1-14 Al-Khwarizmi Engineering Journal,Vol. 12, No. 1, P.P. 1 Enhancement of Buckling Resistance Ahmed Naïf Al Hameed Shamkhi Al *,** Department of Mechanical Engineering / University of Technology **Department of Machines and Equipment / (Received Abstract This paper has investigated experimentally the dynamic buckling behavior of AISI 303 stainless steel Aluminized and as received long columns. These columns, hot 22 specimens, without aluminizing (type 1), and 50 specimens, with hot conditions of dipping temperature and dipping time (type 2), are tested under dynamic compression loading and under dynamic combined loading (compression and bending) by using a rotating buckling test machine. The experimental results are compared with Perry Robertson interaction formula that used for long columns. get a mathematical model that descripts the buckling b loading. The experimental results obtained show an advantageous influence of hot dynamic buckling behavior of AISI 303 stainless steel long columns. critical buckling stress, are as follow: (64.8 %) for long columns type (2), compared with columns type (1), under dynamic compression loading, and (56.6 %) for long columns type (2), combined loading, and (33.3 %) for long columns type (2) compared with Keywords: Dynamic buckling, hot-dip Aluminizing, long columns, AISI 303 stainless steel. 1. Introduction Structural members subjected to axial compressive loads may fail in a manner that depends upon their geometrical properties rather than material properties [1]. It common experience, for example, that a long slender structural member will suddenly bow with lateral displacements when subjected to an axial compression load [1, 2]. Long slender members subjected to an axial compressive force are called columns, and the lateral deflection that occurs is called buckling [3]. The buckling behavior of steel columns consider one of the important Khwarizmi Engineering Journal,Vol. 12, No. 1, P.P. 1- 14 (2016) Buckling Resistance of Aluminized Long Columns Stainless Steel AISI 303 Ahmed Naïf Al-Khazraji* Samir Ali Al-Rabii** Hameed Shamkhi Al-Khazalli*** Department of Mechanical Engineering / University of Technology Department of Machines and Equipment / Institute of Technology / Middle Technical University / Baghdad *Email: dr_ahmed53 @yahoo.com *Email: alrabiee202@yahoo.com ***Email: hameedshamkhi@yahoo.com (Received 11 June 2015; accepted 4 August 2015) This paper has investigated experimentally the dynamic buckling behavior of AISI 303 stainless steel Aluminized and as received long columns. These columns, hot-dip aluminized and as received, are tested under dynamic buckling, 22 specimens, without aluminizing (type 1), and 50 specimens, with hot-dip aluminizing at different aluminizing conditions of dipping temperature and dipping time (type 2), are tested under dynamic compression loading and under mpression and bending) by using a rotating buckling test machine. The experimental results are compared with Perry Robertson interaction formula that used for long columns. Greenhill formula is used to get a mathematical model that descripts the buckling behavior of the specimens of type (1) under The experimental results obtained show an advantageous influence of hot-dip aluminizing treatment on dynamic buckling behavior of AISI 303 stainless steel long columns. The improvement based on the average value of critical buckling stress, are as follow: (64.8 %) for long columns type (2), compared with columns type (1), under 56.6 %) for long columns type (2), compared with columns type (1), combined loading, and (33.3 %) for long columns type (2) compared with Perry Robertson critical buckling stress. dip Aluminizing, long columns, AISI 303 stainless steel. Structural members subjected to axial compressive loads may fail in a manner that depends upon their geometrical properties rather than material properties [1]. It common experience, for example, that a long slender structural member will suddenly bow with large lateral displacements when subjected to an axial compression load [1, 2]. Long slender members subjected to an axial compressive force are called columns, and the lateral deflection that occurs is The buckling behavior of columns consider one of the important phenomenon that had been