5 Floor454

Reinforced Concrete Design Project Five Story Office Building

Andrew Bartolini | December 7, 2012 Designer 1 | Partner: Shannon Warchol CE 40270: Reinforced Concrete Design

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

Bartolini | 3 Abstract

This report outlines the structural design of a five-story reinforced concrete office building

following ACI 318-11. 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 318-11.

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

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.

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Figure 2: Elevation View

This report will explain the preliminary design process for this five-story reinforced concrete

office building according to ACI 318-11. 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.

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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

179.4 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 ft2.

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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 in2.

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 slabs 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.

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 0.005 in order to verify a previous assumption that the strength reduction factor

() was 0.90.

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.

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Figure 3: Floor Slab Design

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

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 over-

reinforced 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).

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 8.12.3. 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 one-

quarter 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

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 () 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 () 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 10.3.5 and 10.5.1

and the design strength of the T-beam was checked.

For beam lines C, D and E, the extreme tension stress and 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.

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

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

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 smax 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.

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

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 un-

cracked 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.

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 partitions 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

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.

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 #11

2 4 #7 4 #7 4 #7 4 #9 4 #7 4 #11

3 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

1 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 15 #4 @ 14 #4 @ 15

2 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 15 #4 @ 14 #4 @ 15

3 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14

4 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14 #4 @ 14

5 #4 @ 14 #4 @ 14 #4 @ 15 #4 @ 14 #4 @ 15 #4 @ 14

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.

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 () 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

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

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.

Bartolini | 24 Appendix A: Design Figures

Figure A1: Floor Slab Design

Figure A2: Plan of Floor Slab Design (Top Steel)

Bartolini | 25

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

Bartolini | 26

Figure A4: Roof Slab Design

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

Bartolini | 27

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

Bartolini | 28

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

Bartolini | 29

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

Bartolini | 30

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

Bartolini | 31

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

Bartolini | 32

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

Bartolini | 33

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

Bartolini | 34

Figure A13: Floor Load Shear Diagram for Beam Lines A & G

Figure A14: Roof Load Shear Diagram for Columns A & G

Bartolini | 35

Figure A15: Floor Load Shear Diagram for Columns B & F

Figure A16: Roof Load Shear Diagram for Columns B & F

Bartolini | 36

Figure A17: Floor Load Shear Diagram for Columns C, D & E

Figure A18: Roof Load Shear Diagram for Columns C, D & E

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)

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)

Bartolini | 39 Appendix B: Loading Estimation

Table B1: Roof Load Calculation Un-factored Loads (psf) Load Factor Factored Loads (psf) Snow 30 1.6 48 Roofing Material 7 1.2 8.4 Mech. Eq, Ceiling 15 1.2 18 Slab (7") 87.5 1.2 105

Total 179.4

Table B2: Floor Load Calculation Un-factored Loads (psf) Load Factor Factored Loads (psf) Live Load 50 1.6 80 Mech. Eq., Ceiling 15 1.2 18 Partitions 20 1.6 32 Slab (7") 87.5 1.2 105

Total 235

Bartolini | 40 Appendix C: Slab Design Calculations

Table C1: Slab Design - Floor

Givens

Quadratic Equation Solver wu (lb/ft) 235

a 529200

b 12

b -60000 d 6

0.9 0.85

S1 S2 S3 S4 S5 S6 ln (in) 153.00 153.00 165.00 165.00 177.00 177.00 Mcoeff 0.04 0.07 0.10 0.09 0.06 0.09

Mu (lb-in) 19101 32745 53316 48469 38345 55775 R (psi) 49.13 84.22 137.13 124.66 98.62 143.45

0.00082 0.00142 0.00233 0.00212 0.00167 0.00244

Asreqd (in2) 0.059 0.102 0.168 0.152 0.120 0.176

Asmin (in2) 0.1512 0.1512 0.1512 0.1512 0.1512 0.1512

Asgoverning (in2) 0.151 0.151 0.168 0.152 0.151 0.176 Bar Size and Spacing #4 @ 15" #4 @ 15" #4 @ 14" #4 @ 15" #4 @ 15" #4 @ 13"

Asprovided (in2) 0.155 0.155 0.17 0.155 0.155 0.18 CHECKS

d OK OK OK OK OK OK a 0.228 0.228 0.250 0.228 0.228 0.265 c 0.268 0.268 0.294 0.268 0.268 0.311 t 0.0641 0.0641 0.0582 0.0641 0.0641 0.0548

Max Steel ok if t > 0.004 OK OK OK OK OK OK = 0.90 if t > 0.005 OK OK OK OK OK OK

Max Spacing (1) 21 21 21 21 21 21 Max Spacing (2) 18 18 18 18 18 18

Spacing < Max Spacing OK OK OK OK OK OK Minimum Spacing 10.5 10.5 10.5 10.5 10.5 10.5

