- Email: [email protected]
Structural performance of rotationally restrained steel columns in fire
Fire Safety Journal 36 (2001) 679–691
Structural performance of rotationally restrained steel columns in fire Faris Ali*, David O’Connor Fire Research Center, University of Ulster, Jordanstown, Co. Antrim BT37 0QB, UK Received 24 August 2000; received in revised form 8 December 2000; accepted 28 March 2001
Abstract The paper represents the outcomes of a parametric experimental investigation on the performance of rotationally restrained steel columns in fire. This experimental programme is a part of major research project performed at the Fire Research Center, University of Ulster in collaboration with the University of Sheffield. As a part of steel frames, half scale steel columns were tested in fire under two values of rotational restraint 0.18 and 0.93 and one value of axial restraint of approximately 0.29. Each case of rotational restraint was tested under five loading levels 0, 0.2, 0.4, 0.6 and 0.8. The paper includes a comparison with the behavior of a steel column previously tested in fire under axial restraint only. The paper represents also a method of estimating the effective length of fixed end (partial fixity) columns tested under fire. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Steel columns; Steel frames; Fire; Rotational Restraint; Effective length
1. Introduction When a fire takes place in a building and remains contained in a section of the building other unexposed parts remain relatively cool. This variance in thermal deformations imposes restraint on the structure’s elements under fire. In columns, the imposed restraint can be axial and rotational. Axial restraint opposes thermal axial expansion of the column while rotational restraint resists column’s end rotation. The imposed restraint can generate substantial unforeseen forces in the columns during fire adding another hazard that may cause uncalculated structural failure and increased losses and casualties. Effect of axial restraint on steel columns exposed to fire was investigated over the last twenty years by many researchers *Corresponding author. Tel.: +44-28-9036-8302; fax: +44-28-9036-6826. E-mail address: [email protected] (F. Ali). 0379-7112/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 1 7 - 0
680
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
[1,4–6,8–10] and others. These studies added a vital database to the literature both in the theoretical and the experimental fields of research. However, in practice cases of pure axial restraint can rarely be found. In most cases, in real structures rotational restraint conjuncts axial restraint. This point raises concerns about the necessity of studying the performance of steel columns subjected to both axial and rotational restraint during fire. Despite the fact that this issue has been studied theoretically by many researchers including [3,4,7], experimental investigation has been poor. Therefore a parametric investigation was conducted at the Fire Research Center, University of Ulster, UK (a joint research project with the University of Sheffield, UK) on the behavior of axially and rotationally restrained steel columns under high temperatures focusing on the forces generated during fire. Two parameters were involved in the study: the degree of rotational restraint and the loading level imposed on columns. Two extreme cases of rotational restraint were chosen, very high and very low. This paper presents a parametric experimental investigation of steel columns restrained axially and rotationally during fire. The paper discusses the main outcomes of the research and demonstrates measurements of generated forces, temperatures, lateral and axial displacements of the columns. It also includes a comparison with the behavior of a steel column previously tested in fire under axial restraint only. The paper represents a method of estimating the effective length of fixed end columns (partial fixity) tested under fire.
2. Rotational restraint The degree of rotational restraint r imposed on a column is defined as the ratio of the rotational stiffness of the surrounding (to the column) structure rs to the summation of rotational stiffness of the column rc and the structure rs : rs r¼ : ð1Þ rs þ rc According to Eq. (1) the following boundary conditions can be applied: when rs crc ; then rE1-the column end is fully fixed when rs E0; then r ¼ 0-the column is pin ended. In the experimental investigation which has been carried out, two degrees of rotational restraint were involved. Low value of restraint r1 ¼ 0:186 and high restraint r2 ¼ 0:936 (see Table 1). The rotational stiffness was worked out according to BS 5950, Appendix (E) where a value of column rotational stiffness=256 kN mm was calculated. The first restraint value r1 ¼ 0:186 was achieved by connecting two steel plates 200 10 mm (cross section) and 750 mm length to the top and the bottom of the column specimen (Fig. 1). The second degree of rotational restraint r2 ¼ 0:936 was produced by connecting two heavier steel plates of 200 40 mm2 (cross section) and the same length to the top and the bottom of the column. The two steel plates were connected to steel blocks using light bolts to simulate simple supports. The resulted steel frame is shown in Fig. 1.
