Description of Masonry Design Software for. the National Concrete Masonry Institute. Version 6.0

Description of Masonry Design Software for the National Concrete Masonry Institute Version 6.0 A Report Presented to: National Concrete Masonry Association Prepared by: Tyler Johnson Sami Pant Russell Brown Clemson University Civil Engineering Department November 2013 1

Abstract This special project dealt primarily with a description of changes to NCMA s Structural Masonry Design System Version 6.0. The most significant change in the software was the implementation of the 2011 MSJC and 2012 IBC code provisions. Verification of Version 6.0 is also documented. As in past versions, verification was accomplished through the use of MathCAD software to develop problems that triggered new code provisions which could be compared to the NCMA software. The MSJC 2011 and IBC 2012 code updates that were covered during this project include new provisions relating to shear walls, walls loaded out of plane, columns, and lintels. Files were developed for both reinforced masonry structures and unreinforced masonry structures to reflect provision changes that occurred in both design methodologies. As an additional functionality to the NCMA software, an option for the user to implement more comprehensive seismic design was developed for Version 6.0. This new feature implements a technique for the user to incorporate a portion of the structural elements own weight into the calculations of seismic loads using the software s self weight calculations. This added feature allows a designer to experiment with size and weights of a structural element without requiring a complete independent reevaluation of seismic forces due to wall inertia. Both horizontal and vertical inertia forces are included. The majority of this project dealt with updating and implementation of the new inertial feature into the MathCAD files used for verification of the NCMA software. However, numerous changes in the codes are also implemented as discussed in the sections that follow. 2

Contents 1.0 INTRODUCTION... 2 1.1 Background... 2 1.2 NCMA Software... 3 2.0 LOAD COMBINATION CHANGES... 4 2.1 MSJC... 4 2.1.1 ASCE 7-10 Seismic Load Combination Disparity... 6 3.0 Masonry Element Design Code Changes... 7 3.1 Reinforced Shear Wall Design... 7 3.1.1 Allowable Stress Design of Shear Walls... 7 3.1.2 Strength Design of Shear Walls... 8 3.2 Unreinforced Shear Wall Design... 9 3.2.1 Allowable Stress Design... 9 3.2.2 Strength Design... 11 3.3 Reinforced Out-of-Plane Design... 11 3.3.1 Allowable Stress Design... 11 3.3.2 Strength Design... 11 3.4 Unreinforced Out-of-Plane Design... 12 3.4.1 Allowable Stress Design... 12 3.4.2 Strength Design... 12 4.0 Earthquake Addition... 13 4.1 Purpose... 13 4.2 Wall Inertia Factors f 3 and f 4... 13 4.3 Derivation of Masonry 6.0 Load combinations implementing f 3 and f 4... 14 4.4 Axial and Shear Seismic Addition Calculations... 16 4.5 Seismic Moment Calculations for Shear Walls... 17 4.6 Seismic Moment Calculations for Walls Loaded Out-of-Plane... 18 4.7 Seismic Deflection Calculations... 19 5.0 OTHER CHANGES IN VERSION 6.0... 21 5.1 Change and save new default values within Design Basis... 21 5.2 Two bars in a cell for shearwalls... 21 5.3 User can select using 80 percent of allowable reinforcing steel stress... 22 3

5.4 Use of transverse steel to reduce lapsplice lengths... 23 5.5 Deep beam provisions added... 24 5.6 Error message for excessive steel... 24 5.7 Lintel Bearing Stresses... 24 6.0 CONCLUSIONS... 24 7.0 REFERENCES... 25 4

Description of Masonry Design Software for the National Concrete Masonry Institute Version 6.0 1.0 INTRODUCTION 1.1 Background The National Concrete Masonry Association (NCMA) working in conjunction with Drs. Russell H. Brown and James K. Nelson have developed and produced software used for the design of masonry structures. The previous versions of the software each implemented new features into the software that increased the robustness of the program s capabilities. Phase II of the software included the design of in-plane concrete masonry shear walls, out-of-plane concrete masonry walls, and reinforced masonry lintels using either allowable stress design or strength design procedures in accordance with the Masonry Standards Joint Committee (MSJC) and International Building Code (IBC) building codes MSJC 1995, MSJC 1999, MSJC 2002, and IBC 2000. The verification and validation of this version was conducted by Bryan Thomas Lechner and Johnny Lee McElreath in their 2002 special project report, Verification of Masonry Design Software Developed for the National Concrete Masonry Institute, Phase II 1. Phase III of the software was conducted by Adam Hogan in his thesis entitled, Verification of Masonry Design Software National Concrete Masonry Institute, Phase III. In his work, the capability to design masonry columns using Allowable Stress or strength design was implemented into the software. This version also added the new code requirements contained in IBC 2003 and MSJC 2002 2. 2