Spacing > Min Spacing OK OK OK OK OK OK Temperature/Shrinkage Steel

Asmin (in2) 0.1512 0.1512 0.1512 0.1512 0.1512 0.1512 Bar Size and Spacing #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15"

Asprovided (in2) 0.155 0.155 0.155 0.155 0.155 0.155 Max Spacing (1) 35 35 35 35 35 35 Max Spacing (2) 18 18 18 18 18 18

Spacing < Max Spacing OK OK OK OK OK OK

Bartolini | 41

Table C2: Slab Design - Roof

Givens

Quadratic Equation Solver wu (lb/ft) 179.4

a 529200

b 12

b -60000 d 6

0.9 0.85

S1 S2 S3 S4 S5 S6 ln (in) 153.00 153.00 165.00 165.00 177.00 177.00 Mcoeff 0.04 0.07 0.10 0.09 0.06 0.09

Mu (lb-in) 14582 24997 40701 37001 29273 42579 R (psi) 37.50 64.29 104.68 95.17 75.29 109.51

0.00063 0.00108 0.00177 0.00161 0.00127 0.00186

Asreqd (in2) 0.045 0.078 0.128 0.116 0.091 0.134

Asmin (in2) 0.1512 0.1512 0.1512 0.1512 0.1512 0.1512

Asgoverning (in2) 0.151 0.151 0.151 0.151 0.151 0.151 Bar Size and Spacing #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15"

Asprovided (in2) 0.155 0.155 0.155 0.155 0.155 0.155 CHECKS

d OK OK OK OK OK OK a 0.228 0.228 0.228 0.228 0.228 0.228 c 0.268 0.268 0.268 0.268 0.268 0.268 t 0.0641 0.0641 0.0641 0.0641 0.0641 0.0641

Max Steel ok if t > 0.004 OK OK OK OK OK OK = 0.90 if t > 0.005 OK OK OK OK OK OK

Max Spacing (1) 21 21 21 21 21 21 Max Spacing (2) 18 18 18 18 18 18

Spacing < Max Spacing OK OK OK OK OK OK Minimum Spacing 10.5 10.5 10.5 10.5 10.5 10.5

Spacing > Min Spacing OK OK OK OK OK OK Temperature/Shrinkage Steel

Asmin (in2) 0.1512 0.1512 0.1512 0.1512 0.1512 0.1512 Bar Size and Spacing #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15" #4 @ 15"

Asprovided (in2) 0.155 0.155 0.155 0.155 0.155 0.155 Max Spacing (1) 35 35 35 35 35 35 Max Spacing (2) 18 18 18 18 18 18

Spacing < Max Spacing OK OK OK OK OK OK

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/ft2) 235

a 529200

wu (lb/ft) 0.15

b -60000 b 15

h 18 d (positive bending) 15.5 d (negative bending) 16 0.9 0.85 S1 S2 S3 S4 S5

ln (in) 285.00 285.00 315.00 315.00 345.00 Clear Span Length (in) 285.00 285.00 285.00 345.00 345.00

bf (in) - span length 38.75 38.75 38.75 43.75 43.75 bf (in) - slab thickness 57.00 57.00 57.00 57.00 57.00 bf (in) - adjacent span 91.50 91.50 91.50 91.50 91.50

bf (in) - governing 38.00 38.00 38.00 43.00 43.00 Mcoeff 0.06 0.07 0.10 0.09 0.06

Mu (k-in) 769 878 1502 1366 1126 R (psi) 222.40 106.91 434.70 395.18 121.14

0.00384 0.00181 0.00778 0.00702 0.00206 Asreqd (in2) 0.921 1.067 1.867 1.685 1.371

Bar Size and Spacing 2 #7 2 #7 2 #9 2 #9 3 #7 Asprovided (in2) 1.2 1.2 2 2 1.8

CHECKS Spacing - 9.25 - - 4.1875

d 16.3125 15.5625 16.1875 16.1875 15.5625 a 1.412 0.557 2.353 2.353 0.739 c 1.661 0.656 2.768 2.768 0.869 t 0.0265 0.0682 0.0145 0.0145 0.0507

Max Steel ok if t > 0.004 OK OK OK OK OK = 0.90 if t > 0.005 OK OK OK OK OK Minimum Steel (1) 0.76 0.74 0.76 0.76 0.74 Minimum Steel (2) 0.80 0.78 0.80 0.80 0.78

Governing Minimum Steel 0.80 0.78 0.80 0.80 0.78 Steel > Minimum Steel OK OK OK OK OK

Mn 991.06 986.34 1600.94 1600.94 1470.70 Mn > Mu OK OK OK OK OK

Bartolini | 43 Table D2: T-Beam Flexure Design Roof Load Col. A/G

Givens

Quadratic Equation Solver W (lb/ft2) 179.4

a 529200

wu (lb/ft) 0.12

b -60000 b 15





Mu (k-in) 604 690 1181 1073 885 R (psi) 174.76 84.01 341.58 310.53 95.19

0.00299 0.00142 0.00601 0.00544 0.00161 Asreqd (in2) 0.718 0.835 1.443 1.305 1.073

