VERIFICATION OF MASONRY DESIGN SOFTWARE NATIONAL CONCRETE MASONRY INSTITUTE PHASE III

Transcription

1 VERIFICATION OF MASONRY DESIGN SOFTWARE NATIONAL CONCRETE MASONRY INSTITUTE PHASE III A Special Project Report Presented to: The College of Engineering and Science Clemson University In Partial Fulfillment Of the Requirements for the Degree: Master of Engineering Civil Engineering Prepared by: Adam Hogan December 2005 Special Project Advisor: Dr. Russell H. Brown

2 ABSTRACT The National Concrete Masonry Society (NCMA) in conjunction with Dr. James K. Nelson and Dr. Russell H. Brown has developed software for the design of masonry structures. The Phase II software included design modules for the design of out-of-plane concrete masonry walls, in-plane concrete masonry walls, and concrete masonry and reinforced concrete lintels using Allowable Stress or Strength Design methodologies and the requirements of the Masonry Standards Joint Committee (MSJC) and International Building Code building codes (MSJC-95, MSJC-99, MSJC-02, IBC 2000). The 3.0 version of this software was completed in December Its accuracy was verified by Bryan Thomas Lechner and Johnny Lee McElreath in their Special Project Report, Verification of Masonry Design Software Developed for the National Concrete Masonry Institute, Phase II 1. This report presents the verification of Phase III of the NCMA Masonry Design Software (Version 4.1). The Phase III version has the capability to design lintels and walls loaded either out-of-plane or inplane, along with the added capability to design columns, using Allowable Stress or Strength Design methodologies. The software has been improved to include two new design code requirements: IBC 2003 and MSJC 2005, to go along with the MSJC 1995, MSJC 1999, MSJC 1999 with the IBC 2000 provisions, IBC 2000, and MSJC 2002 codes present in the previous version. A major improvement of the Phase III software is the addition of the design capability for hollow clay unit masonry. This will allow designers to use one software package to design either clay or concrete masonry. The accuracy of the new design modules and codes was verified by comparing design results generated by the NCMA Software with results generated from independent algorithms developed in MathCAD 2001 specifically for this Special Project. This special project is a continuation of the work presented in the Phase I and Phase II reports. New MathCAD verification files were independently developed and existing MathCAD files modified to reflect the changes in the design codes to verify each of the design modules. The verification completed in this report returned very positive results. The 4.0 version of the Phase III NCMA Software is expected to be available in December ii

3 TABLE OF CONTENTS 1.0 INTRODUCTION Purpose NCMA Software Phase III Software Capabilities Software Limitations VERIFICATION Objective Philosophy Scope MATERIAL PROPERTIES: CONCRETE & CLAY Description Code Interpretation Mathcad Verification Files MSJC 2005 DESIGN CODE Description Code Interpretation Strength Design Allowable Stress Design Mathcad Verification Files IBC 2003 DESIGN CODE Description Code Interpretation Strength Design Allowable Stress Design Mathcad Verification File COLUMN DESIGN Description Code Interpretation Strength Design Allowable Stress Design Mathcad Verification Files Strength Design Verification Allowable Stress Design Verification DEVELOPMENT & LAP SPLICE LENGTHS Description Code Interpretation Mathcad Verification Files IN-PLANE (SHEAR) WALL DESIGN Description Code Provisions Mathcad Verification iii

4 9.0 OUT-OF-PLANE WALL DESIGN Description Code Interpretation Mathcad Verification LINTEL DESIGN Description Code Interpretation Mathcad Verification CONCLUSION APPENDIX A: IN-PLANE VERIFICATION APPENDIX B: OUT-OF-PLANE VERIFICATION APPENDIX C: LINTEL VERIFICATION APPENDIX D: COLUMN VERIFICATION APPENDIX E: DEVELOPMENT & LAP SPLICE LENGTH VERIFICATION. 450 APPENDIX F: SECTION PROPERTY VERIFICATION REFERENCES iv

5 LIST OF FIGURES AND TABLES Figure 1-1: NCMA Software Interaction Diagram Family of Curves... 2 Figure 1-2: NCMA Software Interaction Diagram... 3 Figure 3-1: NCMA Design Preferences Menu... 9 Figure 3-2: NCMA Design Preferences Menu Unit Section Input Figure 3-3: Hollow Concrete Masonry Unit Figure 3-4: Hollow Clay Masonry Unit Table 4-1: Revised Modulus of Rupture Values for 2005 MSJC Code Figure 4-1: Maximum Permitted Axial Load Fully-Grouted Walls MSJC Figure 6-1: Column Configuration Input Menu Figure 6-2: Column Reinforcement Input Menu Figure 6-3: Column Section Mechanics For Strength Design Figure 7-1: Development Length & Lap Splice Design Figure 10-1: Lintel Dimension Input Figure 10-2: Lintel Menu Input v

6 1.0 INTRODUCTION 1.1 Purpose The National Concrete Masonry Association (NCMA) Masonry Design Software was developed to provide engineers and designers with a valuable resource in the design of concrete masonry structures. While Phase II of the software was met with overwhelming approval by NCMA and masonry designers, Phase III was designed with the objective to expand upon the capabilities of Phase II. A major improvement to the new version of the software is the incorporation of hollow clay unit masonry design. This enables designers to design concrete and clay masonry structures with only one design software package. Other major improvements include the incorporation of the more recent design codes (2003 IBC & 2005 MSJC) and the design of columns. Phase III of the software was developed with these issues in mind. This Special Project focuses on the verification of the Phase III software. The addition of two new design codes, a column design module, and the capability for clay masonry design requires that the new NCMA software is independently verified for accuracy and compliance with the new code provisions before release. This report is a continuation of the work completed in the Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3, Verification of the National Concrete Masonry Association Masonry Design Software (Phase II) An Interim Report 2 and the Verification of Masonry Design Software Developed for the National Concrete Masonry Association 1. The NCMA Masonry Design Software was developed by Dr. James K. Nelson and Dr. Russell H. Brown for the National Concrete Masonry Association (NCMA). 1.2 NCMA Software Phase III The NCMA Design Software (Version 4.1), like Phase II of the software, utilizes the trial-anderror method of design. This software is not an analysis package, although it does have the capability to 1

7 determine the critical design load combination based on the support conditions, the geometry, and userdefined loads acting on the masonry component under consideration. The user has the option of inputting the critical section design forces, designated resistance side design, or allowing the software to compute the critical section from the applied loads, load side design. In order to design a masonry component, all known values and conditions such as the wall dimensions, masonry properties, steel properties, support conditions and applied loads (or critical section design forces) are input and all unknown values, such as bar size, steel or grout spacing and/or wall thickness are assumed. The NCMA Design Software has the capability of developing interaction diagrams based on the input wall properties and can plot the applied loads over this diagram as illustrated in Figure 1-1. Figure 1-1: NCMA Software Interaction Diagram Family of Curves 2

