Reinforced Concrete Design Project Five Story Office Building

Transcription

1 Reinforced Concrete Design Project Five Story Office Building Andrew Bartolini December 7, 2012 Designer 1 Partner: Shannon Warchol CE 40270: Reinforced Concrete Design

2 Bartolini 2 Table of Contents Abstract...3 Introduction...4 Design...5 i. Slab Thickness...6 ii. Loads...6 iii. Estimation of Column Sizes...6 iv. Slab Design...7 v. T-beam Design for Flexure...10 vi. T-beam Design for Shear...14 viii. Crack Control...16 ix. T-beam deflection control...17 x. Column Design...18 Summary and Conclusion...21 Recommendations...22 Appendix A: Design Figures...24 B: Load Estimate Calculations...39 C: Slab Design Calculations...40 D: T-Beam Flexure Calculations...42 E: T-Beam Shear Calculations...48 F: Crack Control Calculations...54 G: Deflection Calculations...56 H: Column Design Calculations...68

3 Bartolini 3 Abstract This report outlines the structural design of a five-story reinforced concrete office building following ACI The framing arrangement and column locations of the building were provided based on architectural and structural requirements. The structure system of the office building is a reinforced concrete frame with a one-way slab and beam floor system. This report covers the design process in the following order: the calculation of the expected loads on the structure, the design of the slab depth, the estimation of the column sizes, the design of the slab reinforcement, the design of the T-beam reinforcement for both flexural and shear, the calculation to check crack control, the calculation to check T-beam deflections and finally the design of the column reinforcement. Additionally, figures displaying the placement of the steel rebar in the structure are contained in the report. The details of the design can be found within the report. The basic design of the office building includes seven (7) inch slabs throughout, fifteen (15) inch by fifteen (15) inch square columns and T-beam depths of eighteen (18) inches for the exterior column spans and twenty (20) inches for the interior column spans. Due to deflection control issues that arose in this preliminary design, some of the interior beam lines have to be re-designed in further iterations of this design. The maximum depth of the interior T-beams would be twenty-two (22 inches). The reinforcement is varied throughout the project depending on necessary loads and ACI The slab reinforcement spacing would also have to be edited in future designs because it did not comply with ACI 318 crack control limits. All beams were designed to be under-reinforced beams in order to provide extensive warning before failure (should it ever occur) and all beams were design for shear in order to avoid a sudden and catastrophic failure. Finally, the column reinforcement was designed under two different loading conditions, the first of which maximized both the axial and moment in the column and the second which maximized the moment but minimized the axial loads for a maximum eccentricity. Three recommendations that I would make if I were re-designing this structure from the beginning would be to use deeper T-beams initially so the building would not fail the deflection limits, use #3 bars for the slab reinforcement while limiting the spacing to twelve (12) inches and use smaller columns dimensions. I would still use at least two T-beam depths, however, as the

4 Bartolini 4 exterior beam lines can be eighteen (18) inches deep while some interior beam lines may need to be twenty-two (22) inches deep. Introduction The framing plan of the five-story reinforced concrete building was provided and can be seen in Figure 1. As shown in the framing plan, the building is six bays by three bays. The outer bays along the six-bay side are 14 feet center-to-center while the inner bays along the six-bay side are 16 feet center-to-center. The outer bays along the three-bay side are 25 feet center-to-center while the inner bay along the three-bay side is 30 feet center-to-center. The framing plan also denotes one-way slabs with T-beams that run along the six-bay columns. Figure 1: Plan View of Five-Story Building The first story height of the building is 16 feet while all the other story heights are 12 feet. An elevation view of the office building can be found in Figure 2.

5 Bartolini 5 Figure 2: Elevation View This report will explain the preliminary design process for this five-story reinforced concrete office building according to ACI It should be noted that this design is preliminary and would undergo a number of iterations. First the slab thickness was found followed by the calculation of loads on the structure. Next an estimation of the column sizes was calculated. The slab reinforcement was then designed followed by the flexure and shear reinforcement of the T-beams. Subsequently the design was checked for crack control and deflection control. Finally, the column reinforcement was designed. This report will detail both the technical design procedure as well as a discussion into the reasons for each type of reinforcement and each step in the design process and why certain decisions were made in the design process. Finally, at the end of this report, there are recommendations on how to adapt the design when future iterations of this design are carried out or if someone was to start the design over from scratch. Design The design of the five-story reinforced concrete structure entailed a number of steps and calculations. Each section listed below describes one step in the process of the design. Attached to the end of this report are sample hand calculations for each step in the design process.

