materials Article
Evaluation of Residual Compressive Strength and Behavior of Corrosion-Damaged Carbon Steel Tubular Members Jin-Hee Ahn 1 , Seok-Hyeon Jeon 1 , Young-Soo Jeong 2 , Kwang-Il Cho 3 and Jungwon Huh 4, * 1 2 3 4
*
ID
Department of Civil Engineering, Gyeongnam National University of Science and Technology, Jinju, Gyeongnam 52725, Korea;
[email protected] (J.-H.A.);
[email protected] (S.-H.J.) Seismic Simulation Test Center, Pusan National University, Yangsan, Gyeongnam 50612, Korea;
[email protected] R&D Team, Tekhan Inc., 601, 324, Gangnam-daero, Gangnam-gu, Seoul 06252, Korea;
[email protected] Department of Civil & Environmental Engineering, Chonnam National University, Yeosu, Jeonnam 59626, Korea Correspondence:
[email protected]; Tel.: +82-61-659-7247
Received: 29 May 2018; Accepted: 18 July 2018; Published: 20 July 2018
Abstract: Local corrosion damage of steel structures can occur due to damage to the paint-coated surface of structures. Such damage can affect the structural behavior and performance of steel structures. Compressive loading tests were, thus, carried out in this study to examine the effect of local corrosion damage on the structural behavior and strength of tubular members. Artificial crosssectional damage on the surface of the tubular members was introduced to reflect the actual corroded damage under exposure to a corrosion environment. The compressive failure modes and compressive strengths of the tubular members were compared according to the localized cross-sectional damage. The compressive loading test results showed that the compressive strengths were affected by the damaged width within a certain range. In addition, finite element analysis (FEA) was conducted with various parameters to determine the effects of the damage on the failure mode and compressive strength of the stub column. From the FEA results, the compressive strength was decreased proportionally with the equivalent cross-sectional area ratio and damaged volume ratio. Keywords: residual compressive strength; tubular member; cross-sectional damage; corrosion; compressive loading test; FEA
1. Introduction Circular steel members have been used as major structural components in various structural systems. In energy power facilities, circular steel members have been used as pipeline or structural members of main platforms or substructures [1–4]. In offshore and maritime structures, they have been used as the main structural components for structural platforms on oilrigs, observation facilities, and wind and power plants. In addition, for infrastructures, circular steel members have been used in bridges, buildings, and plant systems, etc. Generally, paint coating has been applied to these circular members for corrosion protection, aesthetics, and sustainable maintenance. However, due to deterioration or localized damage of the paint-coated surface of circular members, localized corrosion commonly occurs on paint-coated surfaces exposed to atmospheric corrosion environments [5–7]. This localized corrosion damage to the surface of circular steel members can affect their structural safety, performance, and durability, because corrosion damage is related to the cross-sectional damage on the surface of the member. Materials 2018, 11, 1254; doi:10.3390/ma11071254
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The corrosion pit under a pipeline was investigated by electrochemical impedance techniques (EIS) and the corrosion behavior of iron and steel was evaluated depending on carbonate solution, chloride, and carbon dioxide [8–10]. Experimental and numerical studies have been conducted to examine the variation of structural performance of structural members according to cross-sectional damage induced by corrosion [11–16]. Additionally, the reinforcement or rehabilitation method has been used to examine cross-sectional damaged members [17,18]. Some studies have considered the ideal corrosion model for examining even cross-sectional damage on structural member surfaces. To consider the irregular cross-sectional damaged surfaces due to corrosion, compressive loading tests have been conducted on inclined and vertical circular steel members with both uneven and even cross-sectional damage. In these tests, damage was artificially induced by a mechanical process and hand drills to compare the differences between the compressive resistances and cross-sectional damage condition caused by corrosion [19]. In these previous studies, half- and fully-damaged cases of cross-sectional corrosion of the outer circumference of circular steel members [19] were considered. Based on the decreased compressive strength ratios from these compressive loading test results, an equation of residual compressive factors was suggested, depending on the cross-sectional damage ratio [20]. However, it was difficult to determine the effects of local cross-sectional damage caused by corrosion on the compressive behaviors of the members, since relatively widely distributed cross-sectional damage and full damage of the circumference occurred on the surface of the tubular section, as discussed in the previous study [19,20]. The major variables affecting the compressive strength and behavior of the structural members were not able to be determined. In this study, artificial cross-sectional damages with various damaged widths and heights were induced on the surface of tubular specimens to examine the major variables that affect the compressive behaviors of circular tubular members. After compressive loading tests of the circular tubular specimens, their compressive failure modes and compressive resistant capacities were evaluated and compared. To more clearly evaluate their compressive resistant capacities, FEA was additionally conducted to determine the parameters of various cross-sectional damages. Using a range of FEA models, the major variables that affect the compressive strength of the specimens were found and it was, therefore, not necessary to use a large number of specimens for the experiments. A total of 120 FEA models were constructed and used for analysis in this study. After performing the analysis, the failure modes were checked to determine the major factors and the compressive strength values of the members were evaluated to determine the variables affected by the damages. Finally, the effect of the localized cross-sectional damage condition on the compressive resistance of the circular tubular members was quantitatively evaluated. 2. Compressive Test Conditions 2.1. Localized Cross–Sectional Damaged Tubular Specimens To consider the various cross-sectional damaged conditions on the surface of the circular tubular members compared to those on the specimens used in the previous study [19,20], a small circular tubular pipe 89.1 mm diameter (thickness: 3.2 mm) was selected for the compressive loading test specimens. Since the dimensions of the tubular pipe can differ from the official dimensions from the fabrication process, the tubular pipe dimension was measured and its actual diameter was 90 mm. Circular tubular specimens were cut to a 600 mm height and steel plates of 120 mm width and 10 mm thickness were attached to each end of the tubular specimen as shown in Figure 1. These circular tubular specimens were designed as stub columns with a slenderness ratio (λ) of 9.87. The steel grade of the tubular specimens was STK 400, having a yield stress of over 216 MPa and a tensile strength of over 400 MPa. In this study, the yield stress was chosen to be 310 MPa in accordance with the material test. To replicate the corrosion damage occurring in certain areas of the section in the tubular
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Materials 2018, 11, artificial x FOR PEER REVIEWwith continuous pitting shapes were induced on the surface of the 3 of 19 member, damages
tubular specimens using a hand drill with a 12 mm diameter drill bit. Artificial cross-sectional condition wascondition determined consideringconsidering relative ratio to the diameter for circular specimen. Thus, a damage was determined relative ratio to the diameter for circular specimen. total of 18 specimens were fabricated according to the abovementioned artificial total Thus, of 18 aspecimens were fabricated according to the abovementioned artificialcross-sectional cross-sectional damage conditions. damage conditions.
Figure 1. Dimensions thecompressive compressive specimens specimens (unit: Figure 1. Dimensions of of the (unit:mm). mm).
To investigate major variables thecompressive compressive behaviors behaviors ofofthe thethe width of of To investigate the the major variables forforthe thespecimens, specimens, width the artificial cross-sectional damage of specimen was changed from D/3 (about 30 mm) to 1.6D (about the artificial cross-sectional damage of specimen was changed from D/3 (about 30 mm) to 1.6D (about 150 mm) andheight the height also changedfrom fromD/3 D/3(about (about 30 30 mm) mm) to 9090 mm), as shown 150 mm) and the waswas also changed to1.0D 1.0D(about (about mm), as shown in Table 1. Table 1 summarizes the compressive loading test specimens. In the fabrication process, in Table 1. Table 1 summarizes the compressive loading test specimens. In the fabrication process, the weight of each specimen was also measured to check the cross-sectional damage before and after the weight of each specimen was also measured to check the cross-sectional damage before and after inducing artificial damage to the tubular specimens. In particular, in order to examine the uncertainty inducing artificial damage to the tubular specimens. In particular, in order to examine the uncertainty of the artificially damaged section, CD-H7.5W series specimens having an artificial damage with of theaartificially CD-H7.5W series specimens having artificial damage with a height of 75damaged mm weresection, fabricated. The artificial cross-sectional damagean was not calculated at the heightdesign of 75level mmofwere fabricated. Theweight artificial cross-sectional damage not calculated at the the specimen, and the loss was only measured after thewas contrived cross-sectional designdamage. level of the the specimen, and the weight was only measured crossThus, cross-sectional losses of theloss CD-H7.5W series specimensafter werethe not contrived quantitatively dependent on the cross-sectional damaged condition, of the other specimens. From their not sectional damage. Thus, the cross-sectional losses ofunlike the those CD-H7.5W series specimens were measured weight loss, the cross-sectional areas of the specimens were also calculated quantitatively dependent on equivalent the cross-sectional damaged condition, unlike those of the for other the artificial damaged region of the specimens. specimens. From their measured weight loss, the equivalent cross-sectional areas of the specimens were also calculated for the artificial damaged region of the specimens.
