| |
|
 |
||||
 |
|
|
 |
|
 |
|
|
 |
|
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.
The strain relationships at maximum resistance are:
Where: 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).
So 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.
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:
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.
|
|
| |
|
|
|
|
|
|
|
|||||||||