6 Bartolini 6 Slab Thickness The slab thickness was determined to be seven (7) inches by using Table 9.5(a) in ACI 318. The exterior spans required seven-inch slab thickness, which was slightly larger than the slab thickness requirement for the interior spans. For ease of construction and economical purposes, a slab thickness of seven inches was used throughout the entire building. Loads The loads were calculated using ASCE 7 and the load combinations in Table 1.2 of ACI 318. For the floors, the dead loads included the load from the mechanical equipment and the ceiling (15 psf) and the load from the slab (87.5 psf). The live load for the floors was 50 psf while the partition loading (which was also considered a live load) was 20 psf. The dead loads for the roof included the load from the mechanical equipment and the ceiling (15 psf), the load from the roofing material (7 psf) and load from the slab (87.5 psf). The live load for the roof was comprised of the snow load only (30 psf). The load for the slabs was calculated by multiplying the slab thickness by the unit weight of concrete (150 psf). The load combination from Table 1.2 of ACI 318 consisted of a load factor of 1.2 for the dead loads and 1.6 for the live loads. Using this load combination, the roof load was found to be psf and the floor load was found to be 235 psf. Table 1 and 2 in the Appendix B contain the breakdown of the load design along with the final loading values for both the roof and the floor. Estimation of the Column Size The first step in the process of determining the column size was the calculation of the tributary area of the most heavily loaded column, which in this building plan was a column in the interior section of the building, (i.e. C3), which resulted in a tributary area of 440 ft 2.

7 Bartolini 7 The loading of the roof and four floors was multiplied by this tributary area to determine the factored load experience by the ground story column. The area of the concrete needed to support the calculated force was then calculated, taking into account both the strength of the concrete and the steel. Appropriate overall strength reduction factors were included to not only provide a further factor of safety but also account for eccentric loading of the column. It was also assumed that 2% of the area of the column was steel. Using this assumption, the overall area of the column was 209 in 2. Using a square cross-section, the column width and depth were chosen to be fifteen (15) inches. It should be noted that this calculation was for preliminary design only and would be checked later in the design process. Slab Design The slabs were primarily designed with reinforcing steel parallel to the numerical grid lines. This is because the floor system is a one-way slab, which means that bending will occur between the two supporting beams in a parabolic shape, with the largest moments being at the top of the slab near the supports and at the bottom of the slabs at the mid-spans. Steel was also provided in the transverse direction to provide resistance to the temperature and shrinkage cracks in the tension regions. The first step in the slab design was to find the effective span length. For negative moments, the effective span length is taken as the average of the two adjacent clear spans while for positive moments the effective span length is the given slab s clear span. Next, the ACI moment coefficients were found for a spandrel slab with two or more spans. The spandrel slab was used because the majority of the slab acts as a spandrel (i.e. the slab was just supported by beams). Since the portion of the slab that was supported just by the beams is so much greater than the portion of the slab that is supported by the columns, the spandrel condition was used for the moment coefficient. Following ACI 318, the moments were found for the various critical cross sections along the slab.

8 Bartolini 8 Using the moments at the critical sections, the steel required was tabulated along with the minimum steel requirement according to ACI 318. The larger quantity of steel governed and a steel size and spacing combination was chosen. The extreme tension fiber depth was checked to verify that it remain nearly the same as was assumed earlier in the procedure. The strain in the extreme tension fiber was also checked for each critical section of the slab to verify that the strain was above in order to verify a previous assumption that the strength reduction factor (ϕ) was Two additional ACI 318 requirements were then checked. The first was that the maximum steel spacing could not exceed eighteen (18) inches or three (3) times the slab thickness (which is twenty-one (21) inches). Additionally, a practical limit of the spacing being greater than one and a half (1.5) times the slab thickness (which is ten and a half (10.5) inches) was checked. Next, the design of the transverse steel reinforcing was completed. In the transverse direction of the main longitudinal steel, there is a minimum amount of steel required (which is the same as the minimum reinforcing that was referred to in the above calculations). This amount of steel was calculated and a combination of size and spacing of bars was chosen. The maximum spacing of eighteen (18) inches or five (5) times the slab thickness (which is thirty-five (35) inches) was checked along with the same practical limit that was used above. The roof slab design consisted of #4 bars at 15 spacing in both the longitudinal and transverse (for temperature and shrinkage cracks) directions. The floor slab design consisted of #4 bars at 13 to 15 spacing for the longitudinal direction and #4 bars at 15 spacing in the transverse direction (for temperature and shrinkage cracks). Finally, following Figure 5.20(a) from Nilson et al, the simplified standard cut off points for the slab reinforcement were calculated. Sample design drawings of the floor slabs are shown in Figures 3-5. The full set of design drawings are shown in Figures A1-A6 in the Appendix.

