2.4 DETERMINE DEVELOPMENT LENGTH NEEDED FOR FIRE CONDITION
2.5 DESIGN EXAMPLE WITH CONSTANT TEMPERATURE ALONG BOND LENGTH
Using the concrete temperature determined from Figure 4.4.2.2.1a of ACI / TMS 216.1 as θ determine the corresponding bond stress under fire conditions at that temperature, t fire( θ)
. This can then be determined from the graph, or by plugging θ into the provided equations for the Hilti adhesive product.
The maximum temperature, θ max
, is the highest temperature permitted for the adhesive and once beyond that temperature the product is assumed to have no bond stress. For constant temperature along the length of the rebar, if the concrete temperature at the bar exceeds θ max
, then additional concrete cover will be needed. For variable temperature along the length of the rebar, there may be segments where
θ max is exceeded and t fire( θ) is effectively zero and would not contribute to the overall bond stress in that section of the rebar for fire exposure, and the overall bond stress would be taken from the segments in the concrete where θ is less than
θ max
.
2.4 DETERMINE DEVELOPMENT LENGTH NEEDED FOR FIRE CONDITION
For constant temperature along the length of the rebar the value of t fire( θ) determined from the charts will be the value that is then compared to the value of t equiv calculated from the development length at the ambient temperature. From this, the development length needed for the fire condition can be calculated as follows:
l d, fire = t equiv
t fire( θ)
∙ l d
Note: If the development length for the fire condition, l d, fire
, is less than the ambient temperature development length,
l d
, then the ambient temperature development length, l d, should be used. Effectively, as long as the value of t fire( θ) is greater than the value of t equiv along the entire length of the rebar then the ambient temperature development length will control.
For variable temperature along the length of the rebar, the process is more iterative. The value of t fire( θ), seg will need to be determined at each of the equal length segments, l seg
, along the length of the bond length of the rebar, for a total number of segments, n seg
. Then, the value of t fire( θ), seg for each segment is multiplied by the surface area of the bar in each segment to give a segment bond strength N a, fire, seg( θ)
. The segment bond strengths can then be summed up for a total bond strength, N a, fire
. This total bond strength needs to be greater than the yield stress of the rebar.
N a, fire
= Σ n seg i = 1 π ∙ d b ∙ l leg, i ∙ t fire( θ), segi ≥ f y ∙ A se, N
Once the total number of segments is determined then the final development length needed for the fire condition can be calculated.
l d, fire
= n seg
· l seg
Note: The value of t fire( θ) in any individual segment cannot exceed t equiv determined from Section 2.1. Thus a development length for the fire condition will never be smaller than the development length determined at ambient temperature. Similar to the calculation for constant temperature along the length of the rebar, as long as the value of t fire( θ) in the warmest section of the concrete is greater than the value of t equiv then the ambient temperature development length will control and the iterative calculation above does not need to be performed.
Similar to determining the temperature at a specific concrete cover for variable concrete temperature, the smaller the value of l seg will lead to more calculations of t fire( θ), seg but will lead to a less conservative development length in the fire condition when larger values of l seg are used.
2.5 DESIGN EXAMPLE WITH CONSTANT TEMPERATURE ALONG BOND LENGTH
The following design example is for a floor slab extension in 4,000 psi normal weight concrete with carbonate aggregate.
Existing
Given:
Bond length
• ASTM A615 Gr. 60 reinforcement, # 6 rebar installed with HIT-FP 700 R
• Concrete cover, c b
= 2-inch
• Non-seismic floor loads only
New slab
Step 1: Determine ambient temperature development length and equivalent bond stress:
• From Table 3 of Section 3.0( or ACI 318 Chapter 25 Eq. 25.4.2.3) the development length for HIT-FP 700 R with # 6 rebar is determined:
6 September 2024