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 , t fire ( θ )
, is determined for each segment :
• t fire ( θ )
= – 0.1990 ∙ θ + 834.4
• θ max = 937 ° F
• 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
Conc . cover
c b mm
Conc . temp . θ ° F
Bond stress
t fire ( θ ) psi 60 620 711 70 513 732 80 433 748 90 380 759 100 340 767 110 300 775 120 300 775 130 253 784 140 253 784 150 253 784 160 220 791 170 220 791 ≥ 180 220 791
Note : The value of t fire ( θ ) for each segment is greater than t equiv
= 509 psi from Step 1 . In Step 4 below we will limit the segment bond stress t fire ( θ ) accordingly .
Step 4 : Determine the development length needed for the fire condition :
• 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 a , fire =
Σ n seg i = 1 π ∙ d b ∙ l seg ∙ t 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
∙ t fire ( θ ), segi
8 May 2023