CE 4410 Principles of Reinforced Concrete

“Structural Design of Five Story Building”

Professor: Dr. Chao Sun

Submitted By:Chase Andrew Bowman

Date of Submission:May 5th, 2016

Department of Civil and Environmental EngineeringLouisiana State University and Agriculture & Mechanical College

Spring 2016

Table of Contents

ABSTRACT 3

INTRODUCTION 3

DESIGN 4

SLAB THICKNESS 4LOADS 4

ESTIMATION OF COLUMN SIZES 5SLAB DESIGN 5

BEAM DESIGN FOR FLEXURE 5BEAM DESIGN FOR SHEAR 6

CRACK CONTROL 6BEAM DEFLECTION CONTROL 7

COLUMN DESIGN 7

SUMMARY AND CONCLUSIONS 7

APPENDIX 7

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1. Abstract Reinforced concrete has been the main design method for designing building structures

in the past. Since concrete is designed to withstand compressional forces but is not able to withstand much tensional force, steel is required to reinforce the concrete molds from cracking. The processes taught in this CE 4410 course help determine the design dimensions and and criteria to withstand these forces and ensure that the building being designed is safe and structurally sound. Professional structural engineers work on real world problems like the one in this paper on an everyday basis and develop an efficient methodical process to ensure that nothing happens during the building life. Although reinforced-concrete designs have been calculated for many years, it is still a difficult process that requires tedious calculations that will affect the lives of everyone that uses the building. It is important to properly design a reinforced-concrete structure to withstand its self weights, dead loads, and live loads that are predicted and limited to its function. All calculations must be solved carefully and must satisfy regulations set forth by ACI standards. This report covers the structural design of a five story industrial reinforced concrete building. The roof and each story was subjected to specific dead and live loads that were taken into account for the design process. The designing process should result in a structurally sound building that can withstand the parameters given in the beginning. The design process of each part of the building is included under its appropriate section. Full calculations for each section can be found in the appendix and their subsections assigned to each category.

2. Introduction A five story industrial facility that covers approximately 4000 square feet of free space

was designed without any obstructing columns. The beam slab structural system consists of slabs, secondary beams, main beams, columns, and footings all made from reinforced concrete. The plan and cross section drawings of the project can be seen below in Figure 1.

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Figure 1: Project Plan and Cross Section View

During the design process, the critical members, or the members subjected to the highest loads, were considered for design. There was 90 psf of dead load and 50 psf of live load on the roof of the facility. On the floors of the facility, there was 30 psf of dead load and 80 psf of live load. Concrete was the material chosen to design the building structure shown above.

3. Design The following sections include an overview of how each part of the facility was designed.

A full set of calculations for each section can be found on the Appendix.

3.1. Slab Thickness When choosing the slab thickness (h), it depends on the method of slab design chosen.

There is a choice to design a one-way slab that is simply supported,one-end continuous, and both-end continuous. A one-way, both-end continuous slab was chosen which dictates the

thickness of the slab must have a minimum value of h= l28 according to Table 4.1 in Appendix

A. Refer to Appendix C for the calculations of the roof and floor slab.

3.2. Loads The load combinations considered for the industrial facility include both live and dead

loads. The live loads considered on the building included 50 psf on the roof and 80 psf on the

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floor of the facility. The dead loads considered on the building included 90 psf on the roof, 30 psf on the floors, and the weight of concrete which was assumed to be 150 pcf.

A load combination of 1.2 was used for the dead load combinations and a load combination of 1.6 was used for the live load combinations.

3.3. Estimation of Column Sizes An important factor in calculating column size in first to determine the tributary area that

that lies on the most heavily loaded column. The column that had the most concentrated load was column C2. The resulting tributary area for this column was 405 ft2. Calculating the tributary for the corner beams ,C1,was not necessary but it is safe to assume that the beam carries half of the load as beam C2, in result having a tributary area of 202.5 ft2.

Once the tributary area is found, the loading on the roof and floors were multiplied by it to determine the load for the bottom section of the column. This load will be factored in to determine the area of concrete needed to withstand this weight. Both the strength of the concrete and the strength of the steel was taken into consideration when calculating this area. Assuming 3% steel and accounting for reduction factors for safety reasons, the overall area of the column was 132.73¿2.