Bar Size and Spacing 3 #5 3 #5 3 #7 3 #7 2 #7 Asprovided (in2) 0.93 0.93 1.8 1.8 1.2


d 16.4375 15.6875 16.3125 16.3125 15.5625 a 1.094 0.432 2.118 2.118 0.492 c 1.287 0.508 2.491 2.491 0.579 t 0.0353 0.0896 0.0166 0.0166 0.0776




Bartolini | 44 Table D3: T-Beam Flexure Design Floor Load Col. B/F

Givens


a 529200

wu (k/in) 0.31

b -60000 b 15

H 18 d (positive bending) 15.5 d (negative bending) 16 0.9 0.85 S1 S2 S3 S4 S5




Mu (k-in) 1564 1787 3057 2779 2292 R (psi) 452.53 116.43 884.51 804.10 123.24

0.00812 0.00197 0.01742 0.01553 0.00209 Asreqd (in2) 1.950 2.173 4.180 3.727 2.790

Bar Size and Spacing 2 #9 4 #7 7 #7 7 #7 5 #7 Asprovided (in2) 2 2.4 4.2 4.2 3


d 16.1875 15.5625 16.3125 16.3125 15.5625 a 2.353 0.597 4.941 4.941 0.616 c 2.768 0.702 5.813 5.813 0.724 t 0.0145 0.0635 0.0054 0.0054 0.0615




Bartolini | 45 Table D4: T-Beam Flexure Design Roof Load Col. B/F

Givens


a 529200

wu (lb/ft) 0.24

b -60000 b 15





Mu (k-in) 1211 1384 2367 2152 1775 R (psi) 350.44 90.16 684.97 622.70 95.44

0.00618 0.00152 0.01288 0.01156 0.00161 Asreqd (in2) 1.483 1.676 3.091 2.773 2.151

Bar Size and Spacing 5 # 5 3 #7 6 # 7 6 #7 4 #7 Asprovided (in2) 1.55 1.8 3.6 3.6 2.4


d 16.4375 15.5625 16.3125 16.3125 15.5625 a 1.824 0.447 4.235 4.235 0.492 c 2.145 0.526 4.983 4.983 0.579 t 0.0200 0.0857 0.0068 0.0068 0.0776




Bartolini | 46 Table D5: T-Beam Flexure Design Floor Load Col. C/D/E

Givens


a 529200

wu (lb/ft) 0.3303

b -60000 b 15

H 20 d (positive bending) 17.5 d (negative bending) 18 0.9 0.85 S1 S2 S3 S4 S5




Mu (k-in) 1677 1916 3277 2979 2457 R (psi) 383.31 97.91 749.20 681.09 103.65

0.00680 0.00166 0.01429 0.01280 0.00175 Asreqd (in2) 1.835 2.058 3.857 3.455 2.641

Bar Size and Spacing 2 #9 4 #7 4 #9 4 #9 5 #7 Asprovided (in2) 2 2.4 4 4 3


d 18.1875 17.5625 18.1875 18.1875 17.5625 a 2.353 0.597 4.706 4.706 0.616 c 2.768 0.702 5.536 5.536 0.724 t 0.0167 0.0721 0.0069 0.0069 0.0697




Bartolini | 47 Table D6: T-Beam Flexure Design Roof Load Col. C/D/E

Givens


a 529200

wu (lb/ft) 0.26

b -60000 b 15





Mu (k-in) 1300 1486 2541 2310 1905 R (psi) 297.27 75.93 581.03 528.21 80.38

0.00519 0.00128 0.01069 0.00962 0.00136 Asreqd (in2) 1.402 1.590 2.887 2.597 2.041

Bar Size and Spacing 3 #7 3 #7 3 #9 3 #9 4 #7 Asprovided (in2) 1.8 1.8 3 3 2.4


d 18.3125 17.5625 18.1875 18.1875 17.5625 a 2.118 0.447 3.529 3.529 0.492 c 2.491 0.526 4.152 4.152 0.579 t 0.0191 0.0971 0.0101 0.0101 0.0879




Bartolini | 48 Appendix E: T-Beam Shear Design Calculations

Table E1: T-Beam Shear Design Floor Load Col. A/G

Givens W (lb/ft2) 235 wu (k/in) 0.15 b 15 h 18 d (positive bending) 15.5625 0.75 Av 0.4 (#4 stirrups)

A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 21.58 24.81 26.12

Vu at d 19.22 22.46 23.76 Vc 16.61 16.61 16.61

smax (1) 7.78 7.78 7.78 smax (2) 24.00 24.00 24.00 smax (3) 32 32 32 smax (4) 34 34 34 smax 7.5 7.5 7.5 Vs 2.610 5.846 7.152

