1 Introduction
2 Literature Review
3 Finite Element Analysis of Frame Structure
3.1 Initial Assumptions
3.2 Type of Analysis and Finite Elements
3.3 Boundary Condition
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Initial, which is the primary step implemented by the software to introduce the applied boundary conditions,
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Tightening the bolts by applying a double-sided load of 10 kN per bolt of each joint to obtain the initial contact of the joint surface elements, which was to simulate the initial tightening of the bolts,
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Dead and live load as applied gravity load. The self-weight of the steel frame structure and the floor slab with finishing layers was assumed as the permanent load.
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Column removal, which was implemented as a restraint loss at the "0" level for a selected central column in the support node. Two scenarios were adopted for the assessment of resistance:
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The first was to simulate the sudden removal of a column caused by local damage. This scenario was executed by abruptly removing the restraint of the selected support node of the middle column,
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The second scenario, as the gradual removal of the column due to a local fire, was assumed. To represent this state, the curve of the relationship of the temperature reduction coefficient according to (EN 1993-1-2) was used. The standard (EN 1993-1-2) gives three curves of the reduction factor at elevated temperatures. These curves give the values of the reduction coefficient of the steel element load capacity as a function of the increase in temperature.
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3.4 Mechanical Property of the Steel
3.5 Results of Frame Analysis
No | Structure scheme | Type of end-plate | Thickness of end-plate | Column loss scenario | Case indication |
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1 | 2-Bay frame “2B” | Flush end-plate “F” | 10 mm “10” | Sudden “S” | 2B_F10_S |
2 | 2-Bay frame “2B” | Flush end-plate “F” | 15 mm “15” | Sudden “S” | 2B_F15_S |
3 | 2-Bay frame “2B” | Flush end-plate “F” | 20 mm “20” | Sudden “S” | 2B_F20_S |
4 | 2-Bay frame “2B” | Extended end-plate “E” | 10 mm “10” | Sudden “S” | 2B_E10_S |
5 | 2-Bay frame “2B” | Extended end-plate “E” | 15 mm “15” | Sudden “S” | 2B_E15_S |
6 | 2-Bay frame “2B” | Extended end-plate “E” | 20 mm “20” | Sudden “S” | 2B_E20_S |
7 | 2-Bay frame “2B” | Flush end-plate “F” | 10 mm “10” | Gradual “G” | 2B_F10_G |
8 | 2-Bay frame “2B” | Flush end-plate “F” | 15 mm “15” | Gradual “G” | 2B_F15_G |
9 | 2-Bay frame “2B” | Flush end-plate “F” | 20 mm “20” | Gradual “G” | 2B_F20_G |
10 | 2-Bay frame “2B” | Extended end-plate “E” | 10 mm “10” | Gradual “G” | 2B_E10_G |
11 | 2-Bay frame “2B” | Extended end-plate “E” | 15 mm “15” | Gradual “G” | 2B_E15_G |
12 | 2-Bay frame “2B” | Extended end-plate “E” | 20 mm “20” | Gradual “G” | 2B_E20_G |
13 | 3-Bay frame “3B” | Flush end-plate “F” | 10 mm “10” | Sudden “S” | 3B_F10_S |
14 | 3-Bay frame “3B” | Flush end-plate “F” | 15 mm “15” | Sudden “S” | 3B_F15_S |
15 | 3-Bay frame “3B” | Flush end-plate “F” | 20 mm “20” | Sudden “S” | 3B_F20_S |
16 | 3-Bay frame “3B” | Extended end-plate “E” | 10 mm “10” | Sudden “S” | 3B_E10_S |
17 | 3-Bay frame “3B” | Extended end-plate “E” | 15 mm “15” | Sudden “S” | 3B_E15_S |
18 | 3-Bay frame “3B” | Extended end-plate “E” | 20 mm “20” | Sudden “S” | 3B_E20_S |
19 | 3-Bay frame “3B” | Flush end-plate “F” | 10 mm “10” | Gradual “G” | 3B_F10_G |
20 | 3-Bay frame “3B” | Flush end-plate “F” | 15 mm “15” | Gradual “G” | 3B_F15_G |
21 | 3-Bay frame “3B” | Flush end-plate “F” | 20 mm “20” | Gradual “G” | 3B_F20_G |
22 | 3-Bay frame “3B” | Extended end-plate “E” | 10 mm “10” | Gradual “G” | 3B_E10_G |