Phase IV of the software verification was conducted by Clay Putnam in his special project report, Verification of Masonry Design Software National Concrete Masonry Institute, Phase IV. The major inclusions in this version of the software were the code requirements of IBC 2006, as well as the introduction of the IBC Alternative Basic Load Combinations which allowed the use of the 1/3 stress increase to masonry design 3. Phase V was conducted by Jonathan Cox in his special project report, Verification of Structural Masonry Design Software System. This version of the software included the additions of MSJC 2008 and IBC 2009 code provisions 4. This special project report, Phase VI, is a continuation of the works presented by students in Phases II through V. Version 6.0 of the NCMA software includes the addition of the MSJC 2011 and IBC 2012. One major change in this version of MSJC was the removal of independent load combinations from the MSJC code and the adoption of ASCE 7-10 load combinations for both allowable stress design and strength design. Therefore, references to ASCE 7-10 pertain to provisions contained in MSJC 2011. For the scope of work covered in this project, the load combinations in IBC 2012 and MSJC 2011 were equivalent 5,6. The existing MathCAD files from other students were modified to reflect the new design procedures from IBC 2012 and MSJC 2011. Finally, the implementation of new seismic design functionality was built into the MathCAD sheets to be used in the verification of the feature in the NCMA software. 1.2 NCMA Software The NCMA Masonry Software utilizes a clean and efficient trial-and-error approach to design. Unlike an analysis program, the user is required to know or specify values such as wall dimensions, masonry properties, steel properties, and steel spacing which are then evaluated for capacity. Users have the option of checking a structural element based on design loads at the critical section, or by inputting individual loads such as dead, live, snow, etc. and allowing the software to determine the critical section and load combination. For sufficient designs, the 3

user can view all design calculations, load combinations evaluated, and plot an interaction diagram of the element that overlays the applied loads on the diagrams for the design engineer. When a design load exceeds capacity, the system returns an error message to the user. Plots of the interaction diagram are still created for the element, however, design calculations are not returned to the user. At the completion of this update, Version 6.0 of the NCMA software will be capable of handling specific code design requirements from the past 17 years. The following design codes and load combinations are now included in the software: 1. 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, 6. MSJC 2005 Allowable Stress and Strength Design, 7. IBC 2006 Allowable Stress and Strength Design, 8. MSJC 2008 Allowable Stress and Strength Design 9. IBC 2009 Allowable Stress and Strength Design. 10. MSJC 2011 Allowable Stress and Strength Design. 11. IBC 2012 Allowable Stress and Strength Design. 2.0 LOAD COMBINATION CHANGES 2.1 MSJC As a major change to the development for structural masonry design loadings, the 2011 MSJC has opted to no longer publish its own load 4

combinations and instead adopt the load combinations published by the American Society of Civil Engineers in its most recent Minimum Design Loads for Buildings and Other Structures, ASCE 7-10. Included in the adoption of these load combinations is the approach to calculating and implementing wind loadings. In the previous versions of MSJC, the wind loadings were calculated at the allowable stress level, however, in ASCE 7-10 these values are calculated on the strength design level. Therefore, the wind loadings now carry a base coefficient of 1.0 in the strength design and 0.6 in allowable stress design. For example, Equations 5, 6a and 7 in Table one each have a wind load term of 0.6W. In ASCE 7-05, this term was 1.0W. Similarly, equations 4 and 6 in Table 2 contain the term 1.0W which was 1.6W in ASCE 7-05. A similar change was made in ASCE 7-05 when seismic loadings adopted a strength level loading for design calculations. Table 1: ASCE 7-10 Allowable Stress Load Combinations 1- D 2- D + L 3- D + (L r or S or R) 4- D + 0.75L + 0.75(L r or S or R) 5- D + (0.6W or 0.7E) 6a- D + 0.75L + 0.75(0.6W) + 0.75(L r or S or R) 6b- D + 0.75L + 0.75(0.7E) + 0.75S 7-0.6D + 0.6W 8-0.6D + 0.7E Table 2: ASCE 7-10 Strength Design Load Combinations 1-1.4D 2-1.2D + 1.6L + 0.5(L r or S or R) 3-1.2D + 1.6(L r or S or R) + (L + 0.5W) 4-1.2D + 1.0W + L + 0.5(L r or S or R) 5-1.2D + 1.0E + L + 0.2S 6-0.9D + 1.0W 7-0.9D + 1.0E 5