8 If the plotted applied loads are within the envelope of the diagram for a given spacing, the design is sufficient. From Figure 1-1, it can be seen that the 32-inch curve is the greatest spacing that encloses all of the load combinations. The user may choose to display the design calculations or the interaction diagram for the chosen spacing, as is seen in Figure 1-2. When one or more of the load combinations lies outside an envelope, the design is insufficient for that given spacing and the software will return an error message for insufficient capacity rather than display the design calculations. Figure 1-2: NCMA Software Interaction Diagram 3

9 1.2.1 Software Capabilities The software has the capability to design both in-plane masonry walls and out-of plane masonry walls, both pre-cast concrete and masonry lintels, and masonry columns. An important aspect of the Phase III software is the design capability for hollow clay unit masonry. This will allow designers to use one software package to design either clay or concrete masonry. The software will also have the ability to input masonry unit section properties that differ from the default values for both clay and concrete masonry units. The software can design fully grouted or partially grouted walls and the user has the option of choosing unreinforced or reinforced wall design. The software has the capability to design using Allowable Stress or Ultimate Strength Design principles. Based on the section properties, the flexural, axial load and shear capacities are calculated at the critical section and the theoretical area of steel is calculated (out-of-plane design only). Phase III incorporates two new design codes. The code specific design requirements and load combinations are now included for the following design codes: 1. Masonry Society Joint Committee (MSJC) 1995 Allowable Stress Design, 2. MSJC 1999 Allowable Stress Design, 3. IBC 2000 Allowable Stress and Strength Design, 4. MSJC 2002 Allowable Stress and Strength Design, 5. IBC 2003 Allowable Stress and Strength Design, and 6. MSJC 2005 Allowable Stress and Strength Design Methods. Other new design capabilities of the NCMA Software include the ability to input the depth of reinforcing steel for lintels; to calculate service load deflections for lintels; to calculate service deflections for out-of-plane walls; and to display development and lap splice lengths for reinforcing steel. 4

10 1.2.2 Software Limitations The software cannot design pilasters, beams (other than lintels), or out-of-plane walls spanning horizontally. The design algorithms do not apply to shear walls with drift in excess of 1 percent of the story height (as they require boundary elements which the NCMA Software does not have the capability to design). Concentrated axial loads must be distributed over the length of the wall according to the design code under consideration. Prestressed masonry walls and lintels cannot be designed. Walls designed in areas under the jurisdiction of the Unified Building Code (UBC) must be designed using a different design code. 5

11 2.0 VERIFICATION 2.1 Objective The objective of this Special Project is to verify the newly included Phase III design modules, ensure design code compliance and verify any changes to the Phase II design modules. 2.2 Philosophy The software package MathCAD 2001 produced by Mathsoft, Inc. was utilized to facilitate the process of hand checking the NCMA Design Software. A specific Mathcad verification program was developed for each design module and design code. The algorithms for each Mathcad file were derived independently from those used in the NCMA Software using the design code under consideration and principles of mechanics. The Mathcad files and their associated commentary are located in Appendix A and on the CD-ROM attached to the back cover of this Report. The verification was conducted on two distinct fronts: the resistance side and the load side. The resistance side of the software consists of the axial load, moment, and shear capacities associated with the input wall properties and design code. The resistance side for a specific design module was verified by iterating a wall design with respect to several isolated variables, such as bar size or spacing. Sets of axial load, moment and shear capacities for different wall thickness and input variables were then compared to the values generated from the associated Mathcad file. Percent errors in excess of 0.1% were investigated. Large discrepancies were most likely attributed to an isolated variable and were easily diagnosable. The errors were then amended and this process was continued until all trials had been exercised with negligible error (i.e., less than 0.1% error) or until deemed satisfactory to Dr. Brown & NCMA. 6

12 The load side of the software consists of the critical section design forces generated from the userdefined applied loads and the code dependent load combinations. The critical design section for reinforced masonry walls loaded out-of-plane is located where the theoretical area of steel is the highest. In the case of shear walls loaded either in-plane or out-of-plane and unreinforced masonry loaded out-of-plane, the critical section occurs where the ratio of applied moment to moment capacity is highest for the axial load under consideration. The critical design section for shear occurs when the ratio of shear-to-shear capacity, the percentage shear utilization, is the highest. The NCMA Software is verified by comparing the design forces generated from the code specific load combinations and verifying that the critical section and associated load combination indicated by the NCMA Software are in fact the critical location and load case, respectively. The verification can be broken down in this manner because the resistance side and load side design modules are independent from one another. Changes in the load combinations or applied load input will not affect how the section capacities are determined and visa versa. This allowed for much easier resistance side verification. 2.3 Scope The scope of the verification includes: reinforced and unreinforced shear wall (in-plane) design for both Allowable Stress Design and Strength Design; reinforced and unreinforced out-of-plane design for both Allowable Stress Design and Strength Design; and lintel design for both Allowable Stress Design and Strength Design associated with the two additional design codes included in Phase III, IBC 2003 & MSJC All verification tables completed for the Phase III software are located in this report in the specific design code section and on the CD-ROM in the back cover of this report. This report does not include verification for design modules that remain unchanged from Phase II including Allowable Stress design for out-of-plane walls, in-plane walls, and lintels, based on MSJC 1995 and 1999 design codes and Allowable Stress and Strength design for out-of-plane walls, in-plane walls, and lintels for IBC 2000 and MSJC 2002 design codes. For discussion of the verification for Phase II of the 7

13 NCMA Software, completed using Mathcad files developed by Oliver Himbert, Bryan Lechner, and Johnny McElreath, please reference Verification of the National Concrete Masonry Association Masonry Design Software (Phase II) An Interim Report 2 or Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3. 8

14 3.0 MATERIAL PROPERTIES: CONCRETE & CLAY 3.1 Description Two of the key features of the NCMA Software are the ability to design masonry structures of both concrete masonry and hollow clay masonry units and the ability to input masonry unit section properties that differ from the default values. The NCMA Software also has a new enhanced user interface, as seen in Figure 3-1: Figure 3-1: NCMA Design Preferences Menu The Design Code tab allows for a selection of the design code, design procedure, and masonry type. The Concrete Masonry and Clay Masonry tabs allow for the input of masonry unit characteristics including nominal length, nominal height (variable for clay and set at 16 inches long and 8 inches high for 9