9 Bartolini 9 Figure 3: Floor Slab Design Figure 4: Plan of Floor Slab Design (Top Steel)

10 Bartolini 10 Figure 5: Plan of Floor Slab Design (Bottom and Temperature/Shrinkage Steel) The full, tabulated calculations for the floor slab can be found in Appendix C. T-beam Design for Flexure The T-beams were then designed for the flexural forces they would experience. This design comprised of the determination and selection of the adequate amount of steel necessary in each of the critical T-beam sections. The steel reinforcement is necessary in the portions of the T- beam that are in tension because steel is strong in tension while concrete is very weak and brittle in tension. However, the T-beam sections cannot have too much steel or they become overreinforced and the failure mode of an over-reinforcement beam is very sudden. The T-beam should be under-reinforced so there is warning before a failure would occur (under a loading condition that was not designed for).

11 Bartolini 11 There were six unique beam lines to analyze when designing the T-beam for flexure. Beam lines A and G; B and F; and C, D and E are the three groups of identical beam lines and there was both the floor and roof loading cases for each set of beam lines. Along each beam line, there were five critical sections that correlated to the critical sections for the ACI Moment Coefficients. The T-beam width was taken to be fifteen (15) inches to match the column widths in order to make construction easier. The first step in determining the T-beam reinforcement was to calculate the governing T-beam depth. Using ACI code, both the exterior and interior spans were checked and it was found that the interior T-beam depth (17.14 inches) governed the exterior T-beam depth (16.2 inches). Since these are a minimum value, a round value of eighteen (18) inches was used as the T-beam depth. For beams with positive bending (tension is in the bottom of the T-beam), it was assumed the rectangular stress block (which is correlated to the portion of the beam in compression), was fully comprised in the flange (i.e. slab). For beams with negative bending (tension is in the top of the T-beam), the rectangular stress block was assumed to be in the stem (i.e. web). Both of these assumptions would be checked in the design process. Next, the effective width of the slab was calculated according to ACI The effective width of the slab is the portion of the T-beam flange that contributes to the strength of the T-beam. For interior beam lines the effective width of the slab cannot be greater than onequarter of the clear span length and the overhanging flange width must be less than eight times the slab thickness and must also be less than one half the adjacent clear span. For exterior spans, the overhanging flange width cannot exceed one-twelfth the span length of the beam, six times the slab thickness and one-half the clear distance to the next web. After the effective width was calculated, the effective depth was then found. For the positive bending sections, the effective depth was the beam depth minus the two and a half (2.5) inches, which includes the cover distance (1.5 inches), the diameter of the stirrup bar (0.5 inches) and half of the longitudinal rebar diameter (which was assumed to be a #8 bar). For the negative section, the effective depth was the T-beam depth minus the cover (0.75 inches), the transverse rebar (0.5 inches) and half of the longitudinal rebar diameter (which was assumed to be a #8 bar). The distributed load that the T-beam supported was then found by multiplying the tributary

12 Bartolini 12 area of the T-beam (half the center-to-center span to each side of the T-beam) by either the floor or roof load. This value was added to the self-weight of the beam stem for the total line load. Then using the corresponding ACI moment coefficients, the moment for each section was found. Using the moment for the section along with the effective depth of the section, the width of the T-beam and an assumed reduction factor (ϕ) of 0.90, the area of steel required in each section was found and a combination of bar sizes was selected. The effective depth was then check again using the same methodology (but using the actual value of half the diameter of the longitudinal steel) to make sure it was approximately the value that was assumed. The extreme tension strain and the reduction factor (ϕ) were then verified to be the same as the values that were assumed. The clear distance spacing of the bars was also checked using ACI 318. Finally, the minimum and maximum steel requirements were verified according to ACI and and the design strength of the T-beam was checked. For beam lines C, D and E, the extreme tension stress and ϕ factor were not verified as they were assumed and the beams were not in compliance with the code. Therefore, for these beam lines the beam depth was increased to twenty (20) inches and the process was repeated. This beam depth resulted in a design that complied with the code. The reinforcement details (elevation and cross-sections) for floor beam lines A and G can be seen in Figure 6. The elevation and cross-section reinforcement details for all the unique beam lines can be found in Figures A7 to A12 in the Appendix. The T-beam flexural reinforcement calculations can be found in Appendix D. It should be noted that only one steel reinforcement design was used between S3 and S4. The section that requires the larger amount of steel will control the steel region at the first interior support.