Both allowable stress and strength design load combinations provide written portions that describe the inclusion of fluid and soil loadings in these combinations. Soil loadings when present are given a factor of 1.0 in ASD and 1.6 in strength design if the load is contributing to the primary loading. Fluids are modified by the same coefficient as the dead load if present except in ASD load combination 7 and Strength combination 6, where load due to fluid is omitted 5. 2.1.1 ASCE 7-10 Seismic Load Combination Disparity During the implementation of the new seismic inertia calculation into the NCMA Masonry software, a disparity in ASCE 7-10 load combinations was discovered. As previously shown in Table 2, load combination 5 in strength design includes earthquake in conjunction with dead, live, and snow loadings. This was a change from ASCE 7-05 where the snow loading was replaced with an or statement similar to the one in strength load combination 4. However, when investigating the seismic portion of the code in Chapter 12 of ASCE 7-10, the load combinations reverted back to the language of ASCE 7-05 which included the or statement. After some investigation with various sources tied to ASCE, an errata published in January 2011 was discovered which addressed this issue. The correct load combinations for seismic design were the ones published in Chapter 2 of ASCE 7-10. These combinations are reprinted in Chapter 12 of ASCE 7-10 to include the seismic terms as shown in Table 3 7. Table 3: ASCE 7-10 Ch 12 Strength Design Seismic Load Combinations 5- (1.2 + 0.2S DS )D + ρq E + L + 0.2S 6- (0.9-0.2S DS )D + ρq E 6

3.0 Masonry Element Design Code Changes 3.1 Reinforced Shear Wall Design The design of reinforced walls loaded in-plane, or shear walls, was significantly modified by the 2011 MSJC code in several ways. The most significant updates that needed to be implemented into the NCMA software were in the allowable stress design portion as discussed below. 3.1.1 Allowable Stress Design of Shear Walls The design of shear walls by allowable stress design (ASD) included several significant changes in IBC 2012 and MSJC 2011. 1. The first of these changes was the removal of the 1/3 stress increase. Prior to 2011 publication of MSJC, the code permitted a somewhat arbitrary stress increase of 1/3 to the allowable flexural tensile stress of masonry. However, instead of using an arbitrary increase, the performance of masonry elements in bending was subjected to a reliability analysis conducted by Kim and Bennett 5. Based on their conclusions, the code committee determined it prudent to remove the stress increase from the code. At the same time, allowable stresses were increased. 2. The allowable compressive stress of reinforced masonry due to flexure or combination of flexure and axial load was increased from 1/3*f m to 0.45*f m per MSJC 2011 Section 2.3.4.2.1. 3. The allowable stresses in Grade 60 steel reinforcement was increased to 32000 psi from 24000 psi in MSJC 2011 2.3.3 due to sufficiently large safety factor already present in the steel 5. Allowable stresses in other grades of reinforcing steel was not changed. 4. Calculation for the shear resistance of a loaded in-plane wall was significantly modified in MSJC 2011. Prior to this publication, the resistance of the masonry to 7

shearing forces was not added to that provided by the shear reinforcement. This created an all or nothing approach to designing a system to resist shear. If the masonry could not resist all of the shear load, then it was not allowed to contribute anything and the shear reinforcement had to resist all of the shear force. This approach was found to be extremely conservative and was modified in Section 2.3.6 of MSJC 2011. Shear resistance of the masonry is now calculated with the summation of the two material resistances, F vm for masonry and F vs for reinforcing steel. The masonry provides resistance first and the shear steel provides the additional necessary resistance capacity similar to the approach taken in strength design. 1 M P F vm (4.0 1.75( )) f ' m 0. 25 2 Vd MSJC 2011 2-28 A n F vs 1 Av Fs d 2 An s MSJC 2011 2-30 3.1.2 Strength Design of Shear Walls This update of the NCMA software included one significant change in strength design of shear walls. This update dealt with the slenderness reduction factor discussed in Section 3.3.4.1.1 of MSJC 2008. The 2008 code required the multiplication of the axial load by the slenderness reduction factor. The reduction factor was calculated as shown: The first bracketed term pertains to walls having h/r < 99, while the second is for h/r > 99. The philosophy behind this reduction factor was to create a more conservative design. This was true when examining allowable maximum axial loads; however, it had quite the opposite effect in realistic practice. As shown in Figure 1, the slenderness reduction actually increased the moment capacity in 8