Table 1. Summary of the tubular specimen with localized cross-sectional damage. Specimens CR-H0W0-1 CR-H0W0-2 CR-H0W0-3 CRH0W0_mean CD-H3W3 CD-H3W6
Damaged Height (H)/Width (W) (mm) -
Weight Loss after Artificial CrossSectional Damage (g) 0 0 0
Equivalent CrossSectional Area (mm2)/(%) 990.2/100 990.2/100 990.2/100
Artificial CrossSectional Damaged Volume (mm3) 0 0 0
-
0
990.2/100
0
30/30 30/60
14 32
930.7/93.99 854.3/86.28
1783.4 4076.4
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Table 1. Summary of the tubular specimen with localized cross-sectional damage. Specimens
Damaged Height (H)/Width (W) (mm)
CR-H0W0-1 CR-H0W0-2 CR-H0W0-3 CR-H0W0_mean CD-H3W3 30/30 REVIEW Materials 2018, 11, x FOR PEER CD-H3W6 30/60 CD-H3W9 30/90 CD-H6W9 CD-H3W15 30/150 60/90 CD-H6W3 60/3060/150 CD-H6W15 CD-H6W6 60/60 CD-H7.5W3 75/30 CD-H6W9 60/90 CD-H7.5W6 CD-H6W15 60/150 75/60 CD-H7.5W3 75/30 75/90 CD-H7.5W9 CD-H7.5W6 75/60 CD-H7.5W15 75/150 CD-H7.5W9 75/90 CD-H9W3 CD-H7.5W15 75/150 90/30 CD-H9W3 90/30 90/60 CD-H9W6 CD-H9W6 90/60 CD-H9W9 90/90 CD-H9W9 90/90 CD-H9W15 90/150 CD-H9W15 90/150
Weight Loss after Artificial Cross-Sectional Damage (g) 0 0 0 0 14 32 42 69 28 65 83 139 24 40 63 82 42 83 125 209
83 139 24 40 63 82 42 83 125 209
Equivalent CrossSectional Area (mm2 )/(%) 990.2/100 990.2/100 990.2/100 990.2/100 930.7/93.99 854.3/86.28 811.8/81.99 813.9/82.2 697.2/70.41 930.7/93.99 695/70.19 852.2/86.07 949.4/95.88 813.9/82.2 922.2/93.14 695/70.19 949.4/95.88 883.2/89.2 922.2/93.14 850.9/85.94 883.2/89.2 930.7/93.99 850.9/85.94 930.7/93.99 872.7/88.14 872.7/88.14 813.2/82.13 813.2/82.13 694.3/70.12 694.3/70.12
Artificial Cross-Sectional Damaged Volume (mm3 ) 0 0 0 0 1783.4 4076.4 5350.3 10,573.2 8789.8 3566.9 17,707.0 8280.3 3057.3 10,573.2 5095.5 17,707.0 3057.3 8025.5 5095.5 10,445.9 8025.5 5350.3 10,445.9 5350.3 10,573.2 10,573.2 15,923.6 15,923.6 26,624.2 26,624.2
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From the weight loss after the artificial cross-sectional damage, the equivalent damaged From the weight loss after the artificial cross-sectional damage, the equivalent damaged thickness thickness of the tubular member was also calculated along the damaged width of the tubular of the tubular member was also calculated along the damaged width of the tubular specimen. For the specimen. For the names of the specimens in Table 1, “C” refers to the compressive test, “R” is the names of the specimens in Table 1, “C” refers to the compressive test, “R” is the reference, “D” indicates reference, “D” indicates a damaged specimen, “W” indicates the width of the damage, and “H” a damaged specimen, “W” indicates the width of the damage, and “H” indicates the height of the indicates the height of the damage. The number following “W” and “H” represents the damaged damage. The number following “W” and “H” represents the damaged ratio determined from the ratio determined from the diameter of the circular specimen. Thus, specimen CD-H3W3 is the diameter of the circular specimen. Thus, specimen CD-H3W3 is the compressive test specimen with an compressive test specimen with an artificial damage of 30 mm height and 30 mm width. artificial damage of 30 mm height and 30 mm width. 2.2. Loading Loading Test Test Conditions Conditions 2.2. To examine behaviors of the specimens with localized crossTo examine the thecompressive compressiveresistant resistant behaviors of tubular the tubular specimens with localized sectional damage, an electric hydraulic servoservo system (Shimadzu, Kyoto, Japan) withwith a 5000 kN cross-sectional damage, an electric hydraulic system (Shimadzu, Kyoto, Japan) a 5000 capacity universal testing machine (UTM) was used to apply compressive loading to the specimens. kN capacity universal testing machine (UTM) was used to apply compressive loading to the specimens. To control control the the compressive compressive load, load, displacement displacement load load control control was was used used at at aa rate rate of of 1.5 1.5 mm/min. mm/min. To Compressive loading was applied to the test specimens until the occurrence of compressive failure, Compressive loading was applied to the test specimens until the occurrence of compressive failure, such such as a local buckling failure. During compressive loading to the tubular specimens, their as a local buckling failure. During compressive loading to the tubular specimens, their compressive compressive behaviors using atovideo camera to observe the depending failure behaviors behaviors were recordedwere usingrecorded a video camera observe the failure behaviors on the depending on the applied load level. Figure 2 shows the test setup of the compressive loading test applied load level. Figure 2 shows the test setup of the compressive loading test for the CR-H0W0-2 for the CR-H0W0-2 and CR-H7.5W3 specimens. and CR-H7.5W3 specimens.
(a)
(b)
Figure 2. setup of compressive loading test specimen: (a) CR-H0W0-2 specimen; and (b) Figure 2. Experimental Experimental setup of compressive loading test specimen: (a) CR-H0W0-2 specimen; CR-H7.5W3 specimen. and (b) CR-H7.5W3 specimen.