13 Bartolini 13 Figure 6: Floor T-Beam Reinforcing Elevation and Sections for Beam Lines A and G

14 Bartolini 14 T-beam Design for Shear Next in the design process was the determination of the shear reinforcement. Without shear reinforcement the beam would have a catastrophic failure due to shear-web and flexure-shear cracks. These cracks would form due to the shear forces in the beam and cause equivalent tension stresses that would cause failure in the beam since concrete is very weak in tension. This failure would be sudden and extremely dangerous and must be designed against. Additionally, this is incredibly important because this failure occurs substantially before the flexural strength of the beam is reached. Therefore stirrups at a determined spacing are used to provide a source of tensile strength against these shear forces (and equivalent tensile stresses). As was the case with the T-beam flexural design, there are six unique beam lines that must be designed for shear. Additionally, like the T-beam flexural design, beam lines A and G; B and F; and C, D and E compose three groups of identical beam lines and then there are the two loading conditions for each group (i.e. the floor and the roof loads). The shear forces at the critical locations were determined using the shear coefficients from ACI 318 with the same line load that was used in the flexural design (i.e. the tributary area of the T- beam multiplied by the area load combined with the T-beam stem self-weight). The effective depth was also calculated using the most conservative value from the positive moment sections in the flexural design. The shear diagram was then constructed by applying the shear coefficients from ACI 318. The shear at the columns was truncated at a distance d away from the support (so there is a constant shear away from the supports to a distance d away from the support at which the shear will connect back to the original shear diagram). The strength of the concrete in shear was then calculated with a factor of safety. The portions of the beam where the reduced strength of the concrete itself was greater than the factored shear force on the beam are required to have the minimum web reinforcement. A #4 stirrup was used and the required maximum spacing was determined to be seven and a half (7.5) inches. For the portion of the shear diagram that had a shear force above the concrete shear strength, the minimum spacing for strength purposes were tabulated. In all the sections, this value was above the maximum spacing limits that were the same as above (for the region where the reduced

15 Bartolini 15 concrete shear strength was greater than the factored shear force). An additional check was conducted to make sure that the maximum spacing limits could be used according to ACI code. After conducting all of these checks, it was determined that #4 stirrups could be used at seven and a half (7.5) inches for all T-beams in the entire structure. Next, the starting locations were determined with a goal of having them roughly half of the spacing away from the supports. It was actually determined that the stirrups could start exactly one half of the spacing away from the supports, which is three and three-quarter (3.75) inches. Figure 7 shows the shear reinforcement. Figure 7: Shear Reinforcement Figures 8 shows a sample factored shear diagram for the floor load for beam lines A and G. It should be noted that the s max value of seven and a half (7.5) inches can be used everywhere. For the full set of shear diagrams, see Figures A13 to A18 in the Appendix.

16 Bartolini 16 Figure 8: Floor Load Shear Diagram for Beam Lines A & G The full T-beam shear reinforcement design calculations can be found in Appendix E. Crack Control Cracks pose not only aesthetic problems to a building, but cracks also can lead to faster corrosion rates that can accelerate the failure of the beam. Therefore, ACI 318 limits the spacing of the rebar to control the cracking of the concrete. First the T-beams were checked for cracking according to Equation (10-4) in ACI 318 with the assumption that the stress in the rebar was two-thirds the yield stress. Every T-beam section had adequate spacing of the longitudinal rebar. Next, the slab reinforcement was checked. Again using Equation (10-4) in ACI 318 and the assumption that the stress in the rebar was two-thirds the yield stress, the maximum spacing allowed by code was found. However, this maximum spacing was twelve (12) inches, which was smaller than any of the slab reinforcing in the original design. Therefore, the slab reinforcing fails code and must be re-designed with a maximum spacing of twelve inches. The best way to accomplish this would be to reduce the size of the bar to a #3 bar and use the corresponding spacing needed per the strength requirements or twelve inches, whichever is smaller. This would be the most economical way to change the design, as it would most likely

17 Bartolini 17 not rely on an ACI minimum anymore. When a design relies on an ACI minimum it is typically not the most efficient design. The full crack control calculations can be found in Appendix F. T-beam Deflection Control Deflections must be controlled in any structure in order to make the building feels safe and is serviceable. Additionally, deflections must be controlled so that the non-structural components of the building do not fail. For the T-beam deflection control analysis, the un-factored loads were used in the calculation, but were found exactly the same way as they were in the flexural design of the T-beams. Additionally, each span was checked for deflection. Therefore, there were twelve (12) spans that had to be checked, as there were the exterior and interior spans under roof and floor loading for three distinct beam lines. The first step in the deflection calculation was to find the effective moment of inertia of the T- beam cross-section assuming the full load was applied to the building early on in the construction process (this is in order to be conservative). This effective moment of inertia is the moment of inertia for the beam based on the amount of cracking in the beam (it is always somewhere in-between the moment of inertia of a fully cracked beam and a completely uncracked beam). First the gross moment of inertia was found for the T-beam cross-sections (disregarding the fact that there was steel in the T-beam, which is allowed by code and is conservative). Then each critical point on each span (i.e. the negative bending moments near the columns and the positive bending moment at the mid-span) was checked to see if the section was cracked. If the section was cracked (which was the case for the majority of the sections), the cracked moment of inertia for the beam was calculated. Next the effective moment of inertia for each of the critical sections was found according to ACI 318 using the weighted average method for each span (i.e. the mid-span effective moment of inertia was multiplied by one half and each of the support effective moment of inertias was multiplied by one quarter). Using the deflection equation for a continuous span, the deflection under the total load was found.