the bottom portion of the interaction diagram for masonry elements. For example, with an axial load of 400 kips, the difference in moment capacity is about 1200 ftkips. It is in this region where the designs of most shearwalls and fall. Therefore, the MSJC committee decided to remove this reduction from the code in order to keep the previously conservative design methodology. Figure 1: Strength Design Shear Wall Interaction Diagram illustrating the unconservative nature of the slenderness reduction factor. Other significant changes made in the MathCAD files for this portion reflected the inclusion of the new load combinations as previously discussed, and the inclusion of the inertial forces which will be discussed later. 3.2 Unreinforced Shear Wall Design The majority of significant changes to the unreinforced shear wall designs were the addition of load combinations previously discussed, and the inclusion of inertial forces which will be discussed later. Only one other significant change needed to be made pertaining to allowable stress design. 3.2.1 Allowable Stress Design The allowable flexural tensile stresses in clay and concrete masonry were increased in MSJC 2011. These changes are reflected below in a side by side 9

comparison of MSJC Table 2.2.3.2 from the 2011 and 2008 publications. In these tables, PCL refers to Portland cement-lime mortar and MC to masonry cement mortar or air entrained PCL. 10

3.2.2 Strength Design No significant changes were incorporated into the strength design procedures for unreinforced shear walls except for the load combinations as previously discussed, and the inclusion of the inertial forces discussed in a later section. 3.3 Reinforced Out-of-Plane Design Changes to the NCMA software and verification MathCAD files were significant in nature due to the load combination amendments and inclusion of inertial forces which will be discussed in a later section. These changes were implemented in both allowable stress design and strength design. 3.3.1 Allowable Stress Design No significant procedural changes were incorporated in the latest publications of MSJC 2011 and IBC 2012 to the allowable stress design of walls loaded out-of-plane with the exception of the changes in allowable stresses associated with the removal of the 1/3 stress increase previously discussed. 3.3.2 Strength Design One significant change was made to the design of walls loaded out-ofplane in strength design. This change pertained to the calculation of the cracked moment of inertia. Previously the effects of axial loading had not been permitted to be included in the calculation of the cracked moment of inertia. The 2011 MSJC, however, includes this in the contribution to the moment of inertia s value in the calculation of the value c in MSJC 2011 Equation 3-31 and 3-32. MSJC 2011 3-31 MSJC 2011 3-30 11

The force denoted as P u is defined as the axial load that includes externally applied loads and the self weight of the structure. To incorporate this additional contribution, the cracked moment of inertia was recalculated in each load case in the MathCAD files and NCMA software. In the MathCAD files the axial value included the value of wall self weight at a height of half the wall as this will be the best representation of the average value for deflection calculations. In the NCMA software, however, the wall self-weight changed at each of the 100 sections along the wall height, and the moment-area method was used to calculate the deflection for the resulting non-prismatic member. 3.4 Unreinforced Out-of-Plane Design Significant changes to design of unreinforced out-of-plane masonry walls include changes previously discussed for shearwalls. These changes include the amendment of the load combinations as previously discussed and the incorporation of inertial forces as discussed in the following section. These changes were incorporated into both allowable stress design and strength design. 3.4.1 Allowable Stress Design The only significant change to the design of walls loaded-out-of-plane in allowable stress design was the change to the allowable flexural tensile stresses of masonry. These changes are the same as the ones described previously in section 3.2.1 of this document. Refer to the comparison of Table 2.2.3.2 in the 2011 MSJC and 2008 MSJC shown previously. 3.4.2 Strength Design No significant procedural changes were incorporated in the latest publications of MSJC 2011 and IBC 2012 to the strength design of unreinforced walls loaded out-of-plane. 12