23 | 3-Bay frame “3B” | Extended end-plate “E” | 15 mm “15” | Gradual “G” | 3B_E15_G |
24 | 3-Bay frame “3B” | Extended end-plate “E” | 20 mm “20” | Gradual “G” | 3B_E20_G |
25 | 4-Bay frame “4B” | Flush end-plate “F” | 10 mm “10” | Sudden “S” | 4B_F10_S |
26 | 4-Bay frame “4B” | Flush end-plate “F” | 15 mm “15” | Sudden “S” | 4B_F15_S |
27 | 4-Bay frame “4B” | Flush end-plate “F” | 20 mm “20” | Sudden “S” | 4B_F20_S |
28 | 4-Bay frame “4B” | Extended end-plate “E” | 10 mm “10” | Sudden “S” | 4B_E10_S |
29 | 4-Bay frame “4B” | Extended end-plate “E” | 15 mm “15” | Sudden “S” | 4B_E15_S |
30 | 4-Bay frame “4B” | Extended end-plate “E” | 20 mm “20” | Sudden “S” | 4B_E20_S |
31 | 4-Bay frame “4B” | Flush end-plate “F” | 10 mm “10” | Gradual “G” | 4B_F10_G |
32 | 4-Bay frame “4B” | Flush end-plate “F” | 15 mm “15” | Gradual “G” | 4B_F15_G |
33 | 4-Bay frame “4B” | Flush end-plate “F” | 20 mm “20” | Gradual “G” | 4B_F20_G |
34 | 4-Bay frame “4B” | Extended end-plate “E” | 10 mm “10” | Gradual “G” | 4B_E10_G |
35 | 4-Bay frame “4B” | Extended end-plate “E” | 15 mm “15” | Gradual “G” | 4B_E15_G |
36 | 4-Bay frame “4B” | Extended end-plate “E” | 20 mm “20" | Gradual “G" | 4B_E20_G |
3.5.1 Results of the 4B_F20_G Frame Analysis
3.5.2 Results of the 4B_E20_S Frame Analysis
The average required angle of rotation of a joint | ||||||||
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Two-bay frame | Three-bay frame | Four-bay frame | ||||||
Case | Average value of rotation of joint (rad) | Collapse of structure | Case | Average value of rotation of joint (rad) | Collapse of structure | Case | Average value of rotation of joint (rad) | Collapse of structure |
2B_F10_S | > 0.150 | Yes | 3B_F10_S | > 0.118 | Yes | 4B_F10_S | > 0.114 | Yes |
2B_F15_S | > 0.130 | Yes | 3B_F15_S | > 0.087 | Yes | 4B_F15_S | > 0.089 | Yes |
2B_F20_S | > 0.118 | Yes | 3B_F20_S | > 0.068 | Yes | 4B_F20_S | > 0.081 | Yes |
2B_E10_S | 0.166 | No | 3B_E10_S | 0.141 | No | 4B_E10_S | 0.130 | No |
2B_E15_S | 0.090 | No | 3B_E15_S | 0.055 | No | 4B_E15_S | 0.076 | No |
2B_E20_S | 0.072 | No | 3B_E20_S | 0.069 | No | 4B_E20_S | 0.066 | No |
2B_F10_G | > 0.158 | Yes | 3B_F10_G | > 0.134 | Yes | 4B_F10_G | > 0.131 | Yes |
2B_F15_G | > 0.107 | Yes | 3B_F15_G | > 0.089 | Yes | 4B_F15_G | > 0.090 | Yes |
2B_F20_G | > 0.108 | Yes | 3B_F20_G | > 0.080 | Yes | 4B_F20_G | > 0.077 | Yes |
2B_E10_G | 0.197 | No | 3B_E10_G | 0.149 | No | 4B_E10_G | 0.134 | No |
2B_E15_G | 0.096 | No | 3B_E15_G | 0.071 | No | 4B_E15_G | 0.054 | No |
2B_E20_G | 0.084 | No | 3B_E20_G | 0.061 | No | 4B_E20_G | 0.055 | No |
The average required axial force in joint | ||||||||
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Two-bay frame | Three-bay frame | Four-bay frame | ||||||
Case | Average axial force in joint (kN) | Collapse of structure | Case | Average axial force in joint (kN) | Collapse of structure | Case | Average axial force in joint (kN) | Collapse of structure |
2B_F10_S | > 427.5 | Yes | 3B_F10_S | > 395.1 | Yes | 4B_F10_S | > 376.9 | Yes |
2B_F15_S | > 708.9 | Yes | 3B_F15_S | > 635.7 | Yes | 4B_F15_S | > 649.7 | Yes |
2B_F20_S | > 731.0 | Yes | 3B_F20_S | > 626.0 | Yes | 4B_F20_S | > 633.5 | Yes |
2B_E10_S | 750.5 | No | 3B_E10_S | 295.5 | No | 4B_E10_S | 241.0 | No |
2B_E15_S | 452.5 | No | 3B_E15_S | 261.4 | No | 4B_E15_S | 186.1 | No |
2B_E20_S | 400.1 | No | 3B_E20_S | 247.0 | No | 4B_E20_S | 236.1 | No |
2B_F10_G | > 267.2 | Yes | 3B_F10_G | > 292.8 | Yes | 4B_F10_G | > 240.4 | Yes |
2B_F15_G | > 718.4 | Yes | 3B_F15_G | > 631.1 | Yes | 4B_F15_G | > 625.4 | Yes |
2B_F20_G | > 770.2 | Yes | 3B_F20_G | > 632.7 | Yes | 4B_F20_G | > 630.3 | Yes |
2B_E10_G | 520.9 | No | 3B_E10_G | 160.1 | No | 4B_E10_G | 210.7 | No |
2B_E15_G | 305.1 | No | 3B_E15_G | 160.1 | No | 4B_E15_G | 194.8 | No |
2B_E20_G | 269.9 | No | 3B_E20_G | 132.0 | No | 4B_E20_G | 148.7 | No |