18 Bartolini 18 It was assumed that the beam carried a partition that was sensitive to deflections and therefore according to ACI 318, the beam deflection after the partition is installed cannot be greater than the span length divided by 480. The assumed loading history used was that the partitions were installed after the shoring from the dead load of the structure was removed and the immediate deflection due to the dead load was experienced. Therefore, the deflection experienced by the partitions would be the long-term dead load deflection; the immediate live load deflection for both the short-term portion of the live load (50 psf) and the sustained portion of the live load, which was the partition s weight (20 psf); and the long-term deflection from the partitions. Assuming that after the full initial deflection occurred, that the stress-strain plot was linear and passed through the origin, the above deflections were calculated using ACI 318. All the T- beams passed except the interior spans under floor loads for beam column lines B, C, D, E and F. These cross-sections would need to be redesigned with a larger T-beam web depth or maybe additional steel. However, if additional steel was added, the design must be re-checked to make sure the extreme tension fiber stress is below the limits set by ACI 318. The full set of deflection calculations can be found in Appendix G. Column Design The last part of the design that was completed was the determination of the reinforcement for the columns. The columns are the most critical part of the building because the failure of a column, especially a column lower in the building, could have devastating ramifications. The failure of a column could result in the failure of a large portion, or all, of the building. Columns are deemed more important in the design of building than the design of the beams or the floor systems because if a beam or floor collapses, the damage may be contained to a much smaller area than if a column fails. This is called the strong column, weak beam design theory. First the maximum axial and moment loads that each column could experience were found. These loads were divided into the dead loads (i.e. mechanical equipment, roofing material, slab self-weight, column self-weight, T-beam self-weight) and the live loads (i.e. the partitions, general live load, and snow). The top and bottom of each column were analyzed by looking at two different loading conditions. Both conditions include the entire dead load of the structure. However, the loading conditions vary based on which bays the live load is applied. For both

19 Bartolini 19 scenarios the simplest loading scenario that causes the maximum bending is assumed to be the starting point (this is typically achieved by applying the live load on the bay that frames into the section of the column being analyzed that causes that largest moment). In the first loading scenario, the live load is then applied to the other bays of the structure as long as the moment in the column being analyzed is not affected. In the second loading scenario, only the initial live load to cause the maximum moment is applied (i.e. no additional bays are loaded from the first step). In this way, the column is designed for both axial loading and eccentric loading. Using these loading scenarios, the moment was calculated in the beams and using structural analysis the distribution of the moment in the beam to the moments in the column was computed. Then using this moment in the column along with the axial load in the column, the reinforcement was found using Graph A.5 and Graph A.6 in Nilson et al for both loading cases at the top and bottom of each column. Next, the governing steel requirement was found for a given column (i.e. the largest steel requirement from the top and bottom of each column when considering both loading conditions). After the longitudinal steel was chosen, the ties were chosen in accordance to ACI 318. Since #4 bars were used as the stirrups in the T-beams, #4 ties were also chosen so that there was consistency in the materials on the jobsite and no confusion would be made between the bars. Using the constraints that the spacing could not be more than sixteen times the diameter of the longitudinal steel, forty-eight times the diameter of the ties and the least dimension of the compression member, the tie spacing was determined for every floor of every column line as well. The longitudinal reinforcement along with the tie spacing for each story of every column in the building is present in Tables 1 and 2. The exterior column notation refers to columns on grid lines 1 and 4 while the interior column notation refers to columns on grid lines 2 and 3.