15 concrete), and density. The tabs also allow for input of the grout properties and masonry compressive strength. The Steel tab allows for the input of the grade of steel reinforcement. For the selected grade of steel, this menu will display the given properties for yield stress, modulus of elasticity, and allowable stress for Allowable Stress Design. The Unit Size tab allows for the input of section properties of actual widths, face shell thicknesses, and web widths. Default values correspond to minimum requirements for face-shell and web thicknesses as required by the applicable ASTM Standards (C90 for concrete masonry and C652 for clay). The default values and section input menu are shown in Figure 3-2: Figure 3-2: NCMA Design Preferences Menu Unit Section Input Along with the hollow clay masonry units that have been added to the new software, 14 & 16 CMU units have also been added. 10

16 3.2 Code Interpretation Masonry Strength The NCMA Software determines masonry compressive strength by either the unit strength method or the prism method. Compressive strengths for the unit strength method are figured from table values in the appropriate design code, with required minima and maxima also listed. The separate tables for clay and concrete had to be verified in the NCMA Software for each code Modulus of Elasticity Recent codes (1998 and later) state that the design of clay and concrete masonry shall be based on the following modulus of elasticity values: E m = 700 * f m for clay masonry; E m = 900 * f m for concrete masonry. In older codes, the modulus of elasticity for concrete and clay was taken from separate tables that related E m to unit compressive strength Maximum Usable Strain The IBC and MSJC codes both state that the maximum usable strain, ε mu, at the extreme masonry compression fiber shall be assumed to be for clay masonry and for concrete masonry. These values have been consistently used in all versions of the strength design codes. These strain factors are used in the design of reinforced masonry elements Section Properties For the design of concrete and clay masonry, under all design codes, minimum net cross-sectional properties of the member are used in the calculation of area, moment of inertia, section modulus, and radius of gyration for the purpose of calculating stress. Average cross-sectional properties of the member are used in slenderness calculations. 11

17 Figure 3-3 & Figure 3-4 show sketches of concrete and clay masonry units, respectively, showing the dimensions of the input variables that can be entered using the menu displayed in Figure 3-2. Figure 3-3: Hollow Concrete Masonry Unit Actual Length Face Shell Thickness Actual Width Web Thickness Web Thickness Web Thickness Figure 3-4: Hollow Clay Masonry Unit Actual Length Face Shell Thickness Actual Width End Web Thickness Middle Web Thickness End Web Thickness 12

18 3.3 Mathcad Verification Files Clay Mathcad design files were created from their concrete counterparts making the appropriate changes for the material properties and section property dimensions, as were listed above. Independent Mathcad files were created for both concrete and clay to compute unit section properties, as well as wall weights. These Mathcad files can be found in Appendix F. Section properties calculated include the wall area, moment of inertia, section modulus, and radius of gyration. Both average and net section properties are computed. The wall weight is computed using the average area. Net section properties are used for the rest of the design. Input variables for the Mathcad files include actual width, face shell thickness, and web width for concrete masonry and actual width, face shell thickness, end web width, and middle web width for clay masonry. Further input includes grout spacing for ungrouted, partially grouted, and full grouted walls, as well as densities of concrete and clay, which may also be input in the new NCMA Design Preferences Menu. These Mathcad files were used in the developmental phases of the software to be sure that the correct section properties were being used in design. 13

19 4.0 MSJC 2005 DESIGN CODE 4.1 Description The 2005 edition of the Masonry Standards Joint Committee (MSJC) Building Code Requirements for Masonry Structures (ACI 530/ASCE 5/TMS 402) and Specification for Masonry Structures (ACI 530.1/ASCE 6/TMS 602) was approved by the sponsoring societies (the American Concrete Institute (ACI), the Structural Engineering Institute of the American Society of Civil Engineers (SEI/ASCE) and The Masonry Society (TMS)) in the Fall of Code Interpretation Strength Design Masonry Modulus of Rupture (Section MSJC 2005) Under the 2005 MSJC provision, the modulus of rupture has been harmonized in strength design, so that the values for in-plane bending and out-of-plane bending are now the same. Under the 2002 MSJC provision, the modulus of rupture for elements subjected to out-of-plane bending was taken from Table , while the modulus of rupture for elements subjected to in-plane bending was taken as 250 psi. Under the 2005 MSJC code, the modulus of rupture for masonry elements loaded in-plane or out-of-plane is taken from Table The values for the modulus of rupture have also been revised for fully grouted elements with flexural tensile stress normal to the bed joints, as seen in Table 4.1: 14

20 Table 4-1: Revised Modulus of Rupture Values for 2005 MSJC Code Flexural tensile stress normal to bed joints Mortar types in running or stack bond Hollow Units Portland cement/lime or mortar cement Masonry cement or air entrained portland cement/lime Fully grouted M or S N M or S N MSJC 2005 (Table ) 163 (1124) 158 (1089) 153 (1055) 145 (1000) MSJC 2002 (Table ) 170 (1172) 145 (999) 103 (710) 73 (503) Development & Lap Splice Lengths (Section & Section (a) MSJC 2005) Under the 2005 MSJC provision, the required development length of reinforcement bars in tension or compression, l d, shall be calculated by Equation (3-15), but shall not be less than 12 inches. l d * d b * f y * γ = Eq. (3-15) K f ' m where: l d = required development length, inches d b = diameter of reinforcement, inches f y = specified yield stress of the reinforcement or the anchor bolt, psi f`m = specified compressive strength of masonry at age of 28 days, psi K γ = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or five times d b = 1.0 for No. 3 through No. 5 reinforcing bars; 1.3 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars. The strength reduction factor, φ, has been removed from strength design provisions, as was present in the 2002 MSJC code, and the bar-size factor, γ, has been slightly modified. 15