4*sqrt(f'c)*bwd 44.29165148 44.29165148 44.29165148 8*sqrt(f'c)*bwd 88.58330296 88.58330296 88.58330296

Vs < 4*sqrt(f'c)*bwd OK OK OK Vs < 8*sqrt(f'c)*bwd OK OK OK

smin 107.34 47.92 39.17 smax4") OK OK OK SPACING

Exterior - Interior # of spacing 38.00 - 46.00 # of stirrups 38 - 46

# of spacing (actual) 37 - 45 distance away from support 3.75 - 3.75

Bartolini | 49 Table E2: T-Beam Shear Design Roof Load Col. A/G

Givens W (lb/ft2) 179.4 wu (lb/ft) 0.12 b 15 h 18 d (postive bending) 15.5625 0.75 Av 0.4 (#4 stirrups)

A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 16.95 19.50 20.52

Vu at d 15.10 17.65 18.67 Vc 16.61 16.61 16.61

smax (1) 7.78 7.78 7.78 smax (2) 24.00 24.00 24.00 smax (3) 32 32 32 smax (4) 34 34 34 smax 7.5 7.5 7.5 Vs -1.507 1.036 2.062



smin -185.85 270.44 135.85 smax4") OK OK OK SPACING



Bartolini | 50 Table E3: T-Beam Shear Design Floor Load Col. B/F

Givens W (lb/ft2) 235 wu (k/in) 0.31 b 15 h 18 d (postive bending) 15.5625 0.75 Av 0.4 (#4 stirrups)

A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 43.90 50.49 53.14

Vu at d 39.11 45.69 48.35 Vc 16.61 16.61 16.61







Bartolini | 51 Table E4: T-Beam Shear Design Roof Load Col. B/F


A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 34.00 39.10 41.15

Vu at d 30.28 35.38 37.44 Vc 16.61 16.61 16.61







Bartolini | 52 Table E5: T-Beam Shear Design Floor Load Col. C/D/E

Givens W (lb/ft2) 235 wu (lb/ft) 0.3303 b 15 h 20 d (postive bending) 15.5625 0.75 Av 0.4 (#4 stirrups)

A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 47.06 54.12 56.97

Vu at d 41.92 48.98 51.83 Vc 16.61 16.61 16.61







Bartolini | 53 Table E6: T-Beam Shear Design Roof Load Col. C/D/E


A B C ln (in) 285.00 285.00 345.00

Cv 1.00 1.15 1.00 Vu 36.50 41.97 44.18

Vu at d 32.51 37.99 40.20 Vc 16.61 16.61 16.61







Bartolini | 54 Appendix F: Crack Control

Table F1: Crack Control Floor Load Col.

A/G

Givens fy (psi) 60000 fs (psi) 40000 Cover (in) 1.5 Stirrup Diameter (in) 0.5 Width 15

S2 S5 Steel Provided 2 # 7 3 # 7

smax 10 10 smax limit 12 12

smax governing 10 10 s 9.80 4.90

Is s

Bartolini | 55 Table F5: Crack Control Floor Load Col.

C/D/E

Givens fy (psi) 60000 fs (psi) 40000 Cover (in) 1.5 Stirrup Diameter (in) 0.5 Width 15

S2 S5 Steel Provided 4 # 7 5 # 7

smax 10 10 smax limit 12 12

smax governing 10 10 s 3.27 2.45

Is s

Bartolini | 56 Appendix G: Deflection Calculations

Table G1: Deflection Floor Load Col. A/G

Interior Exterior

Loads Dead Load - Mech (psf) 15 15 Dead Load - Slab (psf) 87.5 87.5

Tributary Length 7 7 Width (in) 15 15

T-Beam Depth (in) 18 18 Slab Depth (in) 7 7

concrete (pcf) 150 150 Beam Stem Weight (lb/ft) 171.88 171.88

Total Dead Load (k/ft) 0.89 0.89 Live Load (psf) 50 50

Partition Load (psf) 20 20 Total Live Load (k/ft) 0.49 0.49

Total Load (k/ft) 1.38 1.38

Ig for Uncracked Setion

beff (in) 43 38

yt (in) 6.69 6.95

yb (in) 11.31 11.05

Ig (in4) 11526 10998.4 Check if Negative Section #1 is Cracked

fr (psi) 474.34 474.34

Mcr- (k-ft) 68.134 62.595 Center-to-Center Span (ft) 30 30 Adjacent C-to-C Span (ft) 25 25

Clear Span (ft) 28.75 28.75 Adjacent Clear Span (ft) 23.75 23.75

ln (ft) 26.25 26.25

Ma- 86.41 95.048 Cracked? Yes Yes

Check if Negative Section #2 is Cracked

fr (psi) n/a 474.34

Mcr- (k-ft) n/a 62.595 Center-to-Center Span (ft) n/a 25 Adjacent C-to-C Span (ft) n/a n/a