In result a circular column was used as a design assumption and was proven later in the calculations to be beneficial. Refer to Appendix H for more information. ❑❑

3.4. Slab Design When designing a slab, it must be able to resist bending in a parabolic shape, with the

highest moments being at the top of the slab near the supports and at the bottom of the slab near the mid-span. Overall the moment occurs between the two supporting beams (One-way slab). The first step in the slab design was to find the effective span length. For negative moments, theeffective 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. Refer to Appendix C for slab design calculations.

3.5. Beam Design for Flexure The beams of the project were designed with the flexural stresses that the beam would

be experiencing in mind. A T-beam was originally considered and calculated for the design of this project; however, a rectangular beam was chosen instead because the beams will run parallel with the reinforcing beams in the slab. The slab included reinforcement beams already; therefore, the rectangular sections were added below. Some of the original calculations of the T-beams that were not included in the design can be found in the appendix section titled I: Additional Calculations Not Included in Design.

The steel reinforcement is very important to the beam design because the steel reinforcement is very strong in tension while the concrete is very weak in tension. The following design process was followed in order to determine the concrete beam dimensions as well as the steel reinforcement needed.

The loads applied to the beams were calculated using the load combinations given in section 3.2. Using this factored load combination, including the assumed weight of the beam, a

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maximum moment calculation, Mu, was made and a ρ was assumed. These values were used to choose the section dimensions, b and d. If the selection of these values did not compute a value that was close to the originally assumed values, then a new beam weight should be assumed and new values calculated until an appropriate section is chosen. Once the concrete dimensions were chosen, the required reinforcing areas were calculated and the steel reinforcement bars were chosen from Table A.4 which can be found in the appendix section titled A: Design Figure.

The following beam dimensions and steel reinforcement bars were chosen for the design of the project following the previous steps described. The figure below can be used to further understand the dimensions chosen. For the main beam of the roof, B2, the following dimensions were calculated: b=20 inches, d=34 inches, and h=37 inches with 5#14 bars. For the secondary beam of the floor, B1, the following dimensions were calculated: b=9 inches, d=11.5 inches, and h=14 inches with 4#3 bars.For the secondary beam of the roof, B1, the following dimensions were calculated: b=9 inches, d=11.5 inches, and h=14 inches with 4#3 bars. For the main beam of the floor, B2, the following dimensions were calculated: b=22 inches, d=29.5 inches, and h=33 inches with 3#18 bars.

For each of the beams above, the maximum moment, Mu, had to be checked with the effective moment, Mn where Mn is greater than Mu. These calculations can be seen on the 𝜙 𝜙Flexural Calculations page in the appendix under title D: Beam Flexure Calculations.

3.6. Beam Design for Shear The shear reinforcement of the project is important in order to avoid failure due to

flexure-shear cracks. If closely spaced stirrups enclose the compression steel member, the bars will not buckle until additional moment is applied. In order to determine of stirrups are needed for the beam, the maximum shear stress, Vu, and the effective shear stress, 1/2 Vc, were 𝜙compared. If Vu is less than 1/2 Vc, then stirrups are not needed. If Vu is greater than 1/2 Vc, 𝜙 𝜙then stirrups are needed and the stirrup spacing, s, need to be calculated. In addition to the spacing of the stirrups, the nominal shear stress, Vs, is also calculated in order to confirm the maximum spacing. For B2 of the roof, it was calculated that stirrups were needed and the maximum spacing was 17 inches. For the roof B1 and the floor b1, it was calculated that stirrups were not needed. For B2 of the floor, it was calculated that stirrups were needed and the maximum spacing was 14.75 inches. The full shear calculations can be found in the appendix under the section labeled E: Beam Shear Calculations.