21 The same governing equation and 12 inch minimum also applies to lap splice lengths. The Masonry Society Joint Committee has recognized that forthcoming analyses and research may likely lead to additional revisions to the MSJC s lap and development length requirements. The 2005 MSJC code also requires that when epoxy-coated reinforcing bars are used, development length determined by Eq. (3-15) shall be increased by 50 percent. This has been added to strength design since the 2002 MSJC code and is similar to philosophies historically used for allowable stress design Maximum Area of Flexural Tensile Reinforcement (Section MSJC 2005) The 2005 MSJC provision has set revised guidelines from the 2002 MSJC provision on the maximum steel percentage permitted in out-of-plane walls. The 2005 MSJC code requires the neutral axis location, c, is determined based on a critical steel tensile strain of 1.5 times the yield strain, as opposed to 1.3 in the 2002 MSJC code. The code states that for intermediate reinforced masonry shear walls subject to in-plane loads where M u /V u d v 1, c is determined based on a critical steel tensile strain of 3 times the yield strain, and that for special reinforced masonry shear walls subject to in-plane loads where M u /V u d v 1, c is determined based on a critical steel tensile strain of 4 times the yield strain. For intermediate and special reinforced masonry shear walls subject to out-of-plane loads, the provision with the 1.5 factor shall apply. The 2005 MSJC code provides that the tensile stress in the steel be taken as the product of the modulus of elasticity of the steel and the strain in the reinforcement, and need not be taken as greater than f y, as opposed to the MSJC 2002 which fixes the tensile stress in the steel at 1.25 times the yield stress of steel, regardless of the strain in the steel. The 2005 MSJC code also permits the effect of compression reinforcement, with or without lateral restraining reinforcement, for purposes of calculating maximum flexural tensile reinforcement. The masonry force in the compression zone is based on a Whitney stress block. For a solidly grouted cross-section it is equal to 0.8*c max *0.8*f`m*b. The provisions are illustrated graphically below in Figure 4-1: 16

22 Figure 4-1: Maximum Permitted Axial Load Fully-Grouted Walls MSJC 2005 C max ε mu =.0025 (concrete) ε mu =.0035 (clay) 1.3ε y ( 03 IBC) 1.5ε y ( 05 MSJC) d T = A s f s < 1.00A s f y P u 0.64f`mcb 0.80f`m P u =P max =0.64f`mc max b - ΣT a=0.80c A more convenient application of this provision is to sum the steel force and compression force associated with the neutral axis depth, c max. This sum, P max, is the maximum ultimate axial load that may be placed on the wall in order to satisfy the maximum reinforcement ratio provision. This provision was verified by comparing P max between the NCMA Software and the Mathcad software. The NCMA Software for shear walls designed using strength design under the 2005 MSJC code will list 3 values of P max for special reinforced masonry shear walls, intermediate reinforced masonry shear walls, and other types of reinforced masonry shear walls. The loading combination D +.75L +.525Q E must not exceed P max Effective Compression Width (Section MSJC 2005) Provisions for computing effective compression width have been added to strength design (Section ) using the same requirements historically used in allowable stress design. These requirements state that for running bond masonry, and masonry in other than running bond with bond beams spaced not more than 48 inches center-to-center, the width of the compression area used in stress 17

23 calculations shall not exceed the least of: (1) center-to-center bar spacing, (2) six times the nominal wall thickness, or (3) 72 inches Allowable Stress Design Development and Lap Splice Lengths (Section & Section MSJC 2005) Under the 2005 MSJC provision, the required development length of reinforcement bars in tension or compression, l d, shall be calculated by Equation (2-9), but shall not be less than 12 inches. l d * d b * f y * γ = Eq. (2-9) K f ' m where: l d K γ = required development length, inches = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or five times d b = 1.0 for No. 3 through No. 5 reinforcing bars; 1.3 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars. The same governing equation and 12 inch minimum also applies to lap splice lengths. This has harmonized allowable stress design provisions for development lengths and lap splices with those of strength design. The 2005 MSJC code also requires that when epoxy-coated reinforcing bars are used, development length determined by Eq. (2-9) shall be increased by 50 percent. This is similar to previous allowable stress provisions in 2002 MSJC code. 18

24 Allowable Tensile Stresses (Section MSJC 2005) Under the 2005 MSJC provision, in-plane allowable flexural tension is no longer zero as it has been in previous editions but has been set to the same value as for out-of-plane flexural tension, just as has been in strength design. This will also make allowable stress design and strength design give results that are closer to each other for unreinforced shear walls. The values for allowable flexural tensile stresses are still taken from Table and are the same as in previous editions. 4.3 Mathcad Verification Files Mathcad files for verification of the 2005 MSJC code requirements were created from previous Mathcad files created by Bryan Lechner and Johnny McElreath. These files made the appropriate modifications as listed above to the 2002 MSJC Mathcad design files. The specific ramifications to these modifications and verification will be listed in later sections as a part of each design module. 19

25 5.0 IBC 2003 DESIGN CODE 5.1 Description The 2003 edition of the International Building Code (IBC) was approved by the International Code Counsel and is incorporated into the NCMA Software. 5.2 Code Interpretation Strength Design The load combinations used in strength design under the 2003 IBC code are listed in Section and are the same as those used for strength design under the 2000 IBC code. Like the 2000 IBC code, the 2003 code references Section of ASCE 7 where F, H, P, or T loads are to be considered and references Section of ASCE 7 where F a is to be considered in design (Section ). The strength design of masonry structures in the 2003 IBC code (Section 2108) refers to the requirements of Chapters 1 and 3 of the 2002 MSJC code, with the exception of several modifications. These include modifications pertaining to welded and mechanical splices (Section ) and special prestressed masonry shear walls (Section ). Since these requirements are not a part of the new NCMA Software, they are not discussed any further. The following modifications are incorporated into the new NCMA Software: Minimum Nominal Thickness for Hollow Clay Masonry (Section IBC 2003) The 2003 IBC code, in accordance with Section of the 2002 MSJC code, specifies that the minimum nominal thickness for hollow clay masonry shall be 4 inches. In the 2002 MSJC code, the requirement was 6 inches and did not specify a distinct minimum for hollow clay masonry. 20

26 Relationship between Masonry Compressive Stress & Strain (Section IBC 2003) In addition to assuming a uniformly distributed masonry stress of 0.80f m over a compression zone of a = 0.80c, like the MSJC 2002 (Section 3.2.2(g)), the 2003 IBC code requires that for out-of-plane bending the width of the equivalent stress block shall not be taken greater than six times the nominal thickness of the masonry wall or the spacing between reinforcement, whichever is less. Section also states that for in-plane bending of flanged walls, the effective flange width shall not exceed six times the thickness of the flange. However, flanged walls are not a part of the new NCMA software Effective Compression Width (Section 2108 IBC 2003) Provisions for computing effective compression width have been added to strength design. These requirements state that for running bond masonry, and masonry in other than running bond with bond beams spaced not more than 48 inches center-to-center, the width of the compression area used in stress calculations shall not exceed the least of: (1) center-to-center bar spacing, (2) six times the nominal wall thickness, or (3) 72 inches Allowable Stress Design The load combinations used in allowable stress design under the 2003 IBC code are listed in Section and are the same as those used for allowable stress design under the 2000 IBC code. Like the 2000 IBC code, the 2003 code permits a load reduction of 0.75 for the combined effect of two or more variable loads to be added to the effect of the dead load. The code does not permit increases in allowable stresses as are allowed under the MSJC design codes. The allowable stress design of masonry structures in the 2003 IBC code (Section 2107) refers to the requirements of Chapters 1 and 2 of the 2002 MSJC code, with the exception of several modifications. These include reference requirements for special inspection during construction (Section ) and the design of masonry columns used only to support light-frame roofs of smaller structures (Section ). 21