3. Test Result Evaluation 3.1. Failure Modes In this study, the localized artificial cross-sectional damage determined from the relative ratio of the diameter of the tubular specimen was considered to investigate the major variables affecting compressive
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3. Test Result Evaluation 3.1. Failure Modes In this study, the localized artificial cross-sectional damage determined from the relative ratio of the diameter of the tubular specimen was considered to investigate the major variables affecting compressive behaviors related to failure modes and the variation of compressive strengths. It was found that the failure modes could be affected by major variables, such as height, width, and damaged depth related to their cross-sectional damaged condition. Thus, the damaged width and height were changed from D/3 (about 30 mm) to 1.6D (about 150 mm for width) and 1.0D (about 90 mm for height). After compressive loading tests, the failure modes among the CR-H0W0 series specimens were compared to determine the specified failure modes. Figure 3 shows the compressive behaviors of the representative tubular specimens depending on the applied load level (at yield load, at compressive loading, and at final failure). The failures of the tubular specimens without artificial cross-sectional damage were initiated by local buckling near the loading plate, which was accompanied by lateral buckling of the tubular Materials 2018, 11, x FOR PEER REVIEW 5 of 19 specimen after the initial local buckling, as shown in Figure 3a–d. On the other hand, the tubular specimens withFigure artificial cross-sectional damage showed various local buckling failure modes failure modes. 3 shows the compressive behaviors of thefinal representative tubular specimens that were squashed or folded in the artificial damaged section depending on their cross-sectional depending on the applied load level (at yield load, at compressive loading, and at final failure). damaged condition as shown Figures 4–8. In theartificial case of the CR-H3W6 specimen, with initiated a relatively The failures of the tubularinspecimens without cross-sectional damage were by lower cross-sectional damage height, shownwas in Figure 4, a localby buckling mode wastubular found local buckling near the loading plate,aswhich accompanied lateral failure buckling of the with the fold in the the initial artificial cross-sectional region. the case with certain specimen after local buckling, as damage shown in FigureIn3a–d. On of thespecimens other hand, thea tubular cross-sectional damage height of 60 mm and width of 60 mm, a local buckling failure mode with specimens with artificial cross-sectional damage showed various final local buckling failure modes unusual deformation (such as shear failure modedamaged of thin plate) wasdepending observed due the cross-sectional cross-sectional that were squashed or folded in the artificial section on to their damaged condition, as shown in Figures 5 and 6. For the specimen with the wider cross-sectional damaged condition as shown in Figures 4–8. In the case of the CR-H3W6 specimen, with a relatively damage of 1.6 D (about 150 mm for width), thein buckling showed irregularly crushed lower cross-sectional damage height, as shown Figure 4,failure a localmode buckling failure mode was found failure in the artificially damaged section as shown in Figures 7 and 8. with the fold in the artificial cross-sectional damage region. In the case of specimens with a certain These differences couldofbe60due to athe cross-sectional resistance and cross-sectional damagebetween height offailure 60 mmmodes and width mm, local buckling failure mode with stress distribution on (such the surface of the damaged by localized damage. unusual deformation as shear failure mode section of thin caused plate) was observedcorrosion due to the crossFrom these failure modes, it can be assumed that the cross-sectional damaged shape and condition sectional damaged condition, as shown in Figures 5 and 6. For the specimen with the wider crosscan be influenced forms of compressive failure modes that are affected byirregularly localized sectional damage ofby1.6various D (about 150 mm for width), the buckling failure mode showed corrosion damage. crushed failure in the artificially damaged section as shown in Figures 7 and 8.
(a)
(b)
(c)
(d)
Figure 3. 3. Compressive Compressivefailure failureprocess processofofspecimen specimenCR-H0W0-1: CR-H0W0-1:(a)(a)before before load; yield load; Figure load; (b)(b) at at yield load; (c) (c) at at compressive strength; and (d) at final failure. compressive strength; and (d) at final failure.
(a)
(b)
(c)
(d)
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure failure process of specimen CR-H0W0-1: (a) before load; (b) at yield load; (c)6 of 20 Materials 2018, 3. 11,Compressive 1254 Figure 3. Compressive failure process of specimen CR-H0W0-1: (a) before load; (b) at yield load; (c) at compressive strength; and (d) at final failure. at compressive strength; and (d) at final failure.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure 4. 4. Compressive failure failure process of of specimen CR-H3W6: CR-H3W6: (a) before before load; (b) (b) at yield yield load; (c) (c) at Figure Figure 4. Compressive Compressive failure process process of specimen specimen CR-H3W6: (a) (a) before load; load; (b) at at yield load; load; (c) at at compressive strength; and (d) at final failure. compressive compressive strength; strength;and and(d) (d)at atfinal finalfailure. failure.
(a)
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(b) (b)
(c) (c)
(d) (d)
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Figure 5. Compressive failure process of specimen CR-H6W6: (a) before load; (b) at yield load; (c) at Figure 5. Compressive failure process of specimen CR-H6W6: (a) before load; (b) at yield load; (c) at compressive strength; and (d) at final failure. compressive strength; and (d) at final failure.
(a)
(b)
(c)
(d)
Figure 6. 6. Compressive Compressive failure failure process process of of specimen specimen CR-H6W9: CR-H6W9: (a) (a) before before load; load; (b) (b) at at yield yield load; load; (c) (c) at at Figure compressive strength; and (d) at final failure. compressive strength; and (d) at final failure.
(a)
(b)
(c)
(d)
Figure 7. Compressive failure process of specimen CR-H7.5W15: (a) before load; (b) at yield load; (c) at compressive strength; and (d) at final failure.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure failure process of specimen CR-H6W9: (a) before load; (b) at yield load; (c) at7 of 20 Materials 2018,6. 11,Compressive 1254 Figure 6. Compressive failure process of specimen CR-H6W9: (a) before load; (b) at yield load; (c) at compressive strength; and (d) at final failure. compressive strength; and (d) at final failure.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure 7. 7. Compressive failure process of of specimen CR-H7.5W15: CR-H7.5W15: (a) before load; (b) at yield load; (c) Figure Figure 7.Compressive Compressivefailure failureprocess process ofspecimen specimen CR-H7.5W15: (a) (a) before before load; load; (b) (b) at at yield yield load; load; (c) (c) at compressive strength; and (d) at final failure. at compressive strength; and (d) at final failure. at compressive strength; and (d) at final failure.
(a) (a)
(b) (b)
(c) (c)
(d) (d)
Figure 8. Compressive failure process of specimen CR-H9W15: (a) before load; (b) at yield load; (c) at Figure8.8.Compressive Compressivefailure failureprocess processof ofspecimen specimenCR-H9W15: CR-H9W15:(a) (a)before beforeload; load;(b) (b)at atyield yieldload; load;(c) (c)at at Figure compressive strength; and (d) at final failure. compressive strength; and (d) at final failure. compressive strength; and (d) at final failure.
These differences between failure modes could be due to the cross-sectional resistance and stress These differences between failure modes could be due to the cross-sectional resistance and stress 3.2. Compressive Loading Results distribution on the surface of the damaged section caused by localized corrosion damage. From these distribution on the surface of the damaged section caused by localized corrosion damage. From these failure modes, it can be assumed that the cross-sectional damaged shape and condition can be failure modes, of it Compressive can be assumed that Tests the cross-sectional damaged shape and condition can be 3.2.1. Summary Loading influenced by various forms of compressive failure modes that are affected by localized corrosion influenced by various forms of compressive failure modes that are affected by localized corrosion In order to quantitatively compare the change in the compressive strengths of circular tubular damage. damage. member specimens according to the localized cross-sectional damage condition, the compressive load-displacement relationships of the specimens are presented in Figure 9. All compressive loading test specimens showed typical compressive loading resistance behaviors, as shown in Figure 9. The CR-H0W0 series specimens showed a relatively larger ductile behavior after yield loading than that of the tubular member specimen with artificial cross-sectional damage. For the tubular member specimen with artificial cross-sectional damage, compressive displacements relatively decreased from yield load to failure; this tendency was greatly affected by the specimens with the higher cross-sectional damage as shown in Figure 9. The compressive loads of the tubular member specimens with artificial damage to the sections affected the cross-sectional resistance condition, as determined by the cross-sectional damaged level. Thus, it is inferred that the compressive loads decreased according to the cross-sectional resistance condition determined from the cross-sectional damaged level. Table 2 summarizes the maximum compressive load of each test specimen to quantitatively show the compressive load and displacement relationships.