681
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691 Table 1 Parameters involved in the testing program of rotationally restrained columnsa Degree of rot. restraint r
Applied rot. restraint rs kN mm
0.936
3746
P3UB1 0 (0)
P3UB2 0.2 (97 kN)
P3UB3 0.4 (145 kN)
P3UB4 0.6 (205 kN)
P3UB5 0.8 (284 kN)
0.186
58.5
P3UB6 0 (0)
P3UB7 0.2 (97 kN)
P3UB8 0.4 (145 kN)
P3UB9 0.6 (205 kN)
P3UB10 0.8 (284 kN)
Group 1 (H.R.R) Group 2 (L.R.R) a
Column ref., loading levels and loads
H.R.R.=High rotational restraint, L.R.R.=low rotational restraint; for r see Eq. (1).
3. The experimental programme In the research programme 10 columns 127 76UB13 were tested. All the columns were half scale with 1800 mm length. Table 1 shows the parameters involved in the investigation. As mentioned before, two degrees of rotational restraint were tested. Each degree was tested under five loading levels from 0% to 80% of the estimated compressive design load BS5950, Part 1. All the columns were subjected to an axial restraint degree of approximately 0.29 (imposed axial stiffness E57 kN/mm) [1,2]. The test programme was designed to be compatible with previously performed tests on columns with axial restraint only. Details of these tests including the rig and instrumentation can be found in references [1,2]. The rig used in the tests is the same as that used previously in the programme of tests on the axially restrained columns [1,2]. The rig was modified in order to impose rotational restraint in conjunction with axial restraint. The furnace used in these tests is the same furnace that was used in reference [1,2] with some alterations. The rig and the furnace layout are shown in Fig. 2. The top and the bottom plates of the steel frame were located outside the furnace (see Fig. 2) which allowed heating of the column only, leaving other parts of the steel frame at room temperature. The axial restraint imposed on the column was produced by the rig’s own stiffness (see Refs. [1,2]). The heated length of the column was E1750 mm. All the tests were performed following the same procedure to ensure repeatability. The axial load was first applied to the column by 5% load increments until the desired level was reached and this load was kept constant during the fire test. The applied loads were measured using two load cells of capacity 200 kN each. The nuts responsible for imposing axial restraint were then tightened to apply the axial restraint (Fig. 2), [1,2]. Then the fire was ignited until failure took place by losing stability (column buckling). All the columns were heated in the same rate. Typical time–temperature curves for the furnace (average of three points top, bottom and middle) and the steel column are shown in Fig. 3. The curve representing the column temperature is the average temperature of 20 thermocouples distributed on four levels over the column length at height 300, 600, 1200 and 1500 mm. At each level
682
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 1. Steel frame involved in the tests.
five thermocouples were used (see Fig. 2). Four of the thermocouples were attached to the column flanges and one to the center of the web as shown in Fig. 2. During the fire test the column expansion was monitored and recorded using LVDTs (Linear Variable Displacement Transducer) at the top and the bottom of the column. The lateral displacements were also recorded using LVDTs on both sides at the middle of the steel column. During the tests, the axial forces generated in the columns (due to the imposed restraint) were measured using two load cells (capacity 400 kN each). A reasonably good temperature distribution along the column length was achieved. The maximum difference between the average temperature at the top and the bottom of the column was between 10 and 15%. Curves representing the temperature profile along one of the heated columns are shown in Fig. 4. 4. Test results All the tests showed that imposing axial and rotational restraint during the fire causes additional forces to be generated in the column. Fig. 5 shows curves of
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
683
Fig. 2. Rig, furnace and instruments used in the tests.
applied and generated forces, lateral and axial displacement of column reference P3UB4 tested under high rotational restraint (r ¼ 0:936) and loading level=0.6 of the design load (see Table 1). From Fig. 5 it can be seen that after smooth and low rate of generation, the axial force reached a maximum value of 143 kN and then started to decrease gradually as the mechanical properties of the column deteriorates with time and rise of temperature. At the failure stage, the lateral displacement of the column begins to increase slowly as the column starts losing its stability for a period of time and then a sudden column buckling takes place as shown in Fig. 5. This can
684
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 3. Typical fire curves adopted in the tests.