20 Bartolini 20 Table 1: Column Longitudinal Reinforcement Story Column Lines A and G Column Lines B and F Column Lines C, D and E Exterior Interior Exterior Interior Exterior Interior 1 4 #7 4 #7 4 #7 4 #9 4 #7 4 # #7 4 #7 4 #7 4 #9 4 #7 4 # #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 5 4 #7 4 #7 4 #11 4 #7 4 #11 4 #7 Table 2: Column Tie Spacing Story Column Lines A and G Column Lines B and F Column Lines C, D and E Exterior Interior Exterior Interior Exterior Interior A number of the column longitudinal reinforcement was based on the ACI minimum of 1% steel in the column. This indicates an efficient design. Ideally the percentage of steel in the column should be closer to 4%. Therefore, in future iterations of this design, a smaller columns size should be used. The pattern in the column reinforcement is that on the exterior of the building, the roof experiences considerable bending and therefore more steel is needed in these regions. Additionally, the interior middle column lines of the structure also need additional reinforcement at the lower stories due to the large axial loads that the columns are subjected to. Figure 9 shows the column cross-sections for column lines B2, B3, F2 and F3.

21 Bartolini 21 Figure 9: Column Reinforcement for Interior Column Lines B and F (B2, B3, F2, F3) The cross-sections showing the reinforcement for all the column lines can be found in Appendix A (FigureA19 to Figure A23). The tabulated data for the design of the columns can be found in Appendix H. In these tabulations, any column reinforcement that is denoted with an asterisk means that for this value, a higher value of the reduction factor (ϕ) was used to keep the necessary steel reinforcement to a minimum. This higher value was checked for each section in which it was used and all calculations comply with ACI 318. Summary and Conclusions Using ACI 318, a preliminary design of a five-story office reinforced concrete office building was completed. Overall, the structure is a very efficient building with only a couple of edits needed in future iterations of the design. It was determined that the design did not fully comply with ACI 318 code, but that these flaws would be revised in future edits to the overall design. The loads for the structure were determined from ASCE 7 with the load combinations from ACI 318. The columns were determined to be fifteen (15) inches by fifteen (15) inches with a slab thickness of seven (7) inches and T-beam depths that varied from eighteen (18) inches to twenty (20) inches in the first design. These T-beam depths would be increased for selected beam lines up to twenty-two (22) inches for deflection control reasons. The chosen T-beam flexural reinforcement was verified through crack control checks and strength checks, as was the T-beam shear reinforcement. However, the slab reinforcement did not comply the ACI 318 crack control standards. Therefore, the size and spacing of the slab reinforcing would have to be edited in the

22 Bartolini 22 next design check to make sure the spacing was no more than twelve (12) inches. Finally, the reinforcement in the columns varied throughout the structure with the maximum reinforcement in the top of the exterior column lines (due to high bending) and at the bottom of the interior columns lines (due to large axial loads). The ties for the columns were also designed according to ACI 318. Because the minimum steel reinforcement according to ACI 318 was used for the columns, these columns should be made smaller in future iterations of the design so the structure can be more efficient. The next step in this design project would be to complete a number of iterations on the design until it compiles with ACI 318. Recommendations This design is only a preliminary design for this reinforced concrete building and several further revisions are still needed for this design to be complete. In future revisions to this building, there are a handful of recommendations that I would make. The first is to reduce the slab reinforcement to #3 bars, which would mean a closer spacing. This would be the most economic solution to the problem with the spacing of the slab reinforcement that arose when checking the crack control. Whenever a design is forced to use a minimum value in the code, which was the case in the slab spacing, that design is typically not as economical as it could be. In this case, simply reducing the spacing while still using #4 bars would not be economical. Using a #3 bar at a smaller spacing would result in a more efficient design, as less material would be used. Additionally, I would increase the depth of the T-beams under floor loading on beam lines B and F to twenty (20) inches and then I would increase the depth of the T-beams under floor loading on beam lines C, D and E to twenty-one (21) or twenty (22) inches. These changes would result in all the T-beams being in compliance with ACI 318 deflection limits. Finally, since the column reinforcement was commonly governed by the ACI minimum, in future iterations I would decrease the column sizes so that the columns would be more efficient

23 Bartolini 23 and have closer to 4% steel instead of the minimum 1% steel. As stated above, whenever the design is limited by the ACI minimum, it means there is a more efficient way to the design the structure. In this case it would be smaller column sizes and more column steel reinforcement.