studying and analysis from a long time. For combined axial and bending loads, European standard (Eurocode 3 ENV 1939 1-4), American standard (SEI/ASCE 8 Australian/ New Zealand standar are suggested to use the guidance developed for carbon steel to determine the resistance of stainless steel members [ experimentally tests are carried on cold formed austenitic stainless steel square, rectangular, and circular hollow section members to examine the buckling behavior of columns and beams under effect of gradually increased single and combined loads (compression, bending, and compression bending) with two types of ends conditions pin Al-Khwarizmi Engineering Journal (2016) Long Columns of Rabii** Department of Mechanical Engineering / University of Technology Middle Technical University / Baghdad This paper has investigated experimentally the dynamic buckling behavior of AISI 303 stainless steel Aluminized dip aluminized and as received, are tested under dynamic buckling, dip aluminizing at different aluminizing conditions of dipping temperature and dipping time (type 2), are tested under dynamic compression loading and under mpression and bending) by using a rotating buckling test machine. The experimental Greenhill formula is used to ehavior of the specimens of type (1) under dynamic compression dip aluminizing treatment on based on the average value of critical buckling stress, are as follow: (64.8 %) for long columns type (2), compared with columns type (1), under compared with columns type (1), under dynamic critical buckling stress. phenomenon that had been studying and analysis For combined axial and bending loads, European standard (Eurocode 3 ENV 1939- 4), American standard (SEI/ASCE 8-02), and Australian/ New Zealand standard (AS/NZE 4673 are suggested to use the guidance developed for carbon steel to determine the resistance of stainless steel members [4]. A series of experimentally tests are carried on cold formed austenitic stainless steel square, rectangular, and hollow section members to examine the buckling behavior of columns and beams under effect of gradually increased single and combined loads (compression, bending, and compression- bending) with two types of ends conditions pin- Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 2 ends and fixed-ends [5]. The buckling of solid and hollow CK35 and CK45 alloy steel columns under combined dynamic loading has been studied experimentally and the obtained results showed that the failure resistance of the columns depends on the type of cross-section and initial deflection of column [6]. The nitride case hardening (liquid nitriding) surface treatment is used to enhance the buckling resistance of square columns with different length, material (CK45, CK67, CK101), and constant cross section (10 ×10) mm subjected to the effect of single and combined dynamic loads. The results of the study showed experimentally that the resistance and the number of cycles to failure were increased by using this method [7]. The surface treatment by shot peening is used to enhance the buckling resistance of a series of (CK35) steel column with solid circular cross-section under single and combined dynamic loads by increasing the yield and ultimate strength of columns material [8]. Because of the many practical applications of stainless steel columns in constructions of the buildings, ships, bridges, airplanes, spaceships, etc., there were many of studies and researches to improve the buckling resistance of columns by using of number of methods, for example: • Improvement of the mechanical properties of the columns material by using new special metal alloys, or by using of composite materials. • Improvement of columns section design by using of the modern design methods that increases of the columns resistance to the buckling. • Using of the surface treatments methods such as: shot-peening and heat treatment. Surface coating is an efficient and economical way to obtain the desirable material properties by altering physical, chemical, or electrical characteristics of a material. Surface modification by coatings has become an essential step to improve the surface properties such as, resistance to wear, corrosion and oxidation [9, 10].The influence of surface coating treatment on the surface