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Recent Projects

Featured Projects

Naval Air Station

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shim_trans  Summery
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shim_trans  Objective
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shim_trans  Project Background
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shim_trans  Scope of Work
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shim_trans  Bravo 25 Description
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shim_trans  Overview
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shim_trans  Crane Rail Removal
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shim_trans  Loss of Transverse
 Negative Moment
 Capacity over the
 Outboard Crane Rail
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shim_trans  Concrete Repair
 Materials
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shim_trans  Top Deck
 Repair Procedure
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shim_trans  Under Deck Repairs
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shim_trans  Cathodic Protection
 System
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shim_trans  Cathodic Protection
 System Installation
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shim_trans  Grout Resistivity
 Measurements
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shim_trans  Reinforcing Steel
 Lead Wire Installation
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shim_trans  Upgrade Reinforcement
 Introduction
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shim_trans  Analysis of Bravo-25
 Load Response
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arrow_right  Calculation of
 Bravo 25 Resistence
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shim_trans  Modes of Failure
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shim_trans  Bravo 25
 Upgrade Design
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shim_trans  Concrete Surface
 Preparation
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shim_trans  Embedded
 Reinforcement
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shim_trans  Wet Lay-up
 Composite Laminate
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shim_trans  Proof Tests using
 Impact Load Method
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shim_trans  Costs
 Acknowledgements
 References
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Turbine Deck Load Capacity Restored


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Home > Featured Project > Pearl Harbor

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Calculation of Bravo 25 Resistance

The original designers detailed Bravo 25 to be “under-reinforced” using the “working stress” method that was employed in the first half of the twentieth century. The reinforcing steel was detailed not to exceed an elastic limit (of 20 ksi (140mPa)) under design loads while the concrete stress remained below (an assumed elastic limit) 0.45fc’ (1,350 psi (9.3mPa)). This design procedure produces a highly “ductile” failure that is preceded by large cracks and deformation. The ultimate capacity is attained after the reinforcing steel yields followed by a concrete “failure” (defined at strain levels of 0.3 percent).

 

The “ultimate strength” flexural resistance of the existing sections is calculated from simple equilibrium analysis while maintaining compatibility of strains. The ultimate resistance of a conventionally steel reinforced section that is post reinforced with a carbon rod or laminate is different from the conventional section because the CFRP is linear-elastic to failure and has no plastic reserve. Given the under-reinforced sections of Bravo 25, the design objective was to obtain the maximum deck slab bending resistance after the reinforcing steel yields. Reinforcing steel yielding is followed by CFRP reinforcement failure and concrete crushing (0.3 percent concrete strain). This assumes that there is sufficient concrete strength to offset all tensile forces (under reinforced), there is sufficient shear strength, and the carbon composite and reinforcing steel retains firm bonding with the concrete up to failure. Lower bending resistance results if the concrete fails first (over-reinforced), if shear failure occurs, or if anchorage (bond) is compromised. The upgrade sections were checked to assure that these design assumptions were valid.

The following constituent assumptions were applied to calculating the bending resistance of a reinforced concrete cross section:

Idealized stress-strain for concrete, steel and CFRP. Steel strain hardening is ignored.
Concrete tensile force is ignored.
Strains are linearly distributed across the section in proportion to distance from the neutral axis (section planes remain plane).
The position of the forces and neutral axis remain constant.

 

Figure 46 shows the state of strain, stress, and force for calculating the bending resistance of a post strengthened reinforced-concrete section with embedded carbon bars. Similar methodology was applied to bending resistance of external carbon laminate where the dimension, h, would be replaced by the full depth of the concrete section.

 

figure46_m
Figure 46. Post strengthened cross section using embedded composite bars. Assumed stress, strain, and internal forces for calculation of bending resistance.

figure46a

figure46b

 

The strain relationships at maximum resistance are:

figure46c

 

Where: figure46d

The value of a/2 is normally dependent on the concrete strength, fc?. The average compressive stress in the concrete is 0.85 fc' (the standard American Concrete Institute (ACI) Code allowance).

figure46e

 

So figure46f

where “b” is the width of the section (or each unit width of a slab). Changing the concrete strength of an under reinforced section typical of those encountered in an existing, older Navy pier has little effect on its flexural resistance, Mr, because the value of a/2 is a small percentage of the total slab depth.

figure46g

 

The above relationship should be valid as long as the steel yields prior to a laminate failure and prior to the concrete strain reaching 0.003. This will be the case when the following relationship holds, which is the case for Bravo 25:

figure46h

 

In designing an upgrade to post-strengthen a section, the steel stress should be limited to its yield value and the carbon laminate stress should be limited to less than half of its measured strength. This sets the value of the total tensile force of the internal couple, which, in turn, sets the compression force. With the compression force known, the Whitney compression stress block is defined and the resisting moment can be determined with the equation above. Setting the laminate stress also sets the laminate strain so a check of neutral axis location and concrete strain can be made by compatibility of strain requirements and since planes remain plane. The equations above have been organized in an EXCEL® spreadsheet program to design flexural members using CFRP (i.e., laminate, pultruded strips, and embedded rods). The spreadsheet was used to detail the upgrade reinforcement knowing the response from the FEA analysis of Bravo 25.

 

In order to control crack width, the strain in the laminate may be restricted in the future to more than the limits listed above. This is important when it is deemed necessary to protect existing steel reinforcing from corrosion. For example, given a carbon laminate with an ultimate strength of 300 ksi and a modulus of 20,000 ksi (140 mPa), the laminate strain for a stress limit of 150 ksi (1,030 mPa) would be 0.0075 in./in. (m/m). The average crack width will be almost 0.1 inch (0.25 cm) for average crack spacing of 12 inches (30.5 cm) (larger for greater spacing). The ACI code (Section 9.4) limits reinforcement design strength to 80,000 psi (550 mPa) to control deformation and cracking. It would seem that similar restrictions may be necessary for CFRP reinforcement in future designs. There are no current guidelines limiting carbon laminate design stresses for the purpose of limiting deformation and control cracks. However, the ACI is formulating stress limits for carbon and other fiber composite reinforcement. Until the ACI code provisions are approved, NFESC recommends that the carbon fiber design stress never be allowed to exceed one half of the ultimate strength.

 

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ACE Restoration & Waterproofing, Inc.
620 E. Walnut Ave.
Fullerton, CA 92831
714.526.7366
Fax: 714.526.7965

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  ACE Restoration and Waterproofing Quick Service Overview:
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  by ACE Restoration and Waterproofing.

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