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Table 2. Summary of test results of the tubular specimen with localized cross-sectional damage. Specimens
Damaged Height (H)/Width (W) (mm)
Damaged Volume (mm3 )
Converted CrossSectional Area (mm2 )
Compressive Strength (kN)
Displacement (mm)
CR-H0W0-1 0 990.2/100 0 12.0 CR-H0W0-2 0 990.2/100 0 10.0 Materials 2018, 11, x FOR PEER- REVIEW 7 of 19 CR-H0W0-3 0 990.2/100 0 10.9 CR-H0W0_mean 0 990.2/100 0 4.2 CD-H3W3 30/30 1783.4 930.7/93.99 1783.4 4.0 3.2. Compressive Loading30/60 Results CD-H3W6 4076.4 854.3/86.28 4076.4 4.7 CD-H3W9 30/90 5350.3 811.8/81.99 5350.3 3.4 30/150 8789.8 697.2/70.41 8789.8 4.5 3.2.1.CD-H3W15 Summary of Compressive Loading Tests CD-H6W3 60/30 3566.9 930.7/93.99 3566.9 6.3 CD-H6W6 60/60 8280.3 8280.3 4.3 In order to quantitatively compare the change in852.2/86.07 the compressive strengths of circular tubular CD-H6W9 60/90 10,573.2 813.9/82.2 10,573.2 2.5 member specimens according to the 17,707.0 localized cross-sectional condition, the compressive CD-H6W15 60/150 695/70.19 damage 17,707.0 5.3 CD-H7.5W3 75/30 949.4/95.88 in Figure3057.3 3.9 loading load-displacement relationships of the 3057.3 specimens are presented 9. All compressive CD-H7.5W6 75/60 5095.5 922.2/93.14 5095.5 4.3 test CD-H7.5W9 specimens showed75/90 typical compressive as shown in Figure 8025.5 loading resistance 883.2/89.2 behaviors, 8025.5 4.5 9. The CD-H7.5W15 75/150 10,445.9 850.9/85.94 10,445.9 5.4 CR-H0W0 series specimens showed a relatively larger ductile behavior after yield loading than that CD-H9W3 90/30 5350.3 930.7/93.99 5350.3 4.3 of the tubular member specimen with artificial cross-sectional damage. For the tubular CD-H9W6 90/60 10,573.2 872.7/88.14 10,573.2 3.6 member CD-H9W9 90/90 15,923.6 813.2/82.13 15,923.6 specimen with artificial cross-sectional damage, compressive displacements relatively 3.6 decreased CD-H9W15 90/150 26,624.2 694.3/70.12 26,624.2 12.0
from yield load to failure; this tendency was greatly affected by the specimens with the higher crosssectional damage as shown in Figure 9. The compressive loads of the tubular member specimens with As shown 9, theaffected compressive strengths ofresistance the tubular members with artificial artificial damageinto Figure the sections the cross-sectional condition, as determined by cross-sectional damage were affected by the cross-sectional damaged conditions. To compare the the cross-sectional damaged level. Thus, it is inferred that the compressive loads decreased according effect the cross-sectional damaged width of the tubular on their compressive behavior, to the of cross-sectional resistance condition determined from members the cross-sectional damaged level. Table the compressive load-displacement relationships of the tubular members were compared separately in 2 summarizes the maximum compressive load of each test specimen to quantitatively show the accordance with cross-sectional condition, as derived from Figures 10a–d and 11a–d. compressive loadthe and displacementdamaged relationships.
Figure of all all specimens. Figure 9. 9. Compressive Compressive load-displacement load-displacement relationships relationships of specimens.
As shown in Figure 9, the compressive strengths of the tubular members with artificial cross3.2.2. Effect of the Cross-Sectional Damaged Condition on Compressive Strength sectional damage were affected by the cross-sectional damaged conditions. To compare the effect of For specimens damaged with the same damaged width, the compressive the cross-sectional widthcross-sectional of the tubular members on their compressivestrengths behavior,were the determined from the certain cross-sectional damaged width within a certain range as shown in compressive load-displacement relationships of the tubular members were compared separately in Figure 10. For the specimens with a greater cross-sectional damaged width, as shown in Figure 10d, accordance with the cross-sectional damaged condition, as derived from Figures 10a–d and 11a–d. the compressive strengths were more strongly affected by the cross-sectional damaged height than Table 2. Summary of test results of the tubular specimen with localized cross-sectional damage.
Specimens
Damaged Height
Damaged Volume
Converted Cross-
Compressive
Displacement
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by the cross-sectional damaged width. Their compressive behaviors were also shown to concur with the change in their compressive strength. Thus, for specimens with different cross-sectional damaged widths ranging from 30 mm to 90 mm, their compressive behaviors from yield load to failure were relatively similar to those of specimens with the same cross-sectional damaged widths. Conversely, for the specimen with a 150 mm damaged width, the compressive behaviors changed depending on their cross-sectional damaged height. Figure 12 summarizes the compressive strength of each tubular specimen depending on the artificial cross-sectional damaged width. The compressive strength of the tubular specimen series with the same artificial cross-sectional damaged width was slightly decreased compared to that of the specimen series with no cross-sectional damage, except for the CD-W15 series, since their compressive strengths were determined from their cross-sectional damaged width within a specific2018, range. their critical value was not clear. Materials 11, xHowever, FOR PEER REVIEW 9 of 19
(a)
(b)
(c)
(d)
Figure 10. Compressive Compressiveload-displacement load-displacement relationships depending on cross-sectional damaged Figure 10. relationships depending on cross-sectional damaged width: width: (a) 30 mm damaged width; (b) 60 mm damaged width; (c) 90 mm damaged width; and (d) 150 (a) 30 mm damaged width; (b) 60 mm damaged width; (c) 90 mm damaged width; and (d) 150 mm mm damaged width. damaged width.
Figure 11 shows that the compressive strengths and behaviors of specimens were compared to those of specimens with the same cross-sectional damaged. The compressive strength of CD-H3W15 specimen was decreased by compared to CD-H3W3 which is affected by the cross-sectional damaged width for the same damaged height condition as shown in Figure 12. Figure 13 summarizes the compressive strength of each tubular specimen depending on the artificial cross-sectional damaged height. In the compressive strength of the tubular specimen series with the same artificial cross-sectional damaged height, the compressive strengths decreased depending on each cross-sectional damaged condition. For specimens with relatively lower cross-sectional damaged height, the difference between the compressive strength of each specimen decreased, as shown in Figure 13. In the case of the specimens with lower cross-sectional damaged height (less than (a) (b)
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Figure 10. Compressive load-displacement relationships depending on cross-sectional damaged
60 mm in damaged compressive affected the cross-sectional width: (a) 30 mmheight), damagedthe width; (b) 60 mm strength damaged decreased, width; (c) 90 which mm damaged width; and (d) 150 damaged width. mm damaged width.
(a)
(b)
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Figure 11. Compressive load-displacement relationships depending on cross-sectional damaged height: (a) mm damaged height; (b) 60 mm damaged height; (c) 75 damaged height; and (d) 90(a) mm Figure11.30Compressive load-displacement relationships depending onmm cross-sectional damaged height: 30 damaged height. mm damaged height; (b) 60 mm damaged height; (c) 75 mm damaged height; and (d) 90 mm damaged height.
Figure 12. Compressive strength depending on sectional damaged width. Figure 12. Compressive strength depending on sectional damaged width.
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Figure 12. Compressive strength depending on sectional damaged width.