properties and some of the mechanical properties was investigated by many researchers. A new pack cementation process technique was used to enhance the hot corrosion and oxidation resistance of stainless steel AISI 316L by using two different kinds of coating, the first one was Si-modified aluminide coating and the second was the Ce-deped silicon modified aluminide coating [11]. Hot dip aluminizes samples with (1-6 wt %) silicon concentration of aluminizing melt and samples aluminized in pure aluminum were tested by using a 3-point bend device in order to compare the relative ductility and formability of the aluminized steel and to determine the influence of silicon concentration and coating thickness on these properties [12]. There are many fields of practical applications that needs to use of steel columns meet between the strength and resistance of the external environment conditions (corrosion, wear, and high temperature oxidation). From this point of design, the designer used numbers of procedures to maintain the above requirements. The surface coating by using aluminum (aluminizing process) was one of the popular methods to develop protection layer for substrate material from environment conditions. This paper examine the effect of hot-dip aluminizing process (HDA) on dynamic buckling of long columns subjected to compression and compression-bending loads, of stainless steel (AISI 303) material by series of circular cross- section columns, of different slenderness ratio, with and without HDA surface treatment at different dipping temperatures (���) and dipping times (���). 2. Theory 2.1. Perry Robertson Interaction Formula It is important to evaluate the compressive buckling strength of real columns,���, in the presence of initial mechanical and geometrical imperfections, a Perry Robertson interaction formula [4, 13, 14, and 15] is adopted as follow: ��� = �� … �1� and ��� = � × ��� … (2) where: = 1� + ��� − ������.� ≤ 1 …�3� in which: � = 0.5 !1 + "!� − �#$ + ����$ … �4� � = �&' .(�� ) …�5� Where the value of the imperfection factor (") and the limiting non-dimensional slenderness ratio are defined in Table (1). The value of the effective slenderness ratio (�&) is calculated by using the relation [3]: �& = *+� = +,� … (6) Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 3 The value of slenderness ratio above which column’s type is long is obtained using the following relation [16]: �� = �& = '.- )�./ … �7� and by substituted the value of E, �./ from Table (2), and the value of K=0.7 (for fixed-pinned ends) in Eq. (7), we find that the value of critical slenderness ratio is �� = 86.5. Table 1, Values of imperfection factor and limiting slenderness ratio for flexural, torsional and torsional- flexural buckling [14]. Buckling mode Type of member 3 45 Flexural Cold formed open sections Hollow sections (welded and seamless) Welded open sections (major axis) Welded open sections (minor axis) 0.49 0.49 0.49 0.78 0.40 0.40 0.20 0.20 Torsional and torsional-flexural All members 0.34 0.20 2.2. Spatial Buckling Under Torque and Axial Force Spatial buckling of twisted and compressed shafts is important for the design of rotors of turbines, generators, and other rotating machinery. Spatial buckling may also be important for frames. Recently, design of latticed struts that can be collapsed for transport by means of torsion became of interest for construction of an orbiting space station [17]. Consider a geometrically perfect beam or shaft supported on two spherical hinges, loaded by axial force P and torque 67, which is assumed to keep its direction during buckling; see Fig. (3-10), where the axial vector of torque is represented by a double arrow. According to Greenhill (1883), the relation between the buckling load P and torque 67 is given by [17]. ����� + 8 676��� 9 � = 1 … �8� where ���� = :;<=+; 6��� = > :<=+ … (9) ���� is the critical load for buckling without torque (Euler formula), and 6��� is the critical torque for buckling without axial force. Equation (8) is plotted in Fig. (1). By using effective length (?&� instead of (L), Eq. (8) can be used to determine the theoretical buckling load (�) for other form of ends support. From Eqs. (8) and (9), one can be write � = 81 − @ ABACDE F �9 ∗ ���� … (10) and > = AB∗+,:<=∗�HI JJCDE �K/M … (11) In this work, k consider as a function of buckling parameters in order to fit the experimental results with a mathematical model. 