1 Introduction
- \(HL\)—is the Leeb hardness,
- \(V_{R}\)—is the bounce back velocity of the object,
- \(V_{A}\)—is the impact velocity of the object.
2 Experimental Program
2.1 Fire Test Set Up
2.2 Test specimens
Steel grade | Cooling mode | Fire exposure time (min) | Temperature (°C) | |||||
---|---|---|---|---|---|---|---|---|
100 | 200 | 300 | 400 | 500 | 600 | |||
Q235 | Water cooling | 5 | \({\text{AW}}_{1}^{5}\) | \({\text{AW}}_{2}^{5}\) | \({\text{AW}}_{3}^{5}\) | \({\text{AW}}_{4}^{5}\) | \({\text{AW}}_{5}^{5}\) | \({\text{AW}}_{6}^{5}\) |
10 | \({\text{AW}}_{1}^{10}\) | \({\text{AW}}_{2}^{10}\) | \({\text{AW}}_{3}^{10}\) | \({\text{AW}}_{4}^{10}\) | \({\text{AW}}_{5}^{10}\) | \({\text{AW}}_{6}^{10}\) | ||
15 | \({\text{AW}}_{1}^{15}\) | \({\text{AW}}_{2}^{15}\) | \({\text{AW}}_{3}^{15}\) | \({\text{AW}}_{4}^{15}\) | \({\text{AW}}_{5}^{15}\) | \({\text{AW}}_{6}^{15}\) | ||
Natural cooling | 5 | \({\text{AN}}_{1}^{5}\) | \({\text{AN}}_{2}^{5}\) | \({\text{AN}}_{3}^{5}\) | \({\text{AN}}_{4}^{5}\) | \({\text{AN}}_{5}^{5}\) | \({\text{AN}}_{6}^{5}\) | |
10 | \({\text{AN}}_{1}^{10}\) | \({\text{AN}}_{2}^{10}\) | \({\text{AN}}_{3}^{10}\) | \({\text{AN}}_{4}^{10}\) | \({\text{AN}}_{5}^{10}\) | \({\text{AN}}_{6}^{10}\) | ||
15 | \({\text{AN}}_{1}^{15}\) | \({\text{AN}}_{2}^{15}\) | \({\text{AN}}_{3}^{15}\) | \({\text{AN}}_{4}^{15}\) | \({\text{AN}}_{5}^{15}\) | \({\text{AN}}_{6}^{15}\) | ||
Q345 | Water cooling | 5 | \({\text{BW}}_{1}^{5}\) | \({\text{BW}}_{2}^{5}\) | \({\text{BW}}_{3}^{5}\) | \({\text{BW}}_{4}^{5}\) | \({\text{BW}}_{5}^{5}\) | \({\text{BW}}_{6}^{5}\) |
10 | \({\text{BW}}_{1}^{10}\) | \({\text{BW}}_{2}^{10}\) | \({\text{BW}}_{3}^{10}\) | \({\text{BW}}_{4}^{10}\) | \({\text{BW}}_{5}^{10}\) | \({\text{BW}}_{6}^{10}\) | ||
15 | \({\text{BW}}_{1}^{15}\) | \({\text{BW}}_{2}^{15}\) | \({\text{BW}}_{3}^{15}\) | \({\text{BW}}_{4}^{15}\) | \({\text{BW}}_{5}^{15}\) | \({\text{BW}}_{6}^{15}\) | ||
Natural cooling | 5 | \({\text{BN}}_{1}^{5}\) | \({\text{BN}}_{2}^{5}\) | \({\text{BN}}_{3}^{5}\) | \({\text{BN}}_{4}^{5}\) | \({\text{BN}}_{5}^{5}\) | \({\text{BN}}_{6}^{5}\) | |
10 | \({\text{BN}}_{1}^{10}\) | \({\text{BN}}_{2}^{10}\) | \({\text{BN}}_{3}^{10}\) | \({\text{BN}}_{4}^{10}\) | \({\text{BN}}_{5}^{10}\) | \({\text{BN}}_{6}^{10}\) | ||