Figure depending on on cross-sectional damaged height. height. Figure 13. 13. Compressive Compressive strength strength depending cross-sectional damaged
3.3. FEA of Compressive Loading Cases 3.3. FEA of Compressive Loading Cases 3.3.1. FEA and Parameters Parameters 3.3.1. FEA Model Model and In order orderto tocompare comparethe thecompressive compressive strength stub steel tubular member in test the test result In strength of of thethe stub steel tubular member in the result and and determine the factors that affect the compressive strength of stub tubular members with crossdetermine the factors that affect the compressive strength of stub tubular members with cross-sectional sectional their damage, their compressive were examined the FEA Abaqus program6.14. Abaqus damage, compressive strengths strengths were examined using the using FEA program The 6.14. FEA The FEA model was made with the same dimensions as the model for the loading tests; thus, the model was made with the same dimensions as the model for the loading tests; thus, the model has model has three components: a pipe of 600 mm length with a diameter of 89.1 mm and a thickness of three components: a pipe of 600 mm length with a diameter of 89.1 mm and a thickness of 3.2 mm, 3.2 mm, mm rectangular plates a thickness of 10 The mm.FEA The model FEA model simulated in and twoand 120 two mm120 rectangular plates with a with thickness of 10 mm. simulated in this this research was fabricated of steel with a modulus of elasticity of 205 GPa and Poisson’s ratio of 0.3. research was fabricated of steel with a modulus of elasticity of 205 GPa and Poisson’s ratio of 0.3. The yield yield stress stress value value was was selected selected to to be be 310 310 MPa, MPa, based based on on the the material material tests. tests. The The bilinear bilinear isotropic isotropic The hardening behavior plastic behavior of of thethe material tested. In hardening behavior of ofthis thismodel modelwas wasmade madetotosimulate simulatethe the plastic behavior material tested. addition, the plates were rigid plates to avoid deformation. In this model, displacement was applied In addition, the plates were rigid plates to avoid deformation. In this model, displacement was applied at the the center at center of of the the top top plate plate to to simulate simulate the the real real loading loading test. test. In In addition, addition, the the boundary boundary condition condition was was considered to ensure the simulation was as close to the experiment as possible. The bottom was considered to ensure the simulation was as close to the experiment as possible. The bottom plate plate was defined as the fixed boundary condition and the lateral displacement of the top plate was restrained. defined as the fixed boundary condition and the lateral displacement of the top plate was restrained. Figure 14 14 shows shows the the FEA FEA model model for for this this study. study. Figure To simulate and identify the compressive strength values and behaviors of the specimens, their crosssectional damage parameters were selected. A range of models were developed with different corroded depths, heights, and widths: the corroded depth varied from 0.5 mm to 2 mm with a 0.5 mm increment, the corroded height varied from 60 mm to 300 mm with a 60 mm increment, and the corroded width varied from 28 mm to 280 mm with a 28 mm increment. Similar to the compressive loading test specimens, the name of the FEA model was determined such that “C” refers to the compressive test, “D” refers to a damaged specimen, “W” indicates the damaged width, and “H” indicates the damaged height. The value after “CD” refers to the damaged thickness of the FEA model. Thus, the CD0.5-H60W28 model refers to a compressive analysis model with an artificial damage of 0.5 mm thickness, a 60 mm height, and a 28 mm width. Table 3 summarizes the properties of the FEA models. Table 3. Analysis parameters of the tubular members with localized cross-sectional damage. Parameter of Analysis Model Corroded depth Corroded height Corroded width
0.5, 1, 1.5, 2 mm 60, 120, 180, 240, 300 mm 28, 56, 84, 112, 140, 280 mm
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Figure 14. FEA Figure 14. FEA model. model.
To simulate and identify the compressive strength values and behaviors of the specimens, their 3.3.2. FEA Model and Parameters cross-sectional damage parameters were selected. A range of models were developed with different To verify the FEA model, compressive loadingdepth test result wasfrom compared to the theaFEA corroded depths, heights, andthe widths: the corroded varied 0.5 mm to 2result mm of with 0.5 model. It is difficult to develop an FEA model for60 a compressive loading with irregular mm increment, the corroded height varied from mm to 300 mm with atest 60 specimen mm increment, and the cross-sectional The 28 CR-H0W0 specimen without cross-sectional damagetowas and corroded widthdamage. varied from mm to 280 mm with a 28 mm increment. Similar themodeled compressive its load-displacement curves were compared. this was comparison, the measured dimensions loading test specimens, the name of the FEA For model determined such that “C” refers towere the applied to the FEA model. 15 shows the load-displacement forwidth, the CR-H0W0 compressive test, “D” refersFigure to a damaged specimen, “W” indicates comparison the damaged and “H” specimen.the Asdamaged shown in Figure 15,value its ultimate strength yield load were similar to those of the indicates height. The after “CD” refersand to the damaged thickness of the FEA model. test results and the tendency of the load-displacement curve also model agreedwith withan that of the test results. Thus, the CD0.5-H60W28 model refers to a compressive analysis artificial damage of Thus, the compressive strength and behavior of the stub compressive tubular members with local 0.5 mm thickness, a 60 mm height, and a 28 mm width. Table 3 summarizes the properties of the FEA cross-sectional damage by corrosion can be examined using this model. models. Materials 2018, 11, x FOR PEER REVIEW 12 of 19 Table 3. Analysis parameters of the tubular members with localized cross-sectional damage.
Parameter of Analysis Model Corroded depth 0.5, 1, 1.5, 2 mm Corroded height 60, 120, 180, 240, 300 mm Corroded width 28, 56, 84, 112, 140, 280 mm 3.3.2. FEA Model and Parameters To verify the FEA model, the compressive loading test result was compared to the result of the FEA model. It is difficult to develop an FEA model for a compressive loading test specimen with irregular cross-sectional damage. The CR-H0W0 specimen without cross-sectional damage was modeled and its load-displacement curves were compared. For this comparison, the measured dimensions were applied to the FEA model. Figure 15 shows the load-displacement comparison for the CR-H0W0 specimen. As shown in Figure 15, its ultimate strength and yield load were similar to those of the test results and the tendency of the load-displacement curve also agreed with that of the Figure 15. Comparison of the FEA result and the test result. test results. Thus, the compressive strength and behavior of and the the stub compressive tubular members Figure 15. Comparison of the FEA result test result. with local cross-sectional damage by corrosion can be examined using this model. In this study, tubular specimens with localized artificial cross-sectional damage were tested for their cross-sectional damage ratio for their diameter. The loading test results showed that squashed or folded failure modes occurred in the artificially-damaged section. The FEA results showed that the compressive failure modes were similar to the six failure cases shown in Figure 16. To determine the failure mode, local buckling failure and lateral buckling failure were considered from each FEA model result. In failure mode 2, lateral buckling failure occurred and two local buckling failures were
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In this study, tubular specimens with localized artificial cross-sectional damage were tested for their cross-sectional damage ratio for their diameter. The loading test results showed that squashed or folded failure modes occurred in the artificially-damaged section. The FEA results showed that the compressive failure modes were similar to the six failure cases shown in Figure 16. To determine the failure mode, local buckling failure and lateral buckling failure were considered from each FEA model result. In failure mode 2, lateral buckling failure occurred and two local buckling failures were observed at the cross-sectional damage boundary. In failure mode 3, lateral buckling failure Figure 15. Comparison of the FEA result and the test result. occurred and one local buckling failure was observed at the cross-sectional damage section. In failure mode 4, two local buckling failures were observed at the damaged boundary, without lateral buckling. In this study, tubular specimens with localized artificial cross-sectional damage were tested for In failure mode 5, only one local buckling failure was observed at the damage section. their cross-sectional damage ratio for their diameter. The loading testcross-sectional results showed that squashed Failure mode 6 as similar that of failure 4, but was determined other factors (cross-sectional or folded failure modes to occurred in the mode artificially-damaged section.byThe FEA results showed that damage condition) than those for failure mode 3. The failure modes of the specimen were by the compressive failure modes were similar to the six failure cases shown in Figure 16. Toaffected determine their damaged condition, such as the damaged height and damaged width. Their damaged depth was the failure mode, local buckling failure and lateral buckling failure were considered from each FEA also affected failure mode. model result.by Intheir failure mode 2, lateral buckling failure occurred and two local buckling failures were In the case of a relatively higher cross-sectional damaged model withbuckling lower damaged depth, observed at the cross-sectional damage boundary. In failure mode 3, lateral failure occurred their failure showed might beatdue to Failures 2 or 3. Forsection. higher In damaged depth4, and one localmodes buckling failurethat wasitobserved the cross-sectional damage failure mode modes, the failure modes could be due to Failures 4 and 5. In particular, Failure 6 occurred in the two local buckling failures were observed at the damaged boundary, without lateral buckling. In fully-damaged model. However, because it was difficult to select the critical damage case to determine failure mode 5, only one local buckling failure was observed at the cross-sectional damage section. the failure mode6 of specimen, theofcritical case determined by by the other damaged condition Failure mode asthe similar to that failuredamage mode 4, butwas was determined factors (crossand boundary condition from the compressive loading test results. However, it can be concluded sectional damage condition) than those for failure mode 3. The failure modes of the specimen were that local by buckling failure accompanied lateral buckling failure, as well local buckling affected their damaged condition, by such as the damaged height andasdamaged width.failure Their occurred in the damaged region. damaged depth was also affected by their failure mode.