4.0 Earthquake Addition 4.1 Purpose As part of the new version of the NCMA Masonry software, an expansion into designing masonry structures with earthquake loadings is being added. The proposal for version 6.0 included enabling the software to use a portion of the wall weight to compute addition seismic inertial forces. The purpose of this addition is to simplify the calculation of earthquake load input, E, in load equations for the design engineer as these forces vary if the designer chooses to examine a design. This variation of inertial forces comes from different self weights that result when factors such as wall thickness, height, and even grout spacing are varied. Therefore, in the Masonry software, two new factors which the design engineer may choose to enable called f 3 and f 4 were created. 4.2 Wall Inertia Factors f 3 and f 4 The factor f 3 will be used to assign a portion of wall weight and the superimposed dead load to the vertical earthquake loading (i.e. the axial loading). Factor f 4 will be used to assign a ratio of wall weight to the horizontal earthquake loading. This means that factor f 4 will be used in both shear and moment calculations. Related to the provision outlined in ASCE 7-10 12.4, the values represent by f 3 and f 4 are: E v = f 3 SW = 0.2*S DS SW [Eqn. 1] Eh =f 4 SW =(S DS I E /R)SW [Eqn. 2] The term SW is defined as the self weight of the wall per linear foot and will be discussed later. Section 12.4 of ASCE 7 defines the vertical and horizontal earthquake loadings respectively as E v and E h, and illustrates their implementation into the load combinations of both strength design and allowable stress design. 13

For lateral earthquake loading, the value of E h can be determined using two different methods per ASCE 7-10, section 12.4. In one equation, E h =ρq e where ρ is a redundancy factor applied to the loading. In the other equation E h =Ω o Q e where Ω o is an overstress factor taken from Table 12.2-1. The overstress factor is a factor typically used in diaphragm design for chords and collectors. Its purpose is to over-design these members so that yielding occurs in other members before the diaphragm, thus resulting in failures that hopefully are not catastrophic. 4.3 Derivation of Masonry 6.0 Load combinations implementing f 3 and f 4 Implementation of f 3 and f 4 into the Masonry software requires a derivation into the load combinations provided by ASCE 7-10. In strength design, equations 5 and 7 are modified, and in allowable stress design, equations 5, 6, and 8 are modified as shown in Table 4 per ASCE 7-10, section 12.4.2.3. Table 4: Modified Seismic Loading per ASCE 7-10 Strength Design Equations 5. (1.2 + E v /D)*D + E h + L + 0.2*S 7. (0.9 - E v /D)*D + E h + 1.6*H Allowable Stress Design 5. (1.0 + 0.7*E v /D)*D+ H + F + 0.7*E h 6. (1.0 + 0.75*(0.7*E v /D)*D + H + F + 0.75*(0.7*E h ) + 0.75*l + 0.75*(L r or S or R) 8. (0.6-0.7*E v /D)*D + 0.7*E h + H The expanded version of the load equations inside of Masonry 6.0 will be calculated as shown in Table 5. If the design engineer chooses not to utilize the inertia addition, the values of f 3 and f 4 are set to 0, and design will be carried out using only the external earthquake loads entered by the user. 14

Table 5: Modified Masonry Seismic Loading per ASCE 7-10 Strength Design Equations 5. (1.2 + f 3 )*SW+ 1.2P D +( [V E or M E ]+f 4 *SW) + L + 0.2*S 7. (0.9 - f 3 )* SW + 0.9P D +([V E or M E ]+f 4 *SW) + 1.6*H Allowable Stress Design 5. (1.0 + 0.7*f 3 )* SW + 1.0P D + H + F + 0.7*([V E or M E ]+f 4 *SW) 6. (1.0 + 0.75*0.7*f 3 )* SW + 1.0P D + H + F + 0.75*(0.7 * ([ V E or M E ] + f 4 *SW)) + 0.75*l + 0.75*(L r or S or R) 8. (0.6-0.7*f 3 ) * SW + 0.6P D + 0.7*([ V E or M E ] + f 4 *SW) + H The SW term in the load combinations is the self weight of the masonry element being designed. For the calculation of SW, Figure 2 shows the dimensions of the wall as Masonry 6.0 defines them for the calculation of self weight and seismic inertial forces. M E PE VE h l x Figure 2: Masonry 6.0 wall dimension variables. 15