Clear Span (ft) n/a 23.75 Adjacent Clear Span (ft) n/a n/a

ln (ft) n/a 23.75

Ma- n/a 48.628 Cracked? n/a No, Use Ig

Check if Positive Section is Cracked

fr (psi) 474.34 474.34

Mcr+ (k-ft) 40.27 39.328 Center-to-Center Span (ft) 30 25

Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75

Ma+ 71.23 55.58 Cracked? Yes Yes

Calculate Negative Ict #1 n 8.04 8.04

Steel 2 # 9 2 # 9

As (in2) 1.99 1.99

nAs (in2) 15.99 15.99 d (in) 16 16

Finding kd- A 7.5 7.5 B 15.99 15.99 C -255.9 -255.9

kd- (in) 4.87 4.87 Is kd In Web? Yes Yes

Ict- #2 2558.62 2558.62

Bartolini | 57

Calculate Negative Ict #2 n n/a n/a

Steel n/a n/a

As (in2) n/a n/a

nAs (in2) n/a n/a d (in) n/a n/a

Finding kd- A n/a n/a B n/a n/a C n/a n/a

kd- (in) n/a n/a Is kd In Web? n/a n/a

Ict- #1 n/a n/a

Calculate Positive Ict n 8.04 8.04

Steel 3 # 7 2 # 7

As (in2) 1.80 1.20

nAs (in2) 14.51 9.67 d (in) 15.5 15.5

Finding kd+ A 21.5 19 B 14.51 9.67 C -224.93 -149.95

kd+ 2.91 2.57 Is kd In Slab? Yes Yes

Ict+ 2653.43 1832.44

Calculating Ie

Ie- (#1) 6954.90 4969.18

Less Than Ig? Yes Yes

Ie- (#2) n/a 10998.39

Less Than Ig? n/a n/a

Ie+ 4254.71 5080.54


Average Ie 5604.81 6532.16 Deflection

0.397 0.178 Deflections Affecting Partitions

i,0.70l 0.0989 0.0442

i,0.30l 0.0424 0.0189

2 2

l,0.30l 0.0847 0.0379

3m 1 1

l,d 0.2563 0.1146

total 0.4821 0.21554

all 0.75 0.625 Passed? Yes Yes

Bartolini | 58 Table G2: Deflection Roof Load Col. A/G

Interior Exterior








Ig for Uncracked Section

beff (in) 43 38

yt (in) 6.69 6.95

yb (in) 11.31 11.05

Ig (in4) 11525.6 10998.4 Check if Negative Section #1 is Cracked

fr (psi) 474.34 474.34



ln (ft) 26.25 26.25



fr (psi) n/a 474.34



ln (ft) n/a 23.75



fr (psi) 474.34 474.34

Mcr+ (k-ft) 40.270 39.3277 Center-to-Center Span

(ft) 30 25 Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75



Steel 3 # 7 3 # 7

As (in2) 1.80 1.80

nAs (in2) 14.51 14.51 d (in) 16 16

Finding kd- A 7.5 7.5 B 14.51 14.51 C -232.19 -232.19


Ict- #2 2372.09 2372.09

Bartolini | 59


Steel n/a n/a

As (in2) n/a n/a




Ict- #1 n/a n/a


Steel 2 # 7 3 # 5

As (in2) 1.20 0.92

nAs (in2) 9.67 7.40 d (in) 15.5 15.5

Finding kd+ A 21.5 19 B 9.67 7.40 C -149.95 -114.76

kd+ 2.43 2.27

Is kd In Slab? Yes Yes

Ict+ 1858.31 1444.10

Calculating Ie

Ie- (#1) 10149.29 6641.90


Ie- (#2) n/a 10998.39


Ie+ 4882.00 7311.51




i,l 0.045125

9 0.021905

9

- - -

2 2

- - -

3m 1 1

l,d 0.2016 0.09789

total 0.2468 0.11979


Bartolini | 60 Table G3: Deflection Floor Load Col. B/F

Interior Exterior









beff (in) 86 71

yt (in) 5.44 5.74

yb (in) 12.56 12.26


fr (psi) 474.34 474.34

Mcr- (k-ft) 106.249 94.478 Center-to-Center Span

(ft) 30 30 Adjacent C-to-C Span (ft) 25 25


ln (ft) 26.25 26.25



fr (psi) n/a 474.34

Mcr- (k-ft) n/a 94.478 Center-to-Center Span

(ft) n/a 25 Adjacent C-to-C Span (ft) n/a n/a


ln (ft) n/a 23.75

Ma- n/a 97.279 Cracked? n/a Yes


fr (psi) 474.34 474.34


(ft) 30 25 Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75



Steel 7 # 7 7 # 7

As (in2) 4.21 4.21

nAs (in2) 33.86 33.86 d (in) 16 16

Finding kd- A 7.5 7.5 B 33.86 33.86 C -541.77 -541.77


Ict- #2 4428.89 4428.89

Bartolini | 61