(a)
(b) Figure 16. Cont.
(c)
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(e)
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Figure 16. 16. Representative Representative failure failure modes modes from from FEA: FEA: (a) (a) failure failure mode mode 1; 1; (b) (b) failure failure mode mode 2; 2; (c) (c) failure failure Figure mode 3; 3; (d) (d) failure failure mode mode 44 (e); (e); failure failure mode mode5; 5;and and(f) (f)failure failuremode mode6.6. mode
In the case of a relatively higher cross-sectional damaged model with lower damaged depth, To examine the compressive behaviors, the load-displacement relationships were compared their failure modes showed that it might be due to Failures 2 or 3. For higher damaged depth modes, depending on their damaged depth, as shown in Figure 17. These load-displacement relationships were the failure modes could be due to Failures 4 and 5. In particular, Failure 6 occurred in the fullyselected from the compressive failure modes. As shown in Figure 17, the compressive behaviors and damaged model. However, because it was difficult to select the critical damage case to determine the strengths (yield loads) were affected by their damaged depth and condition. Their compressive yield failure mode of the specimen, the critical damage case was determined by the damaged condition load and strengths decreased with the damaged depth. For the same damaged depth, the compressive and boundary condition from the compressive loading test results. However, it can be concluded that yield load and strengths distinctly changed based on their failure modes and compressive behaviors. local buckling failure accompanied by lateral buckling failure, as well as local buckling failure For a greater damaged depth, their displacement behaviors showed that it was not clear and was occurred in the damaged region. shorter, without ductile behaviors. From these load-displacement relationships, the FEA results of To examine the compressive behaviors, the load-displacement relationships were compared the tubular members with localized cross-sectional damage are summarized in Table 4 as yield loads, depending on their damaged depth, as shown in Figure 17. These load-displacement relationships compressive strengths, and failure modes. were selected from the compressive failure modes. As shown in Figure 17, the compressive behaviors To evaluate the relationships between the cross-sectional damage and compressive strength of and strengths (yield loads) were affected by their damaged depth and condition. Their compressive small tubular members, their yield loads and compressive strengths were evaluated based on the yield load and strengths decreased with the damaged depth. For the same damaged depth, the equivalent cross-sectional area ratio and damaged volume ratio from the test results, as shown in compressive yield load and strengths distinctly changed based on their failure modes and Figures 18 and 19. To determine the main factor affecting compressive strength, other cross-sectional compressive behaviors. For a greater damaged depth, their displacement behaviors showed that it properties of the tubular member were also considered. However, the two values were similar to was not clear and was shorter, without ductile behaviors. From these load-displacement relationships, the decrease in the yield loads and compressive strengths of the stub compressive tubular members the FEA results of the tubular members with localized cross-sectional damage are summarized in with local cross-sectional damage by corrosion. As shown in Figures 18 and 19, the yield loads and Table 4 as yield loads, compressive strengths, and failure modes. compressive strengths were proportionally decreased depending on the equivalent cross-sectional area ratio and damaged volume ratio. However, the test results were distributed to decrease about 40% of the regression line for the FEA results, and it was shown to be effective by the minimum residual thickness and corroded shape. The yield loads decreased according to the equivalent cross-sectional area ratio and volume ratio. The compressive strengths also constantly decreased from a compressive strength of 95%, depending on their cross-sectional area ratios and volume ratios.
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(a)
(b)
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Figure 17. Load-displacement relationship of each corroded depth specimen: (a) 0.5 mm corroded Figure 17. Load-displacement relationship of each corroded depth specimen: (a) 0.5 mm corroded depth; (b) (b) 1.0 1.0 mm mm corroded corroded depth; depth; (c) (c) 1.5 1.5 mm mm corroded corroded depth; depth; and and (d) (d) 2.0 2.0 mm mm corroded corroded depth. depth. depth;
ToTable evaluate the relationships between the cross-sectional damage and compressive strength of 4. Summary of FEA results of the tubular members with localized cross-sectional damage. small tubular members, their yield loads and compressive strengths were evaluated based on the equivalent cross-sectional area ratio and damaged ratioLoad from the test results, as shown in Equivalent CrossVolume Ratio involume the Yield Ultimate Load Specimens Failure Mode 2 )/(%) Sectional Area (mm Damaged Zone (%) (kN)/(%) (kN)/(%) Figures 18 and 19. To determine the main factor affecting compressive strength, other cross-sectional CR-H0W0 863.6/100 100 267.7/100 297.7/100were similar 1 properties of the tubular member were also considered. However, the two values to the CD0.5-H60W28 849.6/98.39 98.39 263.1/95.01 275.4/92.51 3 decrease in the yield loads and compressive strengths of the stub compressive tubular members with CD0.5-H120W28 849.6/98.39 98.39 263.3/95.01 275.9/92.68 2 CD0.5-H180W28 849.6/98.39 98.39 262.8/95.01 277.5/93.23 2 local cross-sectional damage by corrosion. As shown in Figures 18 and 19, the yield loads and CD0.5-H240W28 849.6/98.39 98.39 262.8/95.01 278.1/93.4 3 compressive strengths849.6/98.39 were proportionally decreased depending on the 278.1/93.43 equivalent cross-sectional CD0.5-H300W28 98.39 262.8/95.01 3 835.7/96.78 96.78 the test results 258.7/90.39 268.7/90.27to decrease 2 area CD0.5-H60W56 ratio and damaged volume ratio. However, were distributed about CD0.5-H120W56 835.7/96.78 96.78 258.1/90.39 269.1/90.39 2 40% CD0.5-H180W56 of the regression835.7/96.78 line for the FEA results, and it was shown to be effective by the minimum 96.78 258/90.39 271.7/91.26 2 residual thickness and835.7/96.78 corroded shape. The yield according to the equivalent crossCD0.5-H240W56 96.78 loads decreased 258/90.39 273.3/91.8 3 CD0.5-H300W56 835.7/96.78 96.78 258.1/90.39 273.5/91.87 3 sectional area ratio and volume ratio. The compressive strengths also constantly decreased from a CD0.5-H60W84 821.8/95.17 95.17 254.7/86.49 265.4/89.16 2 compressive strength 821.8/95.17 of 95%, depending on their area ratios265/89.03 and volume ratios. CD0.5-H120W84 95.17 cross-sectional 253.8/86.49 2 CD0.5-H180W84 821.8/95.17 95.17 CD0.5-H240W84 821.8/95.17 95.17 Table 4. Summary of FEA results of the tubular members CD0.5-H300W84 821.8/95.17 95.17 CD0.5-H60W112 807.9/93.55 93.55 Equivalent Volume CD0.5-H120W112 807.9/93.55 93.55 Ratio in CD0.5-H180W112 807.9/93.55 Specimens Cross-Sectional the93.55 Damaged CD0.5-H240W112 807.9/93.55 2 93.55 Area (mm )/(%) Zone (%) CD0.5-H300W112 807.9/93.55 93.55 CD0.5-H60W140 794/91.94 91.94 CR-H0W0 863.6/100 100 CD0.5-H120W140 794/91.94 91.94 CD0.5-H60W28 849.6/98.39 98.39 CD0.5-H180W140 794/91.94 91.94 CD0.5-H120W28 849.6/98.39 98.39 CD0.5-H240W140 794/91.94 91.94 CD0.5-H300W140 794/91.94 91.94