24 Bartolini 24 Appendix A: Design Figures Figure A1: Floor Slab Design Figure A2: Plan of Floor Slab Design (Top Steel)

25 Figure A3: Plan of Floor Slab Design (Bottom and Temperature/Shrinkage Steel) Bartolini 25

26 Bartolini 26 Figure A4: Roof Slab Design Figure A5: Plan of Roof Slab Design (Top Steel)

27 Figure A6: Plan of Roof Slab Design (Bottom and Temperature/Shrinkage Steel) Bartolini 27

28 Bartolini 28 Figure A7: Floor T-Beam Reinforcing Elevation and Sections for Beam Lines A and G

29 Bartolini 29 Figure A8: Roof T-Beam Reinforcing Elevation and Sections for Beam Lines A and G

30 Bartolini 30 Figure A9: Floor T-Beam Reinforcing Elevation and Sections for Beam Lines B and F

31 Bartolini 31 Figure A10: Roof T-Beam Reinforcing Elevation and Sections for Beam Lines B and F

32 Bartolini 32 Figure A11: Floor T-Beam Reinforcing Elevation and Sections for Beam Lines C, D and E

33 Bartolini 33 Figure A12: Roof T-Beam Reinforcing Elevation and Sections for Beam Lines C, D and E

34 Bartolini 34 Figure A13: Floor Load Shear Diagram for Beam Lines A & G Figure A14: Roof Load Shear Diagram for Columns A & G

35 Bartolini 35 Figure A15: Floor Load Shear Diagram for Columns B & F Figure A16: Roof Load Shear Diagram for Columns B & F

36 Bartolini 36 Figure A17: Floor Load Shear Diagram for Columns C, D & E Figure A18: Roof Load Shear Diagram for Columns C, D & E

37 Bartolini 37 Figure A19: Column Reinforcement For Column Lines A and G (A1, A2, A3, A4, G1, G2, G3, G4) Figure A20: Column Reinforcement for Exterior Column Lines B and F (B1, B4, F1, F4) Figure A21: Column Reinforcement for Exterior Column Lines C, D and E (C1, C4, D1, D4, E1, E4)

38 Bartolini 38 Figure A22: Column Reinforcement for Interior Column Lines B and F (B2, B3, F2, F3) Figure A23: Column Reinforcement for Interior Column Lines C, D and E (C2, C3, D2, D3, E2, E3)

39 Bartolini 39 Appendix B: Loading Estimation Table B1: Roof Load Calculation Un-factored Loads (psf) Load Factor Factored Loads (psf) Snow Roofing Material Mech. Eq, Ceiling Slab (7") Total Table B2: Floor Load Calculation Un-factored Loads (psf) Load Factor Factored Loads (psf) Live Load Mech. Eq., Ceiling Partitions Slab (7") Total 235

40 Bartolini 40 Appendix C: Slab Design Calculations Table C1: Slab Design - Floor Givens Quadratic Equation Solver wu (lb/ft) 235 a b 12 b d 6 φ 0.9 β 0.85 S1 S2 S3 S4 S5 S6 ln (in) Mcoeff Mu (lb-in) R (psi) ρ A sreqd (in 2 ) A smin (in 2 ) A sgoverning (in 2 ) Bar Size and Spacing 15" 15" 15" 15" 13" A sprovided (in 2 ) CHECKS d OK OK OK OK OK OK a c εt Max Steel ok if εt > OK OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK OK Max Spacing (1) Max Spacing (2) Spacing < Max Spacing OK OK OK OK OK OK Minimum Spacing Spacing > Min Spacing OK OK OK OK OK OK Temperature/Shrinkage Steel A smin (in 2 ) Bar Size and Spacing 15" 15" 15" 15" 15" 15" A sprovided (in 2 ) Max Spacing (1) Max Spacing (2) Spacing < Max Spacing OK OK OK OK OK OK

41 Bartolini 41 Table C2: Slab Design - Roof Givens Quadratic Equation Solver wu (lb/ft) a b 12 b d 6 φ 0.9 β 0.85 S1 S2 S3 S4 S5 S6 ln (in) Mcoeff Mu (lb-in) R (psi) ρ A sreqd (in 2 ) A smin (in 2 ) A sgoverning (in 2 ) Bar Size and Spacing 15" 15" 15" 15" 15" 15" A sprovided (in 2 ) CHECKS d OK OK OK OK OK OK a c εt Max Steel ok if εt > OK OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK OK Max Spacing (1) Max Spacing (2) Spacing < Max Spacing OK OK OK OK OK OK Minimum Spacing Spacing > Min Spacing OK OK OK OK OK OK Temperature/Shrinkage Steel A smin (in 2 ) Bar Size and Spacing 15" 15" 15" 15" 15" 15" A sprovided (in 2 ) Max Spacing (1) Max Spacing (2) Spacing < Max Spacing OK OK OK OK OK OK

42 Bartolini 42 Appendix D: T-Beam Flexure Design Calculations Table D1: T-Beam Flexure Design Floor Load Col. A/G Givens Quadratic Equation Solver W (lb/ft 2 ) 235 a wu (lb/ft) 0.15 b b 15 h 18 d (positive bending) 15.5 d (negative bending) 16 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 2 #7 2 #7 2 #9 2 #9 3 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