27 Since these requirements are not a part of the new NCMA Software, they are not discussed any further. The following modifications are incorporated into the new NCMA Software: Lap Splices (Section IBC 2003) Under the 2003 IBC provision, the minimum length of lap splices for reinforcing bars in tension or compression, l ld, shall be calculated by Equation 21-2, but shall not be less than 15 inches. l ld * d b * f y * γ = (Equation 21-2) K f ' m where: d b = diameter of reinforcement, inches f y = specified yield stress of the reinforcement or the anchor bolt, psi f m = specified compressive strength of masonry at age of 28 days, psi l ld = minimum lap splice length, inches K = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or five times d b, inches γ = 1.0 for No. 3 through No. 5 reinforcing bars; 1.4 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars Maximum Bar Size (Section IBC 2003) Under the 2003 IBC provision, the bar diameter shall not exceed one-eighth of the nominal wall thickness and shall not exceed one-quarter of the least dimension of the cell, course, or collar joint in which it is placed. 22

28 Splices for Large Bars (Section IBC 2003) Under the 2003 IBC provision, reinforcing bars larger than No. 9 in size shall be spliced using mechanical connectors in accordance with MSJC 2002 Section Maximum Reinforcement Percentage (Section IBC 2003) Under the 2003 IBC provision, special reinforced masonry shear walls having a shear span ratio, M/Vd, equal to or greater than 1.0 and having an axial load, P greater than 0.05f m A n which are subjected to in-plane forces, shall have a maximum reinforcement ratio, ρ max, not greater than that computed as follows: nf ' m ρ max= (Equation 21-3) f y 2 f y n + f ' m where: n = E s / E m E s = modulus of elasticity of steel, psi E m = modulus of elasticity of masonry in compression, psi This maximum reinforcement ratio does not apply in the out-of-plane direction. 5.3 Mathcad Verification File Mathcad files for verification of the 2003 IBC code requirements were created from previous Mathcad files created by Bryan Lechner and Johnny McElreath. These files combined the load side of the previous 2000 IBC Mathcad files and the resistance side of the previous 2002 MSJC Mathcad files with all necessary modifications. The specific modifications to these files will be listed in later sections as a part of each design module. 23

29 6.0 COLUMN DESIGN 6.1 Description Another of the main features added to the new NCMA Software is the design of masonry columns. The design of columns is similar to the design of masonry shear walls, with differences in the orientation of reinforcing steel and bending about both axes. The same basic principles of mechanics apply. Masonry columns are required to be reinforced and have a minimum of four bars, with at least one at each corner of the column. The strength design of masonry columns also requires that they be solidly grouted. Under allowable stress design, masonry columns are not required to be solidly grouted; however, the NCMA Software only allows for the design of solidly grouted columns. One of the main issues concerning the input of the column module was the amount and placement of reinforcing steel. It was determined that symmetric rows of steel would be input on both sides of the column about the centerline. The user inputs the size of the longitudinal bars and the number of bars in each layer. The user also inputs the distance of these layers from the centerline of the column. If a positive integer is entered for the distance, two symmetric layers are placed that distance from the centerline. If zero is entered for the distance, one layer is placed at the centerline of the column. The NCMA Software input allows for a maximum of 8 layers of steel in a column. The area of steel provided by the designer is checked against code minima and maxima. See Figure 6-1 and Figure 6-2 for an illustration of the NCMA Masonry Design Software menus for the column configuration and the reinforcement. 24

30 Figure 6-1: Column Configuration Input Menu Figure 6-2: Column Reinforcement Input Menu 25

31 A simplified free body diagram of a column using Strength Design is illustrated in Figure 6-3. The steel reinforcement arrangement in Figure 6-3 is analogous to the input shown in Figure 6-2, with d 1 equal to 16, d 2 equal to 8, and d 3 equal to 0. Figure 6-3 illustrates five layers of reinforcement, whereas the software permits up to eight. Figure 6-3: Column Section Mechanics For Strength Design b ε mu w c a d 1 t d 2 d 2 Axis of Bending d 3 = 0 P u d 1 ε s A s E s ε s a = 0.80c ; w = 0.80f m b (MSJC 2002, IBC 2003, MSJC 2005) a = 0.85c ; w = 0.85f m b (IBC 2000) 6.2 Code Interpretation Strength Design The provisions for nominal axial, flexural, and shear strength for columns are similar to those provisions for the design of shear walls, with varying provisions set for dimensional and reinforcing limits. As was discussed in Section 6.1 of this report, codes require that columns be solidly grouted (IBC 2000 Section , MSJC 2002 Section & MSJC 2005 Section ) and reinforced. Therefore, the NCMA Software only designs solidly grouted, reinforced masonry columns. 26

32 Longitudinal Reinforcement For the design of masonry columns, codes state that longitudinal reinforcement shall be a minimum of four bars, one in each corner of the column. The code provision for the maximum reinforcement area is the lesser of the ρ max, as set forth in the pertinent code. MSJC provisions go further to state that this area may not exceed 0.04A n. The minimum reinforcement area shall be A n. IBC 2000 does not state a minimum reinforcement area. All codes require that this reinforcement be uniformly distributed throughout the depth of the column. These limits are verified in the Mathcad design files Lateral Ties Provisions are listed in the codes for the minimum amount of lateral ties to be provided for the longitudinal reinforcement. In MSJC, the design for lateral ties is the same in strength design is the same as for allowable stress. However, this is not included in the design in the NCMA Software and is not discussed any further in this report Dimensional Limits The 2005 MSJC, 2002 MSJC, and 2003 IBC codes state that the nominal width of a column shall not be less than 8 inches. These codes also provide that the nominal depth not be less than 8 inches or greater than three times its nominal width. The 2000 IBC code provision sets the minimum width at 12 inches and the nominal depth at 12 inches or three times the nominal width. All of the codes state that the distance between lateral supports of a column not exceed 30 times its nominal width Allowable Stress Design The code provisions for allowable stress design state that columns shall be designed to resist the applied loads. As a minimum, columns shall be designed to resist loads with an eccentricity equal to 0.1 times each side dimension. Each axis is to be considered independently. 27