Fig. 4. Temperature profile in the four levels along the column.
be attributed to the fact that the rig does not allow for load redistribution beyond the moment where the restraint force comes to zero. At this stage the buckling process induces end moments in the steel plates at both ends of the column. These moments are resisted by the rotational restraint imposed by the connected steel plates. In cases where thin steel plates were used in the test (small rotational restraint) the end moments were high enough to bend the thin plates in the pattern shown in Figs. 1
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
685
Fig. 5. Curves of applied and generated forces, lateral and axial displacements of column P3UB4 tested under rotational restraint.
and 6. The plates did not suffer any bending when heavy steel plates were used. The curves shown in Fig. 5 are typical of the curves for all the columns tested. The force generation and displacement curves had nearly the same trend in all the tests but they differed in the values and their rates according to the test parameters. Curves representing the evolution of the generated axial forces for the ten tests are shown in Figs. 7 and 8 respectively. For comparison, the results of a column tested under axial restraint only [2] are shown in Fig. 9. When the column behavior shown in this figure is examined it can be seen that restraint forces generated in a column which is only restrained axially have a trend similar to that in the case of rotationally restrained column (Figs. 5, 7 and 8). The main differences are in the values of these forces and
686
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 6. Deformation in the lower part of the steel frame after the fire test (when thin plates were used).
Fig. 7. Axial forces generated in columns tested under high rotational restraint.
in the failure process. A column with only axial restraint had a sudden failure when the lateral displacement increased suddenly and swiftly due to buckling (Fig. 9). However, when rotational restraint is present the force generated starts to decrease (after the peak point) at a slow rate as shown in Fig. 5. Then a second stage of
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
687
Fig. 8. Axial forces generated in columns tested under low rotational restraint.
sudden failure takes place when the lateral displacement suddenly increases and column buckling occurs. However, a sudden failure pattern can still be seen in rotationally restrained columns (Fig. 8) in cases where the applied loads are significantly higher than the generated forces (columns P3UB8, P3UB9 and P3UB10). Table 2 shows failure temperatures and the maximum generated forces recorded during the tests. By examining Table 2 it can be concluded that increasing the load level decreases the maximum value of the generated forces. The other important conclusion is that changing the degree of rotational restraint between two extreme values did not significantly affect the values of the generated forces. Moreover, Table 2 shows that the generated forces could increase the total imposed load to dangerous levels, which may exceed the column’s design load.
5. Columns effective length There is no methodology to determine the effective length of partially fixed end columns during the tests, but the shape of the cooled column (after test) gave the possibility of calculating the column’s effective length. By using the geometrical data of the deformed column, the positions of contra-flexure points were found. As shown in Fig. 10 the distance between these two points represents the effective length of the column. The effective lengths of the tested columns obtained in this way are shown in Table 3. It is clear from Table 3 that columns with higher rotational restraint value had shorter effective lengths.
688
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 9. Curves of applied and generated force, lateral and axial displacement of column 15UB13 tested under axial restraint only [1].
6. Conclusions 1. Adding rotational restraint had a relatively minor effect on the value of generated restraint forces but failure temperatures were greatly increased under the same load. 2. Changing the value of the applied rotational restraint has an insignificant effect on the values of generated restraint forces.
689
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691 Table 2 Summary of the results of fire tests Column ref.
Loading Failure Max. force Total load level temp. 1C generated in columns (kN) Column strength
Applied Generated
Group one, High P3UB1 rotational restraint P3UB2 P3UB3 P3UB4 P3UB5
0
648
260
1.06
0
0.2 0.4 0.6 0.8
589 525 421 277
220 179 142 69
1.10 1.13 1.18 1.08
0.44 0.81 1.44 4.11
Group two, low P3UB6 rotational restraint P3UB7 P3UB8 P3UB9 P3UB10
0
652
290
1.19
0
0.2 0.4 0.6 0.8
509 379 271 200
256 192 143 97
1.25 1.19 1.18 1.19
0.37 0.75 1.43 2.92
Fig. 10. Measured deformed shape of column P3UB8.
3. The generated forces could increase the total imposed load to dangerous levels which may exceed the column’s design load. 4. Increasing the load level from 0.2 to 0.8 caused a significant drop in the generated restraint forces by up to 45%.
690
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Table 3 Effective lengths of the tested columnsa
Group one (high rotational restraint)
Group two (low rotational restraint)
a
Column ref.
Effective length
P3UB1 P3UB2 P3UB3 P3UB4 P3UB5
N/A 0.56L 0.57L 0.58L 0.52L
P3UB6 P3UB7 P3UB8 P3UB9 P3UB10
N/A 0.61L 0.60L 0.65L 0.61L
(L=Column length=1800 mm).