Calculate Negative Ict #2 n n/a 8.04

Steel n/a 2 # 9

As (in2) n/a 1.99

nAs (in2) n/a 15.99 d (in) n/a 16

Finding kd- A n/a 6.12840 B n/a 15.99 C n/a -255.88

kd- (in) n/a 5.29 Is kd In Web? n/a Yes

Ict- #1 n/a 2439.23


Steel 5 # 7 4 # 7

As (in2) 3.01 2.41

nAs (in2) 24.19 19.35 d (in) 15.5 15.5

Finding kd+ A 43 35.5 B 24.19 19.35 C -374.89 -299.91

kd+ 2.68 2.65


Ict+ 4526.87 3635.39

Calculating Ie

Ie- (#1) 6793.80 5569.62


Ie- (#2) n/a 12780

Less Than Ig? n/a Yes

Ie+ 4865.12 4272.56




i,0.70l 0.203625

2 0.091975

4

i,0.30l 0.0873 0.0394

2 2

l,0.30l 0.1745 0.0788

3m 1 1

l,d 0.4736 0.2139

total 0.9390 0.4241

all 0.75 0.625 Passed? No Yes

Bartolini | 62 Table G4: Deflection Roof Load Col. B/F

Interior Exterior








Ig for Uncracked Setion

beff (in) 86 71

yt (in) 5.44 5.74

yb (in) 12.56 12.26


fr (psi) 474.34 474.34



ln (ft) 26.25 26.25



fr (psi) n/a 474.342



ln (ft) n/a 23.75

Ma- n/a 79.828

Cracked? n/a No, Use

Ig Check if Positive Section is Cracked

fr (psi) 474.34 474.34


(ft) 30 25 Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75



Steel 7 # 7 7 # 7

As (in2) 4.21 4.21

nAs (in2) 33.86 33.86 d (in) 16 16

Finding kd- A 7.5 7.5 B 33.86 33.86 C -541.77 -541.77


Ict- #2 4428.89 4428.89

Bartolini | 63

Calculate Negative Ict #2 n n/a 8.04

Steel n/a 2 # 9

As (in2) n/a 1.99

nAs (in2) n/a 15.99 d (in) n/a 16

Finding kd- A n/a 6.128 B n/a 15.99 C n/a -255.88

kd- (in) n/a 5.29 Is kd In Web? n/a Yes

Ict- #1 n/a 2439.23


Steel 5 # 7 4 # 7

As (in2) 3.01 2.41

nAs (in2) 24.19 19.35 d (in) 15.5 15.5

Finding kd+ A 43 35.5 B 24.19 19.35 C -374.89 -299.91

kd+ 2.68 2.65


Ict+ 4526.87 3635.39

Calculating Ie

Ie- (#1) 8708.48 6493.17


Ie- (#2) n/a 21151.97

Less Than Ig? n/a No

Ie+ 5138.98 4788.43




i,l 0.104965

1 0.0406877

- - -

2 2

- - -

3m 1 1

l,d 0.423 0.1641

total 0.528 0.205


Bartolini | 64 Table G5: Deflection Floor Load Col. C/D/E

Interior Exterior









beff (in) 86 71

yt (in) 5.95 6.32

yb (in) 14.05 13.68


fr (psi) 474.34 474.34



ln (ft) 26.25 26.25



fr (psi) n/a 474.34



ln (ft) n/a 23.75



fr (psi) 474.34 474.34

Mcr+ (k-ft) 56.07 54.259 Center-to-Center Span (ft) 30 25

Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75



Steel 4 # 9 4 # 9

As (in2) 3.98 3.98

nAs (in2) 31.99 31.99 d (in) 16 16

Finding kd- A 7.5 7.5 B 31.99 31.99 C -511.76 -511.76


Ict- #2 4258.47 4258.47

Bartolini | 65


Steel n/a n/a

As (in2) n/a n/a




Ict- #1 n/a n/a


Steel 5 # 7 4 # 7

As (in2) 3.01 2.41

nAs (in2) 24.19 19.35 d (in) 15.5 15.5

Finding kd+ A 43 35.5 B 24.19 19.35 C -374.89 -299.91

kd+ 2.68 2.65


Ict+ 4526.87 3635.39

Calculating Ie

Ie- (#1) 9960.24 7026.39


Ie- (#2) n/a 18780.72


Ie+ 5283.92 5057.20




i,0.70l 0.166 0.0735

i,0.30l 0.071 0.03148

2 2

l,0.30l 0.1424 0.0630

3m 1 1

l,d 0.391 0.173

total 0.7702 0.341

all 0.75 0.625 Passed? No Yes

Bartolini | 66 Table G6: Deflection Roof Load Col. C/D/E

Interior Exterior









beff (in) 86 71

yt (in) 5.95 6.32

yb (in) 14.05 13.68


fr (psi) 474.3 474.3

Mcr- (k-ft) 132.5004 117.50282 Center-to-Center Span

(ft) 30 30 Adjacent C-to-C Span

(ft) 25 25 Clear Span (ft) 28.75 28.75

Adjacent Clear Span (ft) 23.75 23.75