33 The determination of nominal axial, flexural, and shear strength for columns under allowable stress design is similar to those provisions for the design of shear walls, with varying provisions set for dimensional and reinforcing limits. Unlike columns designed by strength design, columns designed by allowable stress are not specifically required to be solidly grouted; however, the NCMA Software limits the design by allowable stress to solidly grouted columns Longitudinal Reinforcement The provisions for longitudinal reinforcement for allowable stress design are similar to those used in strength design. The area of reinforcement shall not be less than A n nor exceed 0.04A n. The code also states that the minimum number of bars shall be four. These requirements are verified in the Mathcad design files Lateral Ties Provisions for lateral ties can be found in the codes with respect to minimum size, spacing, arrangement, etc. As was discussed earlier, lateral ties are not designed in the NCMA Software and are therefore not discussed further in this report Dimensional Limits The allowable stress provisions state that the minimum nominal side dimension shall be 8 inches, similar to the provisions of strength design. The codes also state that the ratio between the effective height and least nominal dimension shall not exceed 25 (compared to 30 for strength design). These requirements are verified in the Mathcad design files. 28

34 6.3 Mathcad Verification Files Strength Design Verification Preliminary Mathcad column design files have been created but will most likely have to be revised to adjust to the input of the NCMA Software. The Mathcad verification files for columns, which include the design codes for 2000 IBC Strength (2000 IBC Strength Column.mcd), 2002 MSJC Strength (2002 MSJC Strength Column.mcd), 2003 IBC Strength (2003 IBC Strength Column.mcd), and 2005 MSJC Strength (2005 MSJC Strength Column.mcd) can be found in Appendix D-1. The column design files, like many of the others, determine the loading for the appropriate code, the moment and shear capacities, and the critical sections. At the time of this report, the column module for the NCMA Software had not been finalized. Initial verifications have been done on P-M pairs for the interaction diagram and on P max values for various codes. Once the column module is in working order and finalized, it will be verified as follows: Verifications of the axial load, moment and shear capacities were completed, for each strength design code, by performing various problems in the NCMA software and comparing them to problems with the same parameters executed in the Mathcad algorithms. Comparisons were completed for all available CMU and clay masonry widths. Each problem that was executed varied by changing one or many of the following parameters: loading patterns, reinforcement sizes, reinforcement arrangements, reinforcement spacing, column width and depth, and column height. Once the problems were performed in both NCMA and Mathcad, values for the factored axial load, factored moment, factored shear, moment capacity, shear capacity, shear force in steel, and the value of maximum allowable axial load were compared. MS Excel spreadsheets will be created as for walls and lintels to verify output of several varying examples between Mathcad and the NCMA Software. However, they are not included as part of this report. 29

35 6.3.2 Allowable Stress Design Verification The Mathcad verification files for columns, which include the design codes for 2000 IBC Allowable Stress (2000 IBC ASD Column.mcd), 2002 MSJC Allowable Stress (2002 MSJC ASD Column.mcd), 2003 IBC Allowable Stress (2003 IBC ASD Column.mcd), and 2005 MSJC Strength (2005 MSJC Strength Column.mcd), can be found in Appendix D-2. These files have the capability of computing the design loads based on the user defined service loads. The nominal axial, moment and shear capacities were determined in the same manner as for shear walls as was described in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3. As is discussed in Section of this report, the column module for the NCMA Software was not ready for verification at the time of this report, and the Mathcad verification files are only in developmental stages and will have to be modified based on the input to the software. 30

36 7.0 DEVELOPMENT & LAP SPLICE LENGTHS 7.1 Description The design of development lengths and lap splices is a new function added to Phase III of the NCMA Software. Development lengths and lap splices in the NCMA Software will be displayed with the reinforced masonry design of walls, loaded either out-of-plane or in-plane, lintels, and columns. 7.2 Code Interpretation Allowable Stress Design MSJC 1995, MSJC 1999 & MSJC 2002 Allowable stress provisions for early MSJC codes adhered to the same requirements. When calculating the development length for design using the ASD method, the designer needs only to consider the diameter of the bar and the allowable steel stress. Section of the 2002 MSJC code refers to development length as embedment length and states that the embedment length should be determined by Equation (2-8), but shall not be less than 12 inches for bars. where: l = d F Eq. (2-8) d b s d b = F s = diameter of reinforcement, inches allowable tensile or compressive stress in reinforcement, psi When epoxy-coated bars are used, the development length determined by Eq. (2-8) shall be increased by 50 percent. Section of the 2002 MSJC code states that the minimum length of lap for bars in tension or compression shall be determined by Equation (2-9), but shall not be less than 12 inches. 31

37 l = d F Eq. (2-8) d b s When epoxy-coated bars are used, lap length determined by Eq. (2-9) shall be increased by 50 percent. Therefore, given a constant allowable steel stress, both development lengths and lap splice lengths will vary linearly with the bar diameter IBC 2000 Section specifies that the minimum length of lap splices for reinforcing bars in tension or compression, l d, shall be calculated by Equation 21-2, but shall not be less than 15 inches. l d * d b * f y * γ = (Equation 21-2) K f ' m The value K is determined for IBC 2003 the same as for MSJC The value γ shall be taken as 1.0 for No. 3 through No. 5 bars; 1.4 for No. 6 through No. 7 bars; and 1.5 for No. 8 through No. 9 bars. Section states that reinforcing bars larger than No. 9 in size shall be spliced using mechanical connectors IBC 2003 The allowable stress provisions for the IBC 2003 code (Section ) are unchanged from those in Section of the IBC 2000 code, as listed in Section above MSJC 2005 As was noted in Section of this report, allowable stress provisions for development lengths and lap splice lengths have been harmonized to agree with the strength design provisions of earlier codes. Under the 2005 MSJC provision, the required development lengths and lap splice lengths of reinforcement bars in tension or compression, l d, shall be calculated by Equation (2-9), but shall not be less than 12 inches. 32

38 l d * d b * f y * γ = Eq. (2-9) K f ' m where: l d K γ = required development length, inches = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or five times d b = 1.0 for No. 3 through No. 5 reinforcing bars; 1.3 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars. The 2005 MSJC code also requires that when epoxy-coated reinforcing bars are used, development lengths and lap splice lengths determined by Eq. (2-9) shall be increased by 50 percent. This is similar to previous allowable stress provisions Strength Design IBC Section specifies that development lengths for tension or compression reinforcement shall be a minimum length of 12 inches or the development length determined by Equation 21-23, whichever is greater. where: lde l d = (Equation 21-23) φ * d b * f y * γ de = (Equation 21-24) K f ' m l 33