Since x is defined from the bottom of a wall, the self weight can be expressed by the formula: SW = Wt*(h-x)*l [Eqn. 3] Where SW is the self weight of the element at the value of x under consideration, Wt is the weight of the masonry in pounds per square foot of wall surface area, and (h-x) is the height of the wall above the section being examined. Calculations of critical flexure and shear sections are done through an iterative process by Masonry 6.0. The height of wall is examined in 1% increments and values of maximum moment and shear are analyzed and compared. For example, the software first analyzes SW as Wt*h*l where x is 0. Subsequently, the value of x become 0.01*h and proceeds through 1.0*h. The maximum utilization for moment capacity and shear capacity are then identified, and the value and the location within the wall are reported. 4.4 Axial and Shear Seismic Addition Calculations The resulting addition of seismic load due to inertial forces is calculated using Equations 4 through 11. The axial and shear forces are calculated by the multiplication of their associated f 3 and f 4 values. These axial and shear loads are calculated in the same manner for all elements address in this special project. P Ei = f 3 * SW [Eqn. 4] P Ei = f 3 * Wt*(h-x)*l [Eqn. 5] V Ei = f 4 * SW [Eqn. 6] V Ei = f 4 * Wt*(h-x)*l [Eqn. 7] The resulting axial and shear inertial forces calculated by the NCMA software are then taken into the load combinations for the member being designed. Tables 6 and 7 illustrate how the load combinations will be implemented into the software for ASD and Strength Design. 16

Table 6: Masonry 6.0 Axial Seismic Load Calculations Strength Design Equations 5. (1.2 + f 3 )*SW +1.2*P D + L + 0.2*S 7. (0.9 - f 3 )*SW +0.9*P D + 1.6*H Allowable Stress Design 5. (1.0 + 0.7*f 3 )SW +P D + H + F 6. (1.0 + 0.75*0.7*f 3 )* SW +P D + H + F + 0.75*l + 0.75*(L r or S or R) 8. (0.6-0.7*f 3 ) SW +0.6*P D + H Table 7: Masonry 6.0 Shear Seismic Load Calculations Strength Design Equations 5. V E + V Ei + L + 0.2*S 7. V E + V Ei + 1.6*H Allowable Stress Design 5. H + F + 0.7*(V E + V Ei ) 6. H + F + 0.75*(0.7*(V E + V Ei )) + 0.75*l + 0.75*(L r or S or R) 8. 0.7*(V E + V Ei ) + H 4.5 Seismic Moment Calculations for Shear Walls Moments from wall or masonry element inertia are calculated in a similar fashion as shear but incorporate the length of the moment arm from the bottom 17

of the critical section of interest. This moment arm can be found as shown in Equation 11. M Ei = (force)*(moment arm) [Eqn. 8] M Ei = [f 4 * SW] * [h-(h-x)/2] [Eqn. 9] M Ei = [f 4 * SW] * [(h+ x)/2] [Eqn. 10] M Ei = [f 4 * Wt*(h-x)*l]* [(h+ x)/2] [Eqn. 11] For elements such as shear walls that contain concentric loadings, this methodology for adding additional inertial forces is sufficient. Implementing this additional moment into the load combinations for ASD and Strength design is achieved as shown in Table 8. Table 8: Masonry 6.0 Moment Seismic Load Calculations Strength Design Equations 5. M E + M Ei + L + 0.2*S 7. M E + M Ei + 1.6*H Allowable Stress Design 5. H + F + 0.7*(M E + M Ei ) 6. H + F + 0.75*(0.7*(M E + M Ei )) + 0.75*l + 0.75*(L r or S or R) 8. 0.7*( M E + M Ei ) + H 4.6 Seismic Moment Calculations for Walls Loaded Out-of-Plane Moment calculations for walls loaded out-of-plane are not as simple to calculate due to eccentricities in the loadings. As discussed in section 5.2, the f 3 factor applies to both wall weight and superimposed dead loads. These superimposed dead loads must be incorporated in the calculation of moment due to seismic loading as shown in Figure 3. 18