5. The failure stage in rotationally restrained columns has no sudden drop in the generated restraint force as in columns restrained axially only (excluding the cases mentioned in 6 below). 6. A sudden failure pattern was noticed in few cases where the applied load is significantly higher than the generated forces. 7. Increasing the loading level also caused a significant drop in the failure temperature. 8. Calculating the effective length of steel columns (using the geometrical data of the cool columns) gave an average value of 0.56L for highly restrained columns and 0.61 for low rotational restraint value.
References [1] Ali FA, Shepherd P, Randall M, Simms IW, O’Connor DJ, Burgess I. The effect of axial restraint on the fire resistance of steel columns. J Constructional Steel Res 1998;98:177. [2] Ali FA, Simms I, O’Connor D. Effect of axial restraint on steel columns behaviour during fire. Proceedings of the Fifth International Fire Safety Conference, Melbourne, Australia, 1997. [3] Bailey CG. Simulation of the structural behavior of steel framed buildings in fire. Ph.D Thesis. University of Sheffield, 1995. [4] Bailey CG, Wadee M, Baltzer K, Newman GM. The behavior of steel columns in fire. Report RT524, Version 1, Submitted by The Steel Construction Institute to the Department of Environment, UK, March 1996. [5] Cabrita-Neves I. The critical temperature of steel columns with restrained thermal elongation. Fire Safety J 1995;24:211–27. [6] Franssen J-M. Axially restrained columns tests database. Report of The University of Liege, Belgium, 1994. [7] Franssen J-M, Dotreppe JC. Fire resistance of columns in steel frames. Fire Safety J 1992;19 (2–3):159–75.
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
691
[8] Lennon T. Local column heating. Proceedings of the First Cardington Conference Building Research Establishment, 1994. [9] Pettersson O, Witteveen J. On the fire resistance of structural steel elements derived from standard fire tests or by calculation. Fire Safety J 1979;2:73–87. [10] Valente JC, Carbita N. Fire resistance of steel columns with elastically restrained axial elongation and bending. J Constructional Steel Res 1999;52:319–31.
Structural performance of rotationally restrained steel columns in fire Faris Ali*, David O’Connor Fire Research Center, University of Ulster, Jordanstown, Co. Antrim BT37 0QB, UK Received 24 August 2000; received in revised form 8 December 2000; accepted 28 March 2001
Abstract The paper represents the outcomes of a parametric experimental investigation on the performance of rotationally restrained steel columns in fire. This experimental programme is a part of major research project performed at the Fire Research Center, University of Ulster in collaboration with the University of Sheffield. As a part of steel frames, half scale steel columns were tested in fire under two values of rotational restraint 0.18 and 0.93 and one value of axial restraint of approximately 0.29. Each case of rotational restraint was tested under five loading levels 0, 0.2, 0.4, 0.6 and 0.8. The paper includes a comparison with the behavior of a steel column previously tested in fire under axial restraint only. The paper represents also a method of estimating the effective length of fixed end (partial fixity) columns tested under fire. r 2001 Elsevier Science Ltd. All rights reserved. Keywords: Steel columns; Steel frames; Fire; Rotational Restraint; Effective length
1. Introduction When a fire takes place in a building and remains contained in a section of the building other unexposed parts remain relatively cool. This variance in thermal deformations imposes restraint on the structure’s elements under fire. In columns, the imposed restraint can be axial and rotational. Axial restraint opposes thermal axial expansion of the column while rotational restraint resists column’s end rotation. The imposed restraint can generate substantial unforeseen forces in the columns during fire adding another hazard that may cause uncalculated structural failure and increased losses and casualties. Effect of axial restraint on steel columns exposed to fire was investigated over the last twenty years by many researchers *Corresponding author. Tel.: +44-28-9036-8302; fax: +44-28-9036-6826. E-mail address: [email protected] (F. Ali). 0379-7112/01/$ - see front matter r 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 7 9 - 7 1 1 2 ( 0 1 ) 0 0 0 1 7 - 0
680
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
[1,4–6,8–10] and others. These studies added a vital database to the literature both in the theoretical and the experimental fields of research. However, in practice cases of pure axial restraint can rarely be found. In most cases, in real structures rotational restraint conjuncts axial restraint. This point raises concerns about the necessity of studying the performance of steel columns subjected to both axial and rotational restraint during fire. Despite the fact that this issue has been studied theoretically by many researchers including [3,4,7], experimental investigation has been poor. Therefore a parametric investigation was conducted at the Fire Research Center, University of Ulster, UK (a joint research project with the University of Sheffield, UK) on the behavior of axially and rotationally restrained steel columns under high temperatures focusing on the forces generated during fire. Two parameters were involved in the study: the degree of rotational restraint and the loading level imposed on columns. Two extreme cases of rotational restraint were chosen, very high and very low. This paper presents a parametric experimental investigation of steel columns restrained axially and rotationally during fire. The paper discusses the main outcomes of the research and demonstrates measurements of generated forces, temperatures, lateral and axial displacements of the columns. It also includes a comparison with the behavior of a steel column previously tested in fire under axial restraint only. The paper represents a method of estimating the effective length of fixed end columns (partial fixity) tested under fire.