39 where: l d = required development length of reinforcement, inches l de = embedment length of reinforcement, inches K = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or three times d b (not to exceed five times d b ), inches γ = 1.0 for No. 3 through No. 5 reinforcing bars; 1.4 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars φ = strength reduction factor; φ = 0.8 Section specifies that lap splice lengths for tension or compression reinforcement shall be a minimum length of 15 inches or the length determined by Equation 21-25, similar to Equation 21-23, whichever is greater MSJC Sections & specifies that development lengths and lap splice lengths for tension or compression reinforcement shall be a minimum length of 12 in. or the development length determined by Eq. (3-13), whichever is greater. where: lde l d = Eq. (3-13) φ l de K γ 0.13* d b * f y * γ = K f ' 2 m = the lesser of the masonry cover, clear spacing between adjacent reinforcement, or five times d b = 1.0 for No. 3 through No. 5 reinforcing bars; 1.4 for No. 6 and No. 7 reinforcing bars; 1.5 for No. 8 through No. 9 reinforcing bars. 34

40 As noted in Section of the MSJC code, the reduction factor for development and splicing of reinforcement shall be taken as IBC The strength design provisions for development lengths and laps splice lengths in the IBC 2003 code follow the requirements of the 2002 MSJC strength provisions, as listed in Section above MSJC Sections and specify that development lengths and lap splice lengths for tension or compression reinforcement shall be a minimum length of 12 in. or the development length determined by Eq. (3-15), whichever is greater. Eq. (3-15) is the same as Eq. (2-9) used in allowable stress design of the 2005 MSJC code, as specified in Section of this report. l d * d b * f y * γ = Eq. (3-15) K f ' m The bar-size factor, γ, has been slightly modified and the strength-reduction factor, φ, has been removed from the previous provision of the 2002 MSJC code, as is specified in Section of this report. 35

41 7.3 Mathcad Verification Files The Mathcad verification files are programmed to determine the development length for design and the lap splice length. The input for the verification files includes the following: masonry compressive stress nominal wall thickness allowable steel stress or steel yield stress bar size bar placement (distance from the center of the cell) bar center-to-center spacing The NCMA Software places the steel for shear walls in the center of the cell. For out-of-plane walls, the NCMA Software allows for bars to be placed off-center and only allows for one bar per cell. These variables are used to determine the K factor, which is a factor of either the masonry cover, center-tocenter bar spacing, or the bar diameter. The cover determined for the K factor is different for each module. The output for the Mathcad files is development lengths and lap splice lengths for regular bars and expoxy-coated bars. An example is shown in Figure 7-1. At the time of this report, development and lap splice lengths had not been incorporated into the NCMA Software. The Mathcad files for verification of development and lap splice lengths are independent of the other Mathcad design files. These lengths will be verified once they are incorporated into the NCMA Software. The Mathcad files for development and lap splice lengths are included in Appendix E. 36

42 Figure 7-1: Development Length & Lap Splice Design 37

43 8.0 IN-PLANE (SHEAR) WALL DESIGN 8.1 Description There is little change to the shear wall design module in the new NCMA Software, other than incorporating the new design codes and the use of clay masonry. The design of walls loaded in-plane in the NCMA Software is the same as previous versions. A full description of wall design loaded in-plane can be found in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner. 8.2 Code Provisions Shear Steel Spacing Determination According to allowable stress design in MSJC code, the steel area to spacing ratio, as shown in Equation 8-1 below, should be calculated with a 1/3 stress increase applied to the allowable steel stress, F s, where appropriate. However, this was not done in the previous release of the NCMA Software, thereby requiring more shear steel than was required by the code. A v V = (Equation 8-1) s Fs * d 0 where: A v = cross-sectional area of shear reinforcement, in 2 s V = spacing of reinforcement, in = shear force, lb F s = allowable tensile or compressive stress in reinforcement, psi d 0 = distance from extreme compression fiber to centroid of tension reinforcement, in 38

44 This has been corrected in the new release of the NCMA Software, thereby requiring less shear steel for walls subjected to wind and earthquake loadings, as can be seen in Appendix A.3-b Maximum Area of Flexural Tensile Reinforcement (Section MSJC 2005) As was discussed in Section , MSJC 2005 has set new requirements for the maximum area of flexural tensile reinforcement. Under this revision, the yield strain factor was changed from 1.3 to 1.5. Sections and of the Code further stipulate that yield strain factors of 3 and 4 shall be used for intermediate reinforced masonry shear walls and special reinforced shear walls, respectively, subject to in-plane loads. Ordinary shear walls, subject to in-plane or out-of-plane loads, and intermediate or special reinforced shear walls, subject to out-of-plane loads, shall adhere to the 1.5 strain factor. These upper limits on flexural tensile reinforcement apply to masonry members where M u /V u d v 1. For masonry members where M u /V u d v 1 and designed using R 1.5, the 1.5 strain factor shall apply, and for masonry members where M u /V u d v 1 and designed using R 1.5, there is no upper limit to the maximum flexural tensile reinforcement. For shear wall calculations under the MSJC 2005 code, the NCMA Software lists, P max values for all three strain factors of 1.5, 3 & 4. It is up to the designer to apply the appropriate upper limit since the Software can not distinguish between ordinary, intermediate, and special reinforced masonry shear walls. The Software at this time does not check for the M u /V u d v 1 requirement and should be checked by the designer Allowable Flexural Tensile Stress (Section MSJC 2005) As was mentioned in Section of this report, allowable tensile stresses in walls loaded inplane is no longer zero. The allowable tensile stresses are now the same as those used for walls loaded outof-plane. This will cause the interaction diagram for unreinforced shear walls designed by allowable stress not to pass through the origin but rather intercept the x-axis at the point f t *S. 39

45 8.3 Mathcad Verification One of the key modifications to the Mathcad shear wall design files was to incorporate the design of clay masonry walls. This mainly required a change to the placement of reinforcement steel, as it could be placed every 4 rather than every 8. This was a critical revision in the calculation of the number of bars in the shear wall, as well as which bars are at yield and which are in compression. It was also necessary to adjust the shear steel calculations for reinforced shear walls using allowable stress design. The previous version of the Software did not use the 1/3 stress increase to determine the steel area to spacing ratio. However, according to code, the steel area to spacing ratio should be calculated with a 1/3 stress increase applied to the allowable steel stress, F s. This will require less shear steel in the wall. This error has been corrected in the new version of the software. For MSJC 2005 strength design, the Mathcad shear wall design files were modified for the P max calculation. Three separate calculations were programmed to output the P max values for special reinforced shear walls, intermediate reinforced shear walls, and all other shear walls. These calculations incorporated the different ductility factors as were added to the MSJC 2005 design code, as discussed in Section of this report. These three values of P max were compared to those output in the NCMA Software. The moment capacities under the MSJC 2005 strength design also had to be revised to include the updated modulus of rupture values rather than the previously used 250 psi. The moment capacities also had to be modified for MSJC allowable stress design for capacities controlled by tension to include the appropriate allowable flexural tensile stress, which was previously not allowed in earlier codes. The IBC 2003 shear wall design files were created using the loading calculations from previous IBC 2000 shear wall design files and the resistance calculations from previous MSJC 2002 shear wall design files. The MathCAD verification files for fully grouted, reinforced and unreinforced shear walls, which include the design codes for 2003 IBC Strength (2003 IBC Strength In-Plane.mcd), 2003 IBC Allowable Stress (2003 IBC Allowable Stress In-Plane.mcd), 2005 MSJC Strength (2005 MSJC Strength In- Plane.mcd), and 2005 MSJC Allowable Stress (2005 MSJC Allowable Stress In-Plane.mcd), can be found 40