CD0.5-H180W28 CD0.5-H240W28 CD0.5-H300W28
849.6/98.39 849.6/98.39 849.6/98.39
98.39 98.39 98.39
253.5/86.49 253.5/86.49
267.2/89.76 268.7/90.27
2 3
251.1/83.55 249.9/83.55 Yield Load 249.6/83.55 (kN)/(%) 249.5/83.55 249.6/83.55 247.7/81.62 267.7/100 246.3/81.62 263.1/95.01 245.9/81.62 263.3/95.01 245.8/81.62 245.8/81.62
263.1/88.36 Ultimate 262/88 263.8/88.61 Load 264.5/88.85 (kN)/(%) 265.1/89.06 261.1/87.71 297.7/100 259.6/87.2 275.4/92.51 261.1/87.69 275.9/92.68 261.3/87.78 261.6/87.89
2 2Failure 2 3Mode 3 2 1 4 3 4 5 2 5
with localized cross-sectional damage. 253.7/86.49 269.2/90.43 3
262.8/95.01 262.8/95.01 262.8/95.01
277.5/93.23 278.1/93.4 278.1/93.43
2 3 3
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Table 4. Cont. CD0.5-H60W280 CD0.5-H120W280 CD0.5-H180W280 CD0.5-H240W280 CD0.5-H300W280 CD1-H60W28 CD1-H120W28 CD1-H180W28 CD1-H240W28 CD1-H300W28 CD1-H60W56 CD1-H120W56 CD1-H180W56 CD1-H240W56 CD1-H300W56 CD1-H60W84 CD1-H120W84 CD1-H180W84 CD1-H240W84 CD1-H300W84 CD1-H60W112 CD1-H120W112 CD1-H180W112 CD1-H240W112 CD1-H300W112 CD1-H60W140 CD1-H120W140 CD1-H180W140 CD1-H240W140 CD1-H300W140 CD1-H60W280 CD1-H120W280 CD1-H180W280 CD1-H240W280 CD1-H300W280 CD1.5-H60W28 CD1.5-H120W28 CD1.5-H180W28 CD1.5-H240W28 CD1.5-H300W28 CD1.5-H60W56 CD1.5-H120W56 CD1.5-H180W56 CD1.5-H240W56 CD1.5-H300W56 CD1.5-H60W84 CD1.5-H120W84 CD1.5-H180W84 CD1.5-H240W84 CD1.5-H300W84 CD1.5-H60W112 CD1.5-H120W112 CD1.5-H180W112 CD1.5-H240W112 CD1.5-H300W112 CD1.5-H60W140 CD1.5-H120W140 CD1.5-H180W140 CD1.5-H240W140 CD1.5-H300W140 CD1.5-H60W280 CD1.5-H120W280 CD1.5-H180W280 CD1.5-H240W280 CD1.5-H300W280 CD2-H60W28 CD2-H120W28 CD2-H180W28 CD2-H240W28 CD2-H300W28
724.4/83.88 724.4/83.88 724.4/83.88 724.4/83.88 724.4/83.88 835.9/96.79 835.9/96.79 835.9/96.79 835.9/96.79 835.9/96.79 808.2/93.59 808.2/93.59 808.2/93.59 808.2/93.59 808.2/93.59 780.5/90.38 780.5/90.38 780.5/90.38 780.5/90.38 780.5/90.38 752.9/87.18 752.9/87.18 752.9/87.18 752.9/87.18 752.9/87.18 725.2/83.97 725.2/83.97 725.2/83.97 725.2/83.97 725.2/83.97 586.8/67.95 586.8/67.95 586.8/67.95 586.8/67.95 586.8/67.95 822.3/95.22 822.3/95.22 822.3/95.22 822.3/95.22 822.3/95.22 781/90.44 781/90.44 781/90.44 781/90.44 781/90.44 739.7/85.66 739.7/85.66 739.7/85.66 739.7/85.66 739.7/85.66 698.4/80.88 698.4/80.88 698.4/80.88 698.4/80.88 698.4/80.88 657.2/76.1 657.2/76.1 657.2/76.1 657.2/76.1 657.2/76.1 450.8/52.2 450.8/52.2 450.8/52.2 450.8/52.2 450.8/52.2 808.8/93.66 808.8/93.66 808.8/93.66 808.8/93.66 808.8/93.66
84.87 84.87 84.87 84.87 84.87 96.79 96.79 96.79 96.79 96.79 93.59 93.59 93.59 93.59 93.59 90.38 90.38 90.38 90.38 90.38 87.18 87.18 87.18 87.18 87.18 83.97 83.97 83.97 83.97 83.97 69.55 69.55 69.55 69.55 69.55 95.22 95.22 95.22 95.22 95.22 90.44 90.44 90.44 90.44 90.44 85.66 85.66 85.66 85.66 85.66 80.88 80.88 80.88 80.88 80.88 76.10 76.10 76.10 76.10 76.10 54.05 54.05 54.05 54.05 54.05 93.66 93.66 93.66 93.66 93.66
226.4/83.88 225.2/83.88 224.8/83.88 224.3/83.88 225.2/83.88 258.1/90.13 257.8/90.13 257.7/90.13 257.8/90.13 258/90.13 248.9/81.12 248.2/81.12 248/81.12 248.2/81.12 248.5/81.12 240.5/73.76 239.4/73.76 239.4/73.76 239.3/73.76 235.5/73.76 233/68.41 231.5/68.41 231.2/68.41 231.2/68.41 231.4/68.41 226/65 224.2/65 223.7/65 223.6/65 223.7/65 183.9/67.95 182.5/67.95 182/67.95 182.5/67.95 182.2/67.95 253.1/85.38 252.8/85.38 252.8/85.38 253/85.38 253.2/85.38 238.9/72.28 238.2/72.28 238.2/72.28 238.6/72.28 239.1/72.28 227.1/61.96 225.1/61.96 224.9/61.96 225.3/61.96 225.9/61.96 215.2/54.79 213.1/54.79 212.9/54.79 213.1/54.79 213.5/54.79 203.9/50.34 200.4/50.34 202.9/50.34 203.3/50.34 203.6/50.34 140/52.2 140.2/52.2 139.9/52.2 141/52.2 139.9/52.2 248.2/80.77 247.8/80.77 247.9/80.77 248.1/80.77 248.5/80.77
250.4/84.1 247.6/83.19 247.6/83.18 247.7/83.21 247.6/83.19 266.7/89.6 267.8/89.94 270.2/90.77 272.9/91.69 273.1/91.74 256.6/86.19 257.5/86.48 259.3/87.11 263.5/88.5 263.8/88.63 248.5/83.47 249.1/83.69 249.1/83.69 254.1/85.34 254.2/85.37 241.3/81.06 241.8/81.22 243.8/81.89 245.6/82.49 245.2/82.37 234.9/78.9 235.1/78.96 237.1/79.64 239.2/80.34 237.9/79.91 196.9/66.14 194.4/65.32 194.8/65.44 194.9/65.47 194.9/65.48 260.6/87.55 261.6/87.87 263.6/88.55 267.4/89.81 268.4/90.14 244.7/82.19 246/82.64 247.5/83.13 250.5/84.16 254.1/85.35 231/77.58 232.9/78.22 234.6/78.81 237.5/79.79 239.6/80.48 218.6/73.42 220.6/74.11 222.7/74.81 225.2/75.64 226.1/75.95 206.7/69.44 208.7/70.09 210.5/70.7 212.8/71.47 214.2/71.95 144.2/48.42 144.5/48.53 144.7/48.59 144.5/48.55 144.8/48.63 254.7/85.55 255.7/85.91 257.5/86.48 261.1/87.7 264/88.68
5 6 6 6 6 2 2 2 3 3 2 2 2 2 3 2 2 2 3 3 4 4 4 5 5 4 4 4 4 5 6 6 6 6 6 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 4 4 4 4 2 4 4 4 4 4 6 6 6 6 6 2 2 2 2 3
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Table 4. Cont. CD2-H60W56 754.1/87.33 CD2-H120W56 754.1/87.33 CD2-H180W56 754.1/87.33 CD2-H240W56 754.1/87.33 CD2-H300W56 754.1/87.33 CD2-H60W84 699.4/80.99 CD2-H120W84 699.4/80.99 CD2-H180W84 699.4/80.99 CD2-H240W84 699.4/80.99 Materials 2018, 11, x FOR PEER REVIEW CD2-H300W84 699.4/80.99 CD2-H60W112 644.7/74.65 CD2-H120W112 644.7/74.65 CD2-H300W112 644.7/74.65 CD2-H180W112 644.7/74.65 CD2-H60W140 589.9/68.31 CD2-H240W112 644.7/74.65 CD2-H300W112 644.7/74.65 CD2-H120W140 589.9/68.31 CD2-H60W140 589.9/68.31 CD2-H180W140 589.9/68.31 CD2-H120W140 589.9/68.31 CD2-H180W140 589.9/68.31 CD2-H240W140 589.9/68.31 CD2-H240W140 589.9/68.31 CD2-H300W140 589.9/68.31 CD2-H300W140 589.9/68.31 CD2-H60W280 316.3/36.63 CD2-H60W280 316.3/36.63 CD2-H120W280 316.3/36.63 CD2-H120W280 316.3/36.63 CD2-H180W280 316.3/36.63 CD2-H180W280 316.3/36.63 CD2-H240W280 316.3/36.63 CD2-H300W280 316.3/36.63
CD2-H240W280 CD2-H300W280
316.3/36.63 316.3/36.63
87.33 87.33 87.33 87.33 87.33 80.99 80.99 80.99 80.99 80.99 74.65 74.65 74.65 74.65 68.31 74.65 74.65 68.31 68.31 68.31 68.31 68.31 68.31 68.31 68.31 68.31 38.37 38.37 38.37 38.37 38.37 38.37 38.37 38.37
38.37 38.37
228.6/63.93 228.6/63.93 228.6/63.93 229.5/63.93 229.1/63.93 204.9/51.22 211.9/51.22 210.9/51.22 206.1/51.22 206.8/51.22 188/42.83 193/42.83 196.2/42.83 192.7/42.83 173.9/37.75 187/42.83 196.2/42.83 170.4/37.75 173.9/37.75 166.8/37.75 170.4/37.75 166.8/37.75 172.5/37.75 172.5/37.75 177.6/37.75 177.6/37.75 97.8/36.63 97.8/36.63 89.9/36.63 89.9/36.63 97.2/36.63 97.2/36.63 98.1/36.63 95.9/36.63