43 Bartolini 43 Table D2: T-Beam Flexure Design Roof Load Col. A/G Givens Quadratic Equation Solver W (lb/ft 2 ) a wu (lb/ft) 0.12 b b 15 h 18 d (positive bending) 15.5 d (negative bending) 16 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 3 #5 3 #5 3 #7 3 #7 2 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

44 Bartolini 44 Table D3: T-Beam Flexure Design Floor Load Col. B/F Givens Quadratic Equation Solver W (lb/ft 2 ) 235 a wu (k/in) 0.31 b b 15 H 18 d (positive bending) 15.5 d (negative bending) 16 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 2 #9 4 #7 7 #7 7 #7 5 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

45 Bartolini 45 Table D4: T-Beam Flexure Design Roof Load Col. B/F Givens Quadratic Equation Solver W (lb/ft 2 ) a wu (lb/ft) 0.24 b b 15 h 18 d (positive bending) 15.5 d (negative bending) 16 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 5 # 5 3 #7 6 # 7 6 #7 4 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

46 Bartolini 46 Table D5: T-Beam Flexure Design Floor Load Col. C/D/E Givens Quadratic Equation Solver W (lb/ft 2 ) 235 a wu (lb/ft) b b 15 H 20 d (positive bending) 17.5 d (negative bending) 18 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 2 #9 4 #7 4 #9 4 #9 5 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

47 Bartolini 47 Table D6: T-Beam Flexure Design Roof Load Col. C/D/E Givens Quadratic Equation Solver W (lb/ft 2 ) a wu (lb/ft) 0.26 b b 15 h 20 d (positive bending) 17.5 d (negative bending) 18 φ 0.9 β 0.85 S1 S2 S3 S4 S5 ln (in) Clear Span Length (in) bf (in) - span length bf (in) - slab thickness bf (in) - adjacent span bf (in) - governing Mcoeff Mu (k-in) R (psi) ρ A sreqd (in 2 ) Bar Size and Spacing 3 #7 3 #7 3 #9 3 #9 4 #7 A sprovided (in 2 ) CHECKS Spacing d a c εt Max Steel ok if εt > OK OK OK OK OK φ = 0.90 if εt > OK OK OK OK OK Minimum Steel (1) Minimum Steel (2) Governing Minimum Steel Steel > Minimum Steel OK OK OK OK OK φmn φmn > Mu OK OK OK OK OK

48 Bartolini 48 Appendix E: T-Beam Shear Design Calculations Table E1: T-Beam Shear Design Floor Load Col. A/G Givens W (lb/ft 2 ) 235 wu (k/in) 0.15 b 15 h 18 d (positive bending) φ 0.75 A v 0.4 (#4 stirrups) A B C ln (in) C v V u V u at d φv c s max (1) s max (2) s max (3) s max (4) smax φv s φ*sqrt(f'c)*bwd φ*sqrt(f'c)*bwd φvs < 4φ*sqrt(f'c)*bwd OK OK OK φvs < 8φ*sqrt(f'c)*bwd OK OK OK smin smax<smin OK OK OK Practical Limit (s>4") OK OK OK SPACING Exterior - Interior # of spacing # of stirrups # of spacing (actual) distance away from support

49 Bartolini 49 Table E2: T-Beam Shear Design Roof Load Col. A/G Givens W (lb/ft 2 ) wu (lb/ft) 0.12 b 15 h 18 d (postive bending) φ 0.75 A v 0.4 (#4 stirrups) A B C ln (in) C v V u V u at d φv c s max (1) s max (2) s max (3) s max (4) smax φv s φ*sqrt(f'c)*bwd φ*sqrt(f'c)*bwd φvs < 4φ*sqrt(f'c)*bwd OK OK OK φvs < 8φ*sqrt(f'c)*bwd OK OK OK smin smax<smin -- OK OK Practical Limit (s>4") OK OK OK SPACING Exterior - Interior # of spacing # of stirrups # of spacing (actual) distance away from support

50 Bartolini 50 Table E3: T-Beam Shear Design Floor Load Col. B/F Givens W (lb/ft 2 ) 235 wu (k/in) 0.31 b 15 h 18 d (postive bending) φ 0.75 A v 0.4 (#4 stirrups) A B C ln (in) C v V u V u at d φv c s max (1) s max (2) s max (3) s max (4) smax φv s φ*sqrt(f'c)*bwd φ*sqrt(f'c)*bwd φvs < 4φ*sqrt(f'c)*bwd OK OK OK φvs < 8φ*sqrt(f'c)*bwd OK OK OK smin smax<smin OK OK OK Practical Limit (s>4") OK OK OK SPACING Exterior - Interior # of spacing # of stirrups # of spacing (actual) distance away from support