Post-Installed Reinforcing in Fire Conditions
Conc. cover c b mm Conc. temp. θ ° F Bond stress τ fire( θ) psi 60 620 783 70 513 834 80 433 873 90 380 898 100 340 917 110 300 937 120 300 937 130 253 959 140 253 959 150 253 959 160 220 975 170 220 975 ≥ 180 220 975
The value of τ fire( θ) for each segment is greater than τ equiv = 509 psi from Step 1. In Step 4 below we will limit the segment bond stress τ fire( θ) accordingly.
Step 4: Determine the development length needed for the fire condition:
•
From the graph above we get the following temperature gradient:
Conc. cover c b mm
Conc. temp. θ ° F 60 620 70 513 80 433 90 380 100 340 110 300 120 300 130 253 140 253 150 253 160 220 170 220 ≥ 180 220
Step 3: Determine the bond stress related to the concrete temperature in fire condition:
• From the equations of Figure 5 of Section 3.0 the bond stress, τ fire( θ), is determined for each segment:
• τ fire( θ) = – 0.480 · θ + 1080.5
• θ max = 1108 ° F
• Determine the yield strength of the rebar:
• N sa, y = f y · A se, N = 60,000ksi · 0.44in 2 = 26,400lb. Determine the total bond strength by summing up the segment bond stresses and multiplying by the bar area: n
• N a, fir = ∑ seg i = 1 π ⋅ db ⋅ l seg ⋅ τ fire( θ), segi
• Using the bond stress at each segment, sum up the segment length bond strengths until the rebar yield strength is reached. In the table below for each 10mm( 0.394-inch) segment a bond strength, N a, fire( θ), is calculated:
• N a, fire( θ) = π · d b · l seg · τ fire( θ), segi
Conc. cover c b mm
Bar length l d, fire in
Conc. temp. θ ° F
Bond stress τ fire( θ) psi
Bond strength N a, fire( θ) lb.
60 0.36 620 509 472 70 0.76 513 509 472 80 1.15 433 509 472 90 1.54 380 509 472 100 1.94 340 509 472 110 2.33 300 509 472 120 2.72 300 509 472 130 3.12 253 509 472 140 3.51 253 509 472 150 3.91 253 509 472 160 4.30 220 509 472 170 4.69 220 509 472 180 5.09 220 509 472 ⇩ ⇩ ⇩ ⇩ ⇩ 590 21.23 220 509 472 600 21.62 220 509 472 610 22.02 220 509 472
Total 26,441 lb.
8