15 | \({\text{BN}}_{1}^{15}\) | \({\text{BN}}_{2}^{15}\) | \({\text{BN}}_{3}^{15}\) | \({\text{BN}}_{4}^{15}\) | \({\text{BN}}_{5}^{15}\) | \({\text{BN}}_{6}^{15}\) | ||
Q390 | Water cooling | 5 | \({\text{CW}}_{1}^{5}\) | \({\text{CW}}_{2}^{5}\) | \({\text{CW}}_{3}^{5}\) | \({\text{CW}}_{4}^{5}\) | \({\text{CW}}_{5}^{5}\) | \({\text{CW}}_{6}^{5}\) |
10 | \({\text{CW}}_{1}^{10}\) | \({\text{CW}}_{2}^{10}\) | \({\text{CW}}_{3}^{10}\) | \({\text{CW}}_{4}^{10}\) | \({\text{CW}}_{5}^{10}\) | \({\text{CW}}_{6}^{10}\) | ||
15 | \({\text{CW}}_{1}^{15}\) | \({\text{CW}}_{2}^{15}\) | \({\text{CW}}_{3}^{15}\) | \({\text{CW}}_{4}^{15}\) | \({\text{CW}}_{5}^{15}\) | \({\text{CW}}_{6}^{15}\) | ||
Natural cooling | 5 | \({\text{CN}}_{1}^{5}\) | \({\text{CN}}_{2}^{5}\) | \({\text{CN}}_{3}^{5}\) | \({\text{CN}}_{4}^{5}\) | \({\text{CN}}_{5}^{5}\) | \({\text{CN}}_{6}^{5}\) | |
10 | \({\text{CN}}_{1}^{10}\) | \({\text{CN}}_{2}^{10}\) | \({\text{CN}}_{3}^{10}\) | \({\text{CN}}_{4}^{10}\) | \({\text{CN}}_{5}^{10}\) | \({\text{CN}}_{6}^{10}\) | ||
15 | \({\text{CN}}_{1}^{15}\) | \({\text{CN}}_{2}^{15}\) | \({\text{CN}}_{3}^{15}\) | \({\text{CN}}_{4}^{15}\) | \({\text{CN}}_{5}^{15}\) | \({\text{CN}}_{6}^{15}\) |
2.3 Parameters Investigated During the Tests
2.4 Test Procedure and Parameters
2.4.1 Fire Test
2.4.1.1 The Fire Temperature and Furnace Temperatures Range
2.4.1.2 Heating Rate and Duration of Fire Exposure
2.4.1.3 Temperature Control
2.4.2 Cooling Process and Parameters
2.4.3 Different Stress State
2.5 Post-fire Leeb Hardness Tests
3 Test Results Analysis
3.1 Effect of Cooling Mode and Fire Exposure Duration of Fire Exposure on Leeb Hardness
3.2 Effect of Steel Strength Grade on Leeb Hardness
3.3 Effect of Stress State on Leeb Hardness
3.4 Different Leeb Hardness on Steel Flange and Web
3.5 Effect of Different Test Locations in the Steel Members on Leeb Hardness
3.6 Limitation of Leeb Hardness Method
4 Correlation Between the Post Fire Residual Strength of the Steel and Leeb Hardness
4.1 Relation Between Tensile Strength and Leeb Hardness Under Ambient Temperature
Regression method | Correlation coefficient | Mean error (%) | Standard deviation of error (%) |
---|---|---|---|
\(\sigma_{\text{b}} = 1. 9 2 9\times HLD - 245.439\) | 0.975 | 2.01 | 2.49 |
\(\sigma_{\text{b}} = 0 . 0 0 8\times HLD^{2} - 3.729 \times HLD + 807.022\) | 0.987 | 12.17 | 12.82 |