2. Rotational restraint The degree of rotational restraint r imposed on a column is defined as the ratio of the rotational stiffness of the surrounding (to the column) structure rs to the summation of rotational stiffness of the column rc and the structure rs : rs r¼ : ð1Þ rs þ rc According to Eq. (1) the following boundary conditions can be applied: when rs crc ; then rE1-the column end is fully fixed when rs E0; then r ¼ 0-the column is pin ended. In the experimental investigation which has been carried out, two degrees of rotational restraint were involved. Low value of restraint r1 ¼ 0:186 and high restraint r2 ¼ 0:936 (see Table 1). The rotational stiffness was worked out according to BS 5950, Appendix (E) where a value of column rotational stiffness=256 kN mm was calculated. The first restraint value r1 ¼ 0:186 was achieved by connecting two steel plates 200 10 mm (cross section) and 750 mm length to the top and the bottom of the column specimen (Fig. 1). The second degree of rotational restraint r2 ¼ 0:936 was produced by connecting two heavier steel plates of 200 40 mm2 (cross section) and the same length to the top and the bottom of the column. The two steel plates were connected to steel blocks using light bolts to simulate simple supports. The resulted steel frame is shown in Fig. 1.
681
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691 Table 1 Parameters involved in the testing program of rotationally restrained columnsa Degree of rot. restraint r
Applied rot. restraint rs kN mm
0.936
3746
P3UB1 0 (0)
P3UB2 0.2 (97 kN)
P3UB3 0.4 (145 kN)
P3UB4 0.6 (205 kN)
P3UB5 0.8 (284 kN)
0.186
58.5
P3UB6 0 (0)
P3UB7 0.2 (97 kN)
P3UB8 0.4 (145 kN)
P3UB9 0.6 (205 kN)
P3UB10 0.8 (284 kN)
Group 1 (H.R.R) Group 2 (L.R.R) a
Column ref., loading levels and loads
H.R.R.=High rotational restraint, L.R.R.=low rotational restraint; for r see Eq. (1).
3. The experimental programme In the research programme 10 columns 127 76UB13 were tested. All the columns were half scale with 1800 mm length. Table 1 shows the parameters involved in the investigation. As mentioned before, two degrees of rotational restraint were tested. Each degree was tested under five loading levels from 0% to 80% of the estimated compressive design load BS5950, Part 1. All the columns were subjected to an axial restraint degree of approximately 0.29 (imposed axial stiffness E57 kN/mm) [1,2]. The test programme was designed to be compatible with previously performed tests on columns with axial restraint only. Details of these tests including the rig and instrumentation can be found in references [1,2]. The rig used in the tests is the same as that used previously in the programme of tests on the axially restrained columns [1,2]. The rig was modified in order to impose rotational restraint in conjunction with axial restraint. The furnace used in these tests is the same furnace that was used in reference [1,2] with some alterations. The rig and the furnace layout are shown in Fig. 2. The top and the bottom plates of the steel frame were located outside the furnace (see Fig. 2) which allowed heating of the column only, leaving other parts of the steel frame at room temperature. The axial restraint imposed on the column was produced by the rig’s own stiffness (see Refs. [1,2]). The heated length of the column was E1750 mm. All the tests were performed following the same procedure to ensure repeatability. The axial load was first applied to the column by 5% load increments until the desired level was reached and this load was kept constant during the fire test. The applied loads were measured using two load cells of capacity 200 kN each. The nuts responsible for imposing axial restraint were then tightened to apply the axial restraint (Fig. 2), [1,2]. Then the fire was ignited until failure took place by losing stability (column buckling). All the columns were heated in the same rate. Typical time–temperature curves for the furnace (average of three points top, bottom and middle) and the steel column are shown in Fig. 3. The curve representing the column temperature is the average temperature of 20 thermocouples distributed on four levels over the column length at height 300, 600, 1200 and 1500 mm. At each level
682
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 1. Steel frame involved in the tests.