98.1/36.63 95.9/36.63
232.4/78.06 233.9/78.55 234.4/78.75 236.7/79.5 241.7/81.18 212.8/71.48 215/72.22 215.9/72.52 218.5/73.41 220.3/73.99 194.5/65.33 196.5/66.02 201.8/67.79 198.4/66.64 177.5/59.63 201.5/67.68 201.8/67.79 179.6/60.34 177.5/59.63 181.4/60.95 179.6/60.34 181.4/60.95 184.4/61.93 184.4/61.93 183.7/61.72 183.7/61.72 98.3/33.03 98.3/33.03 98.3/33.02 98.3/33.02 98.3/33.03 98.3/33.03 98.3/33.03 98.3/33.03
98.3/33.03 98.3/33.03
2 2 2 2 2 4 2 2 2 5 4 4 4 4 4 4 4 4 4 5 6 6 6 6 6
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4 4 4 4 4 5 6 6 6 6 6
(a)
(b) Figure compressive strength depending on damaged area:area: (a) yield load ratioFigure 18. 18. Yield Yieldstrength strengthand and compressive strength depending on damaged (a) yield load equivalent damaged area; and (b) the ultimate load ratio-equivalent damaged area. ratio-equivalent damaged area; and (b) the ultimate load ratio-equivalent damaged area.
(b) Figure Materials 2018,18. 11, Yield 1254 strength and compressive strength depending on damaged area: (a) yield load ratio18 of 20 equivalent damaged area; and (b) the ultimate load ratio-equivalent damaged area.
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(a)
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(b) Figure 19. 19. Yield Yield strength strength and and compressive compressive strength strength depending depending on on the volume of damaged zone: Figure the volume of the the damaged zone: (a) yield load ratio-volume ratio in the damaged zone; and (b) the ultimate load ratio-volume ratio in (a) yield load ratio-volume ratio in the damaged zone; and (b) the ultimate load ratio-volume ratio in the damaged zone. the damaged zone.
4. Conclusions 4. Conclusions This study examined the structural behavior and strength of stub tubular steel members with This study examined the structural behavior and strength of stub tubular steel members with localized cross-sectional cross-sectionaldamage. damage. To consider the localized cross-sectional by localized To consider the localized cross-sectional damage damage caused bycaused corrosion, corrosion, compressive loading tests and numerical analyses of stub circular members were compressive loading tests and numerical analyses of stub circular members were conducted. For the conducted. For the compressive loading test, artificial cross-sectional damages, with various compressive loading test, artificial cross-sectional damages, with various damaged widths and heights, damaged widths and heights, were induced on the surface of the tubular specimens to examine the were induced on the surface of the tubular specimens to examine the major variables that affect the major variables that affect the compressive behaviors of circular tubular members. For numerical compressive behaviors of circular tubular members. For numerical analyses, FEA was conducted to analyses, FEA was conducted to clarify the compressive resistant capacities of the circular tubular clarify the compressive resistant capacities of the circular tubular specimens for various damaged specimens for various damaged parameters, such as corroded depth, damaged width, and damaged parameters, such as corroded depth, damaged width, and damaged height. A total of 120 FEA models height. A total of 120 FEA models were analyzed to investigate the major variables of compressive were analyzed to investigate the major variables of compressive strength with cross-sectional damage strength with cross-sectional damage by corrosion. by corrosion. The compressive loading test results showed that the compressive strengths were affected by The compressive loading test results showed that the compressive strengths were affected by the damaged width within a certain range. The effect of compressive strength according to the the damaged width within a certain range. The effect of compressive strength according to the damaged height was greater than that according to the damaged widths. Thus, the tendencies of yield damaged height was greater than that according to the damaged widths. Thus, the tendencies of yield load and failure on the same damaged width under lower damaged width were similar; however, load and failure on the same damaged width under lower damaged width were similar; however, those of the greater damaged width changed depending on the damaged height. To verify the FEA, those of the greater damaged width changed depending on the damaged height. To verify the the compressive strengths (yield loads) affected by the damaged depth and condition were FEA, the compressive strengths (yield loads) affected by the damaged depth and condition were determined. The compressive yield load was decreased to change the failure modes depending on determined. The compressive yield load was decreased to change the failure modes depending on the damaged depth. To clarity the compressive strength of the circular tubular member according to the damaged depth. To clarity the compressive strength of the circular tubular member according cross-sectional damage, the equivalent cross-sectional area ratio and damaged volume ratio were to cross-sectional damage, the equivalent cross-sectional area ratio and damaged volume ratio were calculated. The compressive strength was decreased proportionally with the equivalent crosssectional area ratio and damaged volume ratio. Author Contributions: J.-H.A. and J.H. conceived the idea and designed the framework; S.-H.J. and Y.-S.J. conducted experiments; S.-H.J. and K.-I.C. supported analysis model for numerical analysis; J.-H.A. and Y.-S.J. analyzed the data; and J.-H.A. and J.H. wrote the paper.
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calculated. The compressive strength was decreased proportionally with the equivalent cross-sectional area ratio and damaged volume ratio. Author Contributions: J.-H.A. and J.H. conceived the idea and designed the framework; S.-H.J. and Y.-S.J. conducted experiments; S.-H.J. and K.-I.C. supported analysis model for numerical analysis; J.-H.A. and Y.-S.J. analyzed the data; and J.-H.A. and J.H. wrote the paper. Funding: This research was funded by Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education [2014R1A1A2055900] and the Ministry of Public Administration and Security as “Disaster Prevention Safety Human resource development Project”. Acknowledgments: This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2014R1A1A2055900) and the Ministry of Public Administration and Security as “Disaster Prevention Safety Human resource development Project”. Conflicts of Interest: The authors declare no conflicts of interest.
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