Figure 3: MathCAD formula for Seismic Moment The equations presented in Figure 3 are for the calculation of moment for three different support types. Support one, SPRT 1, is the moment calculation for a simply supported beam. SPRT 2 is the calculation for cantilever beam and the last formula is for an SPRT 3 condition which is for a pinned cantilever. This calculation further varies from the shear wall calculation in how it arrives at the proper units of force*length for moment. The distribute load w E is given in pounds per square foot, therefore, f 4 must be multiplied by Wt instead of SW. This sum is then multiplied by the height of the wall and distance to the critical section, and finally analysis for a one foot wide strip of wall which gives the correct units for moment. 4.7 Seismic Deflection Calculations Lastly, when designing walls loaded out-of-plane in Strength design, it is necessary to evaluate deflection criteria of the wall. Equations for this were developed in a similar way as the equations for moment that include the new inertial factors. These deflection equations are shown in Figure 4. 19

Figure 4: Deflection equations due to seismic loading and inertial forces. 20

5.0 OTHER CHANGES IN VERSION 6.0 5.1 Change and save new default values within Design Basis Default values for building code and material properties in Design Basis are chosen with input for NCMA staff to represent the most often used values of a particular material property. For example, the default value of f m is 1500 psi. However, in some markets, a higher value of f m is possible. With this feature, the user can change the values of any property, then check Save as default. The next time the user opens the design basis, the newly saved value will appear as the default. 5.2 Two bars in a cell for shearwalls Shearwalls are now permitted to include two reinforcing bars in a cell for both end zone and middle zone regions. For two bars in one cell, the bars are assumed to be placed as shown in the figure below. The default spacing used to calculate K for development length calculations is based on the assumption that the dimensions a and b in the figure below are equal. This optimizes K resulting in the smallest development length. 21

a b a 5.3 User can select using 80 percent of allowable reinforcing steel stress In the Design Basis Reinforcement tab, the user can select using 80% of the allowable steel stress, thus eliminating the 50% increase in lapsplice length required by IBC ASD. This will result in a larger required area of reinforcing steel, but a much smaller lap splice length. 22

5.4 Use of transverse steel to reduce lapsplice lengths Use of transverse reinforcing steel to reduce lapsplice lengths for both ASD and SD has been added. Lap splices are permitted to be reduced where transverse reinforcement (#3 or larger) is placed within 8 of the end of the splice if it is fully developed in grouted masonry. Conditions required to apply this reduction are: Placed within 8 of the end of the splice and fully grouted Not more than 1.5 horizontally from vertical steel Horizontal bar must be fully developed on each side of lapsplice Minimum lap required of 36 bar diameters 23

5.5 Deep beam provisions added Deep beam provisions have been added to the design of lintels.. 5.6 Error message for excessive steel When the total area of reinforcing steel exceeds 4% of a cell area, an error message is displayed. 5.7 Lintel Bearing Stresses Bearing Stresses at lintel supports are now calculated and compared to code limits. 6.0 CONCLUSIONS This special project provides a description of changes to NCMA s Structural Masonry Design System Version 6.0. The most significant change in the software was the implementation of the 2011 MSJC and 2012 IBC code provisions. Verification of Version 6.0 is also documented. As in past versions, verification was accomplished through the use of MathCAD software to develop problems that triggered new code provisions which could be compared to the NCMA software. The MathCAD files used for verification were updated to cover a variety of situations to test the NCMA software. New code provisions relating to design from the IBC 2012 and MSJC 2011 codes have been implemented. Most significantly, methodologies have been developed for how to implement an added seismic functionality to the NCMA software which will greatly benefit design engineers. Several other improvements in Version 6.0 are also described. 24

7.0 REFERENCES 1. Lechner, Bryan, McElreath, Johnny. Verification of Masonry Design Software For the National Concrete Masonry Institute Phase II. Clemson University 2002. 2. Hogan, Adam. Verification of Masonry Design Software For the National Concrete Masonry Institute Phase III. Clemson University 2002. 3. Putnam, Clay Verification of Masonry Design Software For the National Concrete Masonry Institute Phase IV. Clemson University 2006 4. Cox, Jonathan Verification of Structural Masonry Design Software System. Clemson University 2010 5. MSJC 2011, Masonry Standards Joint Committee, Building Code Requirements for Masonry Structures. (ACI 530-11/ASCE 5-11/TMS 402-11) 6. International Code Counsel. International Building Code (Chapters 16 and 21), IBC 2012 7. American Society of Civil Engineers. Minimum Design Loads for Buildings and Other Structures. (ASCE/SEI 7-10), 2010 25