five thermocouples were used (see Fig. 2). Four of the thermocouples were attached to the column flanges and one to the center of the web as shown in Fig. 2. During the fire test the column expansion was monitored and recorded using LVDTs (Linear Variable Displacement Transducer) at the top and the bottom of the column. The lateral displacements were also recorded using LVDTs on both sides at the middle of the steel column. During the tests, the axial forces generated in the columns (due to the imposed restraint) were measured using two load cells (capacity 400 kN each). A reasonably good temperature distribution along the column length was achieved. The maximum difference between the average temperature at the top and the bottom of the column was between 10 and 15%. Curves representing the temperature profile along one of the heated columns are shown in Fig. 4. 4. Test results All the tests showed that imposing axial and rotational restraint during the fire causes additional forces to be generated in the column. Fig. 5 shows curves of
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
683
Fig. 2. Rig, furnace and instruments used in the tests.
applied and generated forces, lateral and axial displacement of column reference P3UB4 tested under high rotational restraint (r ¼ 0:936) and loading level=0.6 of the design load (see Table 1). From Fig. 5 it can be seen that after smooth and low rate of generation, the axial force reached a maximum value of 143 kN and then started to decrease gradually as the mechanical properties of the column deteriorates with time and rise of temperature. At the failure stage, the lateral displacement of the column begins to increase slowly as the column starts losing its stability for a period of time and then a sudden column buckling takes place as shown in Fig. 5. This can
684
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 3. Typical fire curves adopted in the tests.
Fig. 4. Temperature profile in the four levels along the column.
be attributed to the fact that the rig does not allow for load redistribution beyond the moment where the restraint force comes to zero. At this stage the buckling process induces end moments in the steel plates at both ends of the column. These moments are resisted by the rotational restraint imposed by the connected steel plates. In cases where thin steel plates were used in the test (small rotational restraint) the end moments were high enough to bend the thin plates in the pattern shown in Figs. 1
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
685
Fig. 5. Curves of applied and generated forces, lateral and axial displacements of column P3UB4 tested under rotational restraint.
and 6. The plates did not suffer any bending when heavy steel plates were used. The curves shown in Fig. 5 are typical of the curves for all the columns tested. The force generation and displacement curves had nearly the same trend in all the tests but they differed in the values and their rates according to the test parameters. Curves representing the evolution of the generated axial forces for the ten tests are shown in Figs. 7 and 8 respectively. For comparison, the results of a column tested under axial restraint only [2] are shown in Fig. 9. When the column behavior shown in this figure is examined it can be seen that restraint forces generated in a column which is only restrained axially have a trend similar to that in the case of rotationally restrained column (Figs. 5, 7 and 8). The main differences are in the values of these forces and
686
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 6. Deformation in the lower part of the steel frame after the fire test (when thin plates were used).
Fig. 7. Axial forces generated in columns tested under high rotational restraint.
in the failure process. A column with only axial restraint had a sudden failure when the lateral displacement increased suddenly and swiftly due to buckling (Fig. 9). However, when rotational restraint is present the force generated starts to decrease (after the peak point) at a slow rate as shown in Fig. 5. Then a second stage of
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
687
Fig. 8. Axial forces generated in columns tested under low rotational restraint.
sudden failure takes place when the lateral displacement suddenly increases and column buckling occurs. However, a sudden failure pattern can still be seen in rotationally restrained columns (Fig. 8) in cases where the applied loads are significantly higher than the generated forces (columns P3UB8, P3UB9 and P3UB10). Table 2 shows failure temperatures and the maximum generated forces recorded during the tests. By examining Table 2 it can be concluded that increasing the load level decreases the maximum value of the generated forces. The other important conclusion is that changing the degree of rotational restraint between two extreme values did not significantly affect the values of the generated forces. Moreover, Table 2 shows that the generated forces could increase the total imposed load to dangerous levels, which may exceed the column’s design load.