ln (ft) 26.25 26.25



fr (psi) n/a 474.3

Mcr- (k-ft) n/a 117.5 Center-to-Center Span

(ft) n/a 25 Adjacent C-to-C Span

(ft) n/a n/a Clear Span (ft) n/a 23.75

Adjacent Clear Span (ft) n/a n/a

ln (ft) n/a 23.75

Ma- n/a 97.13

Cracked? n/a No, Use

Ig Check if Positive Section is Cracked

fr (psi) 474.3 474.3


(ft) 30 25 Clear Span (ft) 28.75 23.75

ln (ft) 28.75 23.75



Steel 4 # 9 4 # 9

As (in2) 3.98 3.98

nAs (in2) 31.99 31.99 d (in) 16 16

Finding kd- A 7.5 7.5 B 31.99 31.99 C -511.76 -511.76


Ict- #2 4258.47 4258.47

Bartolini | 67


Steel n/a n/a

As (in2) n/a n/a




Ict- #1 n/a n/a


Steel 5 # 7 4 # 7

As (in2) 3.01 2.41

nAs (in2) 24.19 19.35 d (in) 15.5 15.5

Finding kd+ A 43 35.5 B 24.19 19.35 C -374.89 -299.91

kd+ 2.68 2.65


Ict+ 4526.87 3635.39

Calculating Ie

Ie- (#1) 11351.56 7701.80


Ie- (#2) n/a 18780.72


Ie+ 5468.65 5404.14




i,l 0.153624

7 0.0722003

- - -

2 2

- - -

3m 1 1

l,d 0.375 0.176

total 0.529 0.2487


Bartolini | 68 Appendix H: Column Design Calculations

Table H1: Column Reinforcement | Maximum Axial | Exterior Column Lines A and G

1L 1U 2L 2U 3L 3U 4L 4U 5L 5U Unfactored Loads

Beam Moment (DL) (k-ft) 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 31.4 33.1

Beam Moment (LL) (k-ft) 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 17.3 7.4

Distance Ratio 0.213 0.426 0.574 0.5 0.5 0.5 0.5 0.5 0.5 1 Column Moment

(DL) (k-ft) 6.68 13.36 18.00 15.68 15.68 15.68 15.68 15.68 15.68 33.08

Column Moment (LL) (k-ft) 3.68 7.36 9.92 8.64 8.64 8.64 8.64 8.64 8.64 7.40

Axial Force (DL) (k) 70.22 66.48 55.56 52.75 41.82 39.01 28.09 25.27 14.35 11.54

Axial Force (LL) (k) 27.13 27.13 21.00 21.00 14.88 14.88 8.75 8.75 2.63 2.63

Factored Loads Mu (k-ft) 13.9 27.8 37.5 32.6 32.6 32.6 32.6 32.6 32.6 51.5

Pu (k) 127.7 123.2 100.3 96.9 74.0 70.6 47.7 44.3 21.4 18.0

Kn 0.218 0.211 0.171 0.166 0.126 0.121 0.082 0.076 0.037 0.022

Rn 0.02 0.04 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.010

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7* Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 14 14

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (governing) 14 14 14 14 14 14 14 14 14 14

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

Bartolini | 69 Table H2: Column Reinforcement | Minimum Axial | Exterior Column Lines A and G





(DL) (k-ft) 6.68 13.36 18.00 15.68 15.68 15.68 15.68 15.68 15.68 33.08


Axial Force (DL) (k) 70.22 66.48 55.56 52.75 41.82 39.01 28.09 25.27 14.35 11.54

Axial Force (LL) (k) 6.13 6.13 6.13 6.13 6.13 6.13 6.13 6.13 2.63 2.63


Pu (k) 94.1 89.6 76.5 73.1 60.0 56.6 43.5 40.1 21.4 18.0

Kn 0.161 0.153 0.131 0.125 0.103 0.097 0.074 0.069 0.037 0.022

Rn 0.02 0.04 0.05 0.04 0.04 0.04 0.04 0.04 0.04 0.05

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.010

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7* Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 14 14

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (governing) 14 14 14 14 14 14 14 14 14 14

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

Bartolini | 70 Table H3: Column Reinforcement | Maximum Axial | Exterior Column Lines B and F