\(\sigma_{\text{b}} = 102.574 \times {\text{e}}^{0.004 \times HLD}\) | 0.985 | 1.46 | 1.96 |
\(\sigma_{\text{b}} = 0.055 \times {\text{HLD}}^{1.531}\) | 0.979 | 1.98 | 2.42 |
4.2 Relation Between the Post-fire Tensile Strength and Leeb Hardness at Flange
4.2.1 Cooling by Water
4.2.2 Natural Cooling
4.2.3 Comparison of Regression Results to Test Results
HLD | Tested tensile strength (MPa) | Calculated tensile strength (MPa) | Errors (%) | |
---|---|---|---|---|
\(BW_{1}^{5}\) | 392 | 463.69 | 423.99 | 8.6 |
\(BW_{1}^{10}\) | 394 | 475.44 | 428.25 | 9.9 |
\(BW_{1}^{15}\) | 394 | 425.25 | 428.25 | 0.7 |
\(BW_{2}^{5}\) | 394 | 454.38 | 428.25 | 5.8 |
\(BW_{2}^{10}\) | 395 | 427.63 | 430.39 | 0.6 |
\(BW_{2}^{15}\) | 396 | 443.06 | 432.55 | 2.4 |
\(BW_{3}^{5}\) | 397 | 452.00 | 434.72 | 3.8 |
\(BW_{3}^{10}\) | 397 | 476.81 | 434.72 | 8.8 |
\(BW_{3}^{15}\) | 398 | 456.00 | 436.90 | 4.2 |
\(BW_{4}^{5}\) | 399 | 438.31 | 439.09 | 0.2 |
\(BW_{4}^{10}\) | 400 | 457.13 | 441.29 | 3.5 |
\(BW_{4}^{15}\) | 401 | 462.81 | 443.50 | 4.2 |
\(BW_{5}^{5}\) | 403 | 464.06 | 447.96 | 3.5 |
\(BW_{5}^{10}\) | 403 | 476.56 | 447.96 | 6.0 |
\(BW_{5}^{15}\) | 403 | 483.31 | 447.96 | 7.3 |
\(BW_{6}^{5}\) | 405 | 474.31 | 452.46 | 4.6 |
\(BW_{6}^{10}\) | 405 | 490.94 | 452.46 | 7.8 |
\(BW_{6}^{15}\) | 406 | 476.56 | 454.73 | 4.6 |
4.3 Relation Between the Post-fire Tensile Strength and Leeb Hardness at Web
HLD | Tested tensile strength (MPa) | Calculated tensile strength (MPa) | Errors (%) | |
---|---|---|---|---|
\(CN_{1}^{5}\) | 371 | 551.67 | 571.37 | 3.6 |
\(CN_{1}^{10}\) | 372 | 544.75 | 574.24 | 5.4 |
\(CN_{1}^{15}\) | 373 | 574.50 | 577.12 | 0.5 |
\(CN_{2}^{5}\) | 373 | 557.25 | 577.12 | 3.6 |
\(CN_{2}^{10}\) | 374 | 568.33 | 580.01 | 2.1 |
\(CN_{2}^{15}\) | 374 | 555.50 | 580.01 | 4.4 |
\(CN_{3}^{5}\) | 376 | 549.42 | 585.84 | 6.6 |
\(CN_{3}^{10}\) | 376 | 564.75 | 585.84 | 3.7 |
\(CN_{3}^{15}\) | 376 | 551.67 | 585.84 | 6.2 |
\(CN_{4}^{5}\) | 378 | 585.08 | 591.73 | 1.1 |
\(CN_{4}^{10}\) | 379 | 559.33 | 594.69 | 6.3 |
\(CN_{4}^{15}\) | 379 | 570.83 | 594.69 | 4.2 |
\(CN_{5}^{5}\) | 380 | 562.17 | 597.67 | 6.3 |
\(CN_{5}^{10}\) | 381 | 581.75 | 600.67 | 3.3 |
\(CN_{5}^{15}\) | 381 | 588.08 | 600.67 | 2.1 |
\(CN_{6}^{5}\) | 382 | 578.58 | 603.68 | 4.3 |
\(CN_{6}^{10}\) | 383 | 572.25 | 606.70 | 6.0 |
\(CN_{6}^{15}\) | 384 | 575.83 | 609.75 | 5.9 |