46 in Appendix A-1.b, A-2.b, A-3.b, and A-4.b. These verification files were developed in MathCAD 2001 using Johnny McElreath s files. These files have the capability of computing the factored design loads based on the user defined service loads. The nominal axial, moment and shear capacities were determined in the same manner as described in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner, but these capacities were determined for each load combination. The controlling capacity was chosen based on the highest percent utilization from all load combinations. The controlling capacities were displayed for verification purposes. These values were checked for varying loading patterns, wall sizes, and other wall and reinforcing dimensions. MS Excel was used to store these data values and compute the percentage error for each value. All percent errors greater than 0.1% were investigated and amended before verification was deemed complete. Verification results are in Appendix A-1.a, A-2.a, A-3.a, and A-4.a. At the time of this report, limited verification tests had been run on shear walls for partially grouted and ungrouted walls, as well as for previous design codes. The new Software was verified for the older codes (i.e., 2002 MSJC, 2000 IBC, etc.) by comparing results to the results of the same example worked with the previously released version of the Software. 41

47 9.0 OUT-OF-PLANE WALL DESIGN 9.1 Description The design of walls loaded out-of-plane in the NCMA Software is the same as previous versions. A full description of wall design loaded out-of-plane can be found in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner. A major design feature for out-of-plane walls added to the new NCMA Software is the determination of service-level deflections. In previous versions of the software, only the maximum permissible service-level deflection was determined. It was determined in the previous report that these deflections rarely control the design of out-of-plane walls. After further investigation, it was determined that under certain loading conditions, the service-level deflection of the wall could control its design. 9.2 Code Interpretation Deflection Design ( IBC 2000 and MSJC 2002) These provisions state that the horizontal mid-height deflection under service lateral and service axial (unfactored loads) shall be limited to the following: δ h, where δ, is the mid-height deflection and h, is the effective height of the wall. The NCMA Software now checks this limitation. The Software displays what is called δ max, which is multiplied by the effective height. A Mathcad file using the 2002 MSJC Strength design code was developed to verify the serviceload deflection calculated by the Software and determine if the above limitation was ever exceeded. This Mathcad file, along with the corresponding NCMA Software output, is included in Appendix B-5. The deflection determined by Mathcad was inches. The deflection determined by the NCMA Software was inches. This is an error of 1.29%. This is similar to the accuracy of deflection calculations 42

48 covered in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner. Therefore, the service deflection calculation was deemed to be acceptable. 9.3 Mathcad Verification For MSJC 2005 strength design, the Mathcad out-of-plane wall design files were modified slightly per revisions to the modulus of rupture values. The IBC 2003 out-of-plane wall design files were created using the loading calculations from previous IBC 2000 out-of-plane wall design files and the resistance calculations from previous MSJC 2002 out-of-plane wall design files. The MathCAD verification files for fully grouted, reinforced and unreinforced shear walls, which include the design codes for 2003 IBC Strength (2003 IBC Strength Out-of-Plane.mcd), 2003 IBC Allowable Stress (2003 IBC Allowable Stress Out-of-Plane.mcd), 2005 MSJC Strength (2005 MSJC Strength Out-of-Plane.mcd), and 2005 MSJC Allowable Stress (2005 MSJC Allowable Stress Out-of- Plane.mcd), can be found in Appendix B-1.b, B-2.b, B-3.b and B-4.b. These verification files were developed in MathCAD 2001 using Johnny McElreath s files. These files have the capability of computing the factored design loads based on the user defined service loads. The nominal axial, moment and shear capacities were determined in the same manner as described in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner, but these capacities were determined for each load combination. The controlling capacity was chosen based on the highest percent utilization from all load combinations. The controlling capacities were displayed for verification purposes. These values were checked for varying loading patterns, wall sizes, and other wall and reinforcing dimensions. MS Excel was used to store these data values and compute the percentage error for each value. All percent errors greater than 0.1% were investigated and amended before verification was deemed complete. Verification results are in Appendix B-1.a, B-2.a, B-3.a and B-4.a. 43

49 At the time of this report, limited verification tests had been run on out-of-plane walls for partially grouted and ungrouted walls, as well as for previous design codes. The new Software was verified for the older codes (i.e., 2002 MSJC, 2000 IBC, etc.) by comparing results to the results of the same example worked with the previously released version of the Software. 44

50 10.0 LINTEL DESIGN 10.1 Description The lintel design in the NCMA Software is the same as in previous versions. A full description of lintel design can be found in Verification of the National Concrete Masonry Association Masonry Design Software Phase II 3 by Johnny McElreath and Bryan Lechner. The Software has been updated for the design of lintels using the IBC 2003 and MSJC 2005 codes. One of the features added to the design of lintels in the new software is the determination of service level deflections against allowable deflection limits. Other changes to the lintel design module include the ability to input the depth of the steel (h-d), the ability to select a maximum #9 bar size, and the ability to include shear reinforcement (in the form of stirrups) in the design. The verification of the shear reinforcement of lintels was done independently and is not included in the body of this report. The interface of the Software under the lintel module has also been improved for more userfriendly input, as well as inputs for steel placement and shear reinforcement as can be seen in Figure Figure 10-1: Lintel Dimension Input A Height = A d = Bearing = 8 L = 120 X = 1.5 b = Section A - A 45

51 Figure 10-2: Lintel Menu Input 10.2 Code Interpretation Modulus of Rupture (Section MSJC 2005) As was discussed earlier in this report, modulus of rupture values for in-plane bending under the MSJC 2005 design code are now taken from Table instead of being taken as 250 psi as in previous codes. This has led to a lower minimum area of steel in the design of lintels under the 2005 MSJC strength design provisions. 46