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3.7. Crack Control Cracks are going to occur due to concrete’s low tensile strength. Although they cannot

be eliminated, the they can be limited to acceptable sizes by properly distributing the reinforcement. For B2 in the roof, a maximum spacing of 7.5 inches is needed to prevent cracking.For B1 in the floor and the roof, a maximum spacing of 8.75inches is needed to prevent cracking.For B2 in the floor, a maximum spacing of 6.25 inches is needed to prevent cracking. The crack control calculations for the slabs can be found at the bottom of the slab calculations found in the appendix section titled C: Slab Design Calculations. The full calculations of the beams can be found in the section of the appendix titled F: Crack Control Calculations. However, the following calculations did not take miscellaneous cracks into consideration.

3.8. Beam Deflection Control When calculating the deflection of the designed beams, it is important to understand the

movement of the structure under the loads given. When looking at beam 1 at the roof level, the deflection calculates to be 0.2 in. which isn’t a high amount of deflection for a roof. Also no one will be on the roof so more deflection can be handled. The beams 1 on the lower floors have a deflection of 0.32 in. which can be managed as well. The deflection of beam 2 on the roof was calculated to be 3.56 in. that is extremely high when deal with the secondary beams. The secondary beams are in charge of handling the loads for the slab, primary, and the self-weight for the secondary beam. This deflection is due mainly because on the long span we set the beam to be. Recommend shortening girder length or add more reinforcing bars. The deflection for beam 2 on the lower floor levels was high as well with a value of 2.62 in.. The same revision s are recommended to minimize the deflection of the beams. Refer to Appendix G for calculations of deflections.

3.9. Column DesignThe final design step for the project was the supporting columns (C2), which are the

most important step in the building design. If the columns were to fail then the building would fail. On the other hand if a floor column were to fail the damage may be contained before it destroys the entire structure.

The first step was to calculate the maximum axial and moment load that each column was withstood. Multiple column loads were found at the roof section, floor section, and ground sections. The overall load increases as you go down the structure so the column design was based off of the loads at the bottom of the structure (ground) to ensure stability throughout the floors. See Appendix H for ground column summations and and calculations. These load were then divided into the dead and live loads. After all loads under various conditions were found, the area of steel and the total area of the concrete column is found taking into consideration reduction factors and total compressional strength of the concrete. By finding the total area to be 188.05¿2 and the area of steel of the column to be 5.64¿2, we can find the type of rebar that the circula column needs for proper reinforcement. The dimension for the steel reinforcement was found to be 6 #10 bars with 3 ¿2spirals at 2.5 in. spacing. Themselves needed no stirrups since the steel rebar could support the bending moments of the concrete column. See Appendix H for calculations and final column designs.

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4. Summary and ConclusionUsing ACI 318 and the Design of Reinforced Concrete textbooks as guides, a five story

industrial building was designed. The slab was designed with a thickness of 4 inches and was reinforced by steel bars

using #3 bars at 9 inches for the roof slab and #3 bars every 10 inches for the floor slab. For the main beam of the roof, B2, the following dimensions were calculated: b=20

inches, d=34 inches, and h=37 inches with 5#14 bars. For the secondary beam of the floor, B1, the following dimensions were calculated: b=9 inches, d=11.5 inches, and h=14 inches with 4#3 bars.For the secondary beam of the roof, B1, the following dimensions were calculated: b=9 inches, d=11.5 inches, and h=14 inches with 4#3 bars. For the main beam of the floor, B2, the following dimensions were calculated: b=22 inches, d=29.5 inches, and h=33 inches with 3#18 bars.

Both the strength of the concrete and the strength of the steel was taken into consideration when calculating this area. Assuming 3% steel and accounting for reduction factors for safety reasons, the overall area of the column was 132.73. In result a circular column was used as a design assumption and was proven later in the calculations to be beneficial.

This project only includes a preliminary design for an industrial building, the results should be checked and then double checked before it is considered for a final design.

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Appendix

A: Design Figures

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B: Load Estimate Calculations

Refer to other calculations in appendix section.

C: Slab Design Calculations

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D: Beam Flexure Calculations

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E: Beam Shear Calculations

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F: Crack Control Calculations

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G: Deflection Calculations

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H: Column Design Calculations

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I: Additional Calculations Not Included in Design

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