Reinforced concrete: mechanics and design / James K. Wight, F.E. Richart, Jr., James G. Macgregor. Limit States and the Design of Reinforced Concrete In the design and analysis of reinforced concrete members, you are presented with a problem unfamiliar to most of you: “The mechanics of members consisting . kaz-news.info Let Your Life Reinforced Concrete: Design Theory and Examples, Third Edition.
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PDF | Reinforced concrete is widely used in building industry. Hence, graduates of every civil engineering programme must have basic. detailed design and detailing of reinforced concrete work to the Code. Detailing of individual types of members are included in the respective. Reinforced Concrete. PtD Process. Design team meeting. Design. Internal review . Issue for .. kaz-news.info • Behm M.
Sample design drawings of the floor slabs are shown in Figures The full set of design drawings are shown in Figures A1-A6 in the Appendix.
Floor Slab Design Figure 4: 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.
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.
Reinforced Concrete Design
Using ACI code, both the exterior and interior spans were checked and it was found that the interior T-beam depth 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.
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. Both of these assumptions would be checked in the design process.
Next, the effective width of the slab was calculated according to ACI 8. 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.
For the negative section, the effective depth was the T-beam depth minus the cover 0. 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. 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 clear distance spacing of the bars was also checked using ACI Finally, the minimum and maximum steel requirements were verified according to ACI 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. 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.
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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. The shear forces at the critical locations were determined using the shear coefficients from ACI with the same line load that was used in the flexural design i. 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 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. 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. 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. 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.
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. For the full set of shear diagrams, see Figures A13 to A18 in the Appendix. 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 limits the spacing of the rebar to control the cracking of the concrete. First the T-beams were checked for cracking according to Equation in ACI 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 in ACI 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.
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. 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 using the weighted average method for each span i. Using the deflection equation for a continuous span, the deflection under the total load was found. 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. 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 Is our service is satisfied, Anything want to say?
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Reinforced Concrete (analysis and design)
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Civil Reinforced Concrete Design Books.
Gambhir Book Free Download. Other Useful Links. Your Comments About This Post.The use of fibre reinforced concrete FRC for designing structural members in bending and shear has recently been addressed in the fib Model Code His contribution to the field of stability has been recognized and magnified by many high-quality papers in famous international journals such as Engineering Structures, Thin-Walled Structures, Journal of Constructional Steel Research and Journal of Structural Engineering.
Reinforced Concrete Design. Jb for flanged beams. 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 text is backed up by numerous illustrations, design charts and tables referring frequently to the relevant codes of practice. Step 14 below may be omitted if at Step 13 the critical section is selected at a distance of d from the face of support or from the concentrated load.
Accordingly, for some applications the whole-life cost will be price-competitive with steel-reinforced concrete. 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.
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