(DL) (k-ft) 13.07 26.14 35.22 30.68 30.68 30.68 30.68 30.68 30.68 65.07


Axial Force (DL) (k) 123.95 120.21 98.68 95.87 74.34 71.53 50.00 47.18 25.65 22.84

Axial Force (LL) (k) 58.13 58.13 45.00 45.00 31.88 31.88 18.75 18.75 5.63 5.63


Pu (k) 241.7 237.3 190.4 187.0 140.2 136.8 90.0 86.6 39.8 36.4

Kn 0.413 0.406 0.325 0.320 0.240 0.234 0.154 0.148 0.068 0.062

Rn 0.04 0.08 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.14

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.0100 0.0250

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 5.625

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #11 Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 18.048 22.4

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (govering) 14 14 14 14 14 14 14 14 15 15

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 15"

Bartolini | 71 Table H4: Column Reinforcement | Minimum Axial | Exterior Column Lines B and F





(DL) (k-ft) 12.84 25.67 34.59 30.13 30.13 30.13 30.13 30.13 30.13 63.96


Axial Force (DL) (k) 122.17 118.43 97.26 94.45 73.27 70.46 49.29 46.47 25.30 22.49

Axial Force (LL) (k) 13.13 13.13 13.13 13.13 13.13 13.13 13.13 6.13 5.63 5.63


Pu (k) 167.6 163.1 137.7 134.3 108.9 105.6 80.1 65.6 39.4 36.0

Kn 0.287 0.279 0.235 0.230 0.186 0.180 0.137 0.112 0.067 0.062

Rn 0.04 0.08 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.14

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.015 0.0275

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 3.375 6.1875

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #9 4 #11 Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 18.048 22.4

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (govering) 14 14 14 14 14 14 14 14 15 15

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 15"

#4 @ 15"

Bartolini | 72 Table H5: Column Reinforcement | Maximum Axial | Exterior Column Lines C, D and E





(DL) (k-ft) 13.84 27.68 37.30 32.49 32.49 32.49 32.49 32.49 32.49 68.93


Axial Force (DL) (k) 130.44 126.70 103.89 101.08 78.27 75.46 52.65 49.83 27.02 24.21

Axial Force (LL) (k) 62.00 62.00 48.00 48.00 34.00 34.00 20.00 20.00 6.00 6.00


Pu (k) 255.7 251.2 201.5 198.1 148.3 144.9 95.2 91.8 42.0 38.7

Kn 0.437 0.429 0.344 0.339 0.254 0.248 0.163 0.157 0.072 0.048

Rn 0.04 0.08 0.11 0.10 0.10 0.10 0.10 0.10 0.10 0.11

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.0175 0.0250

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 3.9375 5.625

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4#7 4 #9 4 #11* Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 18.048 22.4

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (governing) 14 14 14 14 14 14 14 14 15 15

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 15"

#4 @ 15"

Bartolini | 73 Table H6: Column Reinforcement | Minimum Axial | Exterior Column Lines C, D and E





(DL) (k-ft) 13.84 27.68 37.30 32.49 32.49 32.49 32.49 32.49 32.49 68.93


Axial Force (DL) (k) 130.44 126.70 103.89 101.08 78.27 75.46 52.65 49.83 27.02 24.21

Axial Force (LL) (k) 14.00 14.00 14.00 14.00 14.00 14.00 14.00 6.13 6.00 6.00


Pu (k) 178.9 174.4 147.1 143.7 116.3 112.9 85.6 69.6 42.0 38.7

Kn 0.306 0.298 0.251 0.246 0.199 0.193 0.146 0.086 0.052 0.048

Rn 0.04 0.08 0.11 0.10 0.10 0.10 0.10 0.07 0.07 0.11

pg 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.0175 0.025

Ast (in2) 2.25 2.25 2.25 2.25 2.25 2.25 2.25 2.25 3.9375 5.625

Steel Provided 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7 4 #7* 4 #9* 4 #11* Tie Spacing

smax (1) (in) 14 14 14 14 14 14 14 14 18.048 22.4

smax (2) (in) 24 24 24 24 24 24 24 24 24 24

smax (3) (in) 15 15 15 15 15 15 15 15 15 15

smax (governing) 14 14 14 14 14 14 14 14 15 15

Ties Provided #4 @ 14" #4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 14"

#4 @ 15"

#4 @ 15"

Bartolini | 74 Table H7: Column Reinforcement | Maximum Axial | Interior Column Lines A and G





(DL) (k-ft) 1.19 2.37 3.20 2.79 2.79 2.79 2.79 2.79 2.79 5.88


Axial Force (DL) (k) 137.55 133.81 109.57 106.76 82.51 79.70 55.46 52.65 28.40 25.59

Axial Force (LL) (k) 53.55 53.55 46.20 40.08 32.73 26.60 19.25 13.13 5.78 3.15


Pu (k) 250.7 246.3 205.4 192.2 151.4 138.2 97.4 84.

5 Floor454

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