in beams
Spring, 2019 ME 323 Mechanics of Materials Lecture 15 Strain and stress in beams Reading assignment: 6.1 6.2 News: Instructor: Prof. Marcial Gonzalez Last modified: 1/6/19 9:42:38 PM Beam theory (@ ME
More informationCompression Members. ENCE 455 Design of Steel Structures. III. Compression Members. Introduction. Compression Members (cont.)
ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland Compression Members Following subjects are covered:
More informationChapter 8 Supplement: Deflection in Beams Double Integration Method
Chapter 8 Supplement: Deflection in Beams Double Integration Method 8.5 Beam Deflection Double Integration Method In this supplement, we describe the methods for determining the equation of the deflection
More informationDirect Strength Method for Steel Deck
issouri University of Science and Technology Scholars ine AISISpecifications for the Design of ColdFormed Steel Structural embers WeiWen Yu Center for ColdFormed Steel Structures 112015 Direct Strength
More informationSupplement: Statically Indeterminate Frames
: Statically Indeterminate Frames Approximate Analysis  In this supplement, we consider another approximate method of solving statically indeterminate frames subjected to lateral loads known as the. Like
More informationENCE 455 Design of Steel Structures. III. Compression Members
ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University of Maryland Compression Members Following subjects are covered:
More informationRESILIENT INFRASTRUCTURE June 1 4, 2016
RESILIENT INFRASTRUCTURE June 1 4, 2016 INSTANTANEOUS DEFLECTIONS OF CONCRETE SLABS COMPUTED USING DISCRETIZED ANALYSIS Caitlin Mancuso Western University, Canada F. Michael Bartlett Western University,
More informationMechanics of Materials Primer
Mechanics of Materials rimer Notation: A = area (net = with holes, bearing = in contact, etc...) b = total width of material at a horizontal section d = diameter of a hole D = symbol for diameter E = modulus
More informationSolution: The moment of inertia for the crosssection is: ANS: ANS: Problem 15.6 The material of the beam in Problem
Problem 15.4 The beam consists of material with modulus of elasticity E 14x10 6 psi and is subjected to couples M 150, 000 in lb at its ends. (a) What is the resulting radius of curvature of the neutral
More informationConceptual question Conceptual question 12.2
Conceptual question 12.1 rigid cap of weight W t g r A thinwalled tank (having an inner radius of r and wall thickness t) constructed of a ductile material contains a gas with a pressure of p. A rigid
More informationName :. Roll No. :... Invigilator s Signature :.. CS/B.TECH (CENEW)/SEM3/CE301/ SOLID MECHANICS
Name :. Roll No. :..... Invigilator s Signature :.. 2011 SOLID MECHANICS Time Allotted : 3 Hours Full Marks : 70 The figures in the margin indicate full marks. Candidates are required to give their answers
More information