5. Columns effective length There is no methodology to determine the effective length of partially fixed end columns during the tests, but the shape of the cooled column (after test) gave the possibility of calculating the column’s effective length. By using the geometrical data of the deformed column, the positions of contra-flexure points were found. As shown in Fig. 10 the distance between these two points represents the effective length of the column. The effective lengths of the tested columns obtained in this way are shown in Table 3. It is clear from Table 3 that columns with higher rotational restraint value had shorter effective lengths.
688
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Fig. 9. Curves of applied and generated force, lateral and axial displacement of column 15UB13 tested under axial restraint only [1].
6. Conclusions 1. Adding rotational restraint had a relatively minor effect on the value of generated restraint forces but failure temperatures were greatly increased under the same load. 2. Changing the value of the applied rotational restraint has an insignificant effect on the values of generated restraint forces.
689
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691 Table 2 Summary of the results of fire tests Column ref.
Loading Failure Max. force Total load level temp. 1C generated in columns (kN) Column strength
Applied Generated
Group one, High P3UB1 rotational restraint P3UB2 P3UB3 P3UB4 P3UB5
0
648
260
1.06
0
0.2 0.4 0.6 0.8
589 525 421 277
220 179 142 69
1.10 1.13 1.18 1.08
0.44 0.81 1.44 4.11
Group two, low P3UB6 rotational restraint P3UB7 P3UB8 P3UB9 P3UB10
0
652
290
1.19
0
0.2 0.4 0.6 0.8
509 379 271 200
256 192 143 97
1.25 1.19 1.18 1.19
0.37 0.75 1.43 2.92
Fig. 10. Measured deformed shape of column P3UB8.
3. The generated forces could increase the total imposed load to dangerous levels which may exceed the column’s design load. 4. Increasing the load level from 0.2 to 0.8 caused a significant drop in the generated restraint forces by up to 45%.
690
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
Table 3 Effective lengths of the tested columnsa
Group one (high rotational restraint)
Group two (low rotational restraint)
a
Column ref.
Effective length
P3UB1 P3UB2 P3UB3 P3UB4 P3UB5
N/A 0.56L 0.57L 0.58L 0.52L
P3UB6 P3UB7 P3UB8 P3UB9 P3UB10
N/A 0.61L 0.60L 0.65L 0.61L
(L=Column length=1800 mm).
5. The failure stage in rotationally restrained columns has no sudden drop in the generated restraint force as in columns restrained axially only (excluding the cases mentioned in 6 below). 6. A sudden failure pattern was noticed in few cases where the applied load is significantly higher than the generated forces. 7. Increasing the loading level also caused a significant drop in the failure temperature. 8. Calculating the effective length of steel columns (using the geometrical data of the cool columns) gave an average value of 0.56L for highly restrained columns and 0.61 for low rotational restraint value.
References [1] Ali FA, Shepherd P, Randall M, Simms IW, O’Connor DJ, Burgess I. The effect of axial restraint on the fire resistance of steel columns. J Constructional Steel Res 1998;98:177. [2] Ali FA, Simms I, O’Connor D. Effect of axial restraint on steel columns behaviour during fire. Proceedings of the Fifth International Fire Safety Conference, Melbourne, Australia, 1997. [3] Bailey CG. Simulation of the structural behavior of steel framed buildings in fire. Ph.D Thesis. University of Sheffield, 1995. [4] Bailey CG, Wadee M, Baltzer K, Newman GM. The behavior of steel columns in fire. Report RT524, Version 1, Submitted by The Steel Construction Institute to the Department of Environment, UK, March 1996. [5] Cabrita-Neves I. The critical temperature of steel columns with restrained thermal elongation. Fire Safety J 1995;24:211–27. [6] Franssen J-M. Axially restrained columns tests database. Report of The University of Liege, Belgium, 1994. [7] Franssen J-M, Dotreppe JC. Fire resistance of columns in steel frames. Fire Safety J 1992;19 (2–3):159–75.
F. Ali, D. O’Connor / Fire Safety Journal 36 (2001) 679–691
691
[8] Lennon T. Local column heating. Proceedings of the First Cardington Conference Building Research Establishment, 1994. [9] Pettersson O, Witteveen J. On the fire resistance of structural steel elements derived from standard fire tests or by calculation. Fire Safety J 1979;2:73–87. [10] Valente JC, Carbita N. Fire resistance of steel columns with elastically restrained axial elongation and bending. J Constructional Steel Res 1999;52:319–31.