3. Experimental Work 3.1. Material Used and Buckling Test Machine AISI 303 stainless steel as long columns of circular cross-section, Ø=8 mm, of different slenderness ratio (λ�, with and without hot-dip aluminizing were tested by using rotating column buckling test machine capable to apply compression and compression-bending dynamic loads, with column ends support of fixed- pinned and rotating speed of 17 and 34 r.p.m. in this research it was used low speed (17 r.p.m) in all dynamic buckling experiments. The photograph of the rotating buckling test machine is shown in Fig. (2). More details of buckling test machine, used in this research, were found in Ref. [6]. The detail of the chemical composition of stainless steel; tested and standardized in State Company for Inspection and Engineering Rehabilitation (SIER)/ Baghdad by a certificate No. 1043/2013 at room temperature (25 ℃) and relative humidity (60%), is shown in Table (2). Also, the significant Fig. 1. Beam or shaft subjected to axial force and constant-direction torque [17]. Ahmed Naïf Al-Khazraji mechanical properties, tested in Central Organization for Standardization and Quality Control (C.O.S.Q.C.) / Baghdad, are given in Table (3). While the experiments of hot dip aluminizing AISI 303 stainless steel carried out , by using a self-construction system of hot- dip aluminizing, Fig. (3), in State Company for Electrical Industries/Baghdad/ Unit of casting. A high purity aluminum (99 %) was dipping bath, and the process variables were dipping temperature and dipping time Fig. 2. The photograph of the rotating buckling test machine used in the present research. Table 2, Chemical compositions (wt. %) of AISI 303 stainless steel. Alloy C Si Mn P Used material a 0.114 0.5 39 1.14 0.03 2 Standard (ASM) [18] Up to 0.15 Up to 1.0 Up to 2.0 Up to 0.2 a: Source: State Company for Inspection and Engineering Rehabilitation (SIER)/Baghdad. Al-Khwarizmi Engineering Journal, Vol. 12 4 mechanical properties, tested in Central Organization for Standardization and Quality Control (C.O.S.Q.C.) / Baghdad, are given in the experiments of hot dip aluminizing AISI 303 stainless steel rods are construction system of in State Company for Electrical Industries/Baghdad/ Unit of casting. A high purity aluminum (99 %) was used for dipping bath, and the process variables were ng temperature and dipping time. The photograph of the rotating buckling test machine used in the present research. Chemical compositions (wt. %) of AISI 303 stainless Cr Ni 0.03 18.20 8.19 17-19 8- 10 Source: State Company for Inspection and Engineering Rehabilitation (SIER)/Baghdad. Table 3, Experimental mechanical stainless steel used in present work (Average of three specimens) AISI 303 st. st. PQRS (MPa) PT ∗ (MPa) (GPa) 880 673 204.2 * Proof stress at 0.2% of stain. ** In gauge length ?# 25 VV Fig. 3. Schematic diagram and photograph of the HDA system. 3.2. Specimens Types There are two types of buckling specimens used in this work, these two types are: Type (1) as received specimens (non columns with circular cross 8 VV, X 201.1 VVY, different length. Table (4) gives the geometrical dimensions and buckling parameters of these specimens. Type (2) aluminized specimen aluminized columns with circular cross These specimens have a constant length L=440 mm, but at different hot dipping temperature (700, 740, 780, 820, and 860 O) and different dipping time (1, 2, 3, 4, and 5 minutes). Table (5) gives the parameters of hot dip and buckling of these specimens. 2, No. 1, P.P. 1- 14 (2016) properties of AISI 303 stainless steel used in present work (Average of three specimens) E (GPa) Elong.** % PZR (MPa) 204.2 41.4 269.2 * Proof stress at 0.2% of stain. VV. Schematic diagram and photograph of the There are two types of buckling specimens used in this work, these two types are: as received specimens (non-aluminized): columns with circular cross-section \ ,] 2 VV, and different length. Table (4) gives the geometrical dimensions and buckling parameters of these aluminized specimens: hot-dip aluminized columns with circular cross-section. These specimens have a constant length L=440 mm, but at different hot-dip conditions from dipping temperature (700, 740, 780, 820, and and different dipping time (1, 2, 3, 4, and Table (5) gives the parameters of hot- dip and buckling of these specimens. Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 5 3.3. Failure Criterion of Buckling When the maximum deflection of the column reaches the critical value of deflection (^��) of the column length, then the load measured (by pressure gauge) is the critical buckling load of the column. In the present work, the value of the critical deflection of the column is taken as (^���VV� = �? ∗ 1%� + ^#) [18, 7, and 8]. Because of the rotating effect on the reading of the column deflection using a dial gauge, a laser cell circuit tool has been fabricated, with whistle sound, fixed on electronic vernier (with reading accuracy of 0.01 mm), Fig. (4), to make the reading of critical deflection (^��) more strictness. Table 4, Geometrical dimensions and buckling parameters of specimens type (1). No. Symbol ` (mm) `a * (mm) b5 (mm) bcd ** (mm) 4a �`ad � Type of *** loading Type **** of column 1 1a 260 182 0.7/2 2.95 91 compression Long 2b 260 182 0.78/2 3 91 combined 2 2a 280 196 0.75/2 3.18 98 compression 2b 280 196 0.9/2 3.25 98 combined 3 3a 300 210 0.76/2 3.38 105 compression 3b 300 210 0.85/2 3.43 105 combined 4 4a 320 224 0.76/2 3.58 112 compression 4b 320 224 0.69/2 3.55 112 combined 5 5a 340 238 1.48/2 4.14 119 compression 5b 340 238 0.94/2 3.87 119 combined 6 6a 360 252 0.18/2 3.69 126 compression 6b 360 252 1.35/2 4.275 126 combined 7 6a 380 266 1.43/2 4.52 133 compression 4b 380 266 1.5/2 4.55 133 combined 8 5a 400 280 1.26/2 4.63 140 compression 5b 400 280 1.38/2 4.69 140 combined 9 6a 420 294 1.45/2 4.93 147 compression 6b 420 294 1.4/2 4.9 147 combined 10 7a 440 308 1.58/2 5.19 154 compression 7b 440 308 2.0/2 5.4 154 combined 11 8a 460 322 0.6/2 4.9 161 compression 8b 460 322 2.1/2 5.65 161 combined * `a = e` ** bcd�ff� = �` ∗ K%� + b5 *** Compression load= axial compression load +torsion. Combined load= (axial compression + bending load (at mid span)+torsion **** 4c = g. ( hPZR = ij. k , lm 4a > 4c → R5pq c5RQfp Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 6 Table 5, Geometrical dimensions and buckling parameters of specimens type (2). symbol No. rst �℃� Sst (min) ` (mm) `a (mm) b5 (mm) bcd* (mm) 4a Type of column Type of loading A1 1 700 1 440 308 1.85/2 5.3 154 Long Compression 2 700 2 1.9/2 5.4 3 700 3 1.1/2 5 4 700 4 2.1/2 5.5 5 700 5 1.4/2 5.1 B1 6 740 1 440 308 1.95/2 5.4 154 Long Compression 7 740 2 2.52/2 5.7 8 740 3 0.18/2 4.5 9 740 4 0.76/2 4.8 10 740 5 1.5/2 5.2 C1 11 780 1 440 308 1.5/2 5.3 154 Long Compression 12 780 2 1.92/2 5.4 13 780 3 1.45/2 5 14 780 4 1.7/2 5.3 15 780 5 2.15/2 5.5 D1 16 820 1 440 308 2.5/2 5.7 154 Long Compression 17 820 2 1/2 4.9 18 820 3 1/2 4.9 19 820 4 1.7/2 5.3 20 820 5 1.8/2 5.3 E1 21 860 1 440 308 1.1/2 5 154 Long Compression 22 860 2 2.3/2 5.6 23 860 3 1.45/2 5 24 860 4 0.6/2 4.7 25 860 5 2.7/2 5.8 A2 26 700 1 440 308 2.12/2 5.3 154 Long Combined 27 700 2 0.45/2 5.4 28 700 3 1.25/2 5 29 700 4 1.9/2 5.5 30 700 5 1.8/2 5.1 B2 31 740 1 440 308 1.6/2 5.4 154 Long Combined 32 740 2 2.27/2 5.7 33 740 3 0.6/2 4.5 34 740 4 1.1/2 4.8 35 740 5 1.75/2 5.2 C2 36 780 1 440 308 1.9/2 5.3 154 Long Combined 37 780 2 1.8/2 5.4 38 780 3 1.95/2 5 39 780 4 1.95/2 5.3 40 780 5 1.78/2 5.5 D2 41 820 1 440 308 2.9/2 5.7 154 Long Combined 42 820 2 2.15/2 4.9 43 820 3 1.4/2 4.9 44 820 4 1.23/2 5.3 Ahmed Naïf Al-Khazraji 45 820 5 E2 46 860 1 47 860 2 48 860 3 49 860 4 50 860 5 * ^���VV� = �? ∗ 1%� � Fig. 4. System used to control the deflection of columns during buckling test. 4. Results and Discussion Table (6) shows the experimental results of dynamic buckling test of 303 AISI column specimens without aluminizing (type 1). (6) it can be observed that The critical buckling stress (���) decreased with increasing in effective slenderness ratio (�&) for both dynamic compression load (compression-torsion dynamic combined load (compression torsion load). Also it can be seen that the bending load (�u&v.) is greater than the critical buckling stress for all slenderness ratio, but is al decreased with increased in �&. In order to make a comparison between the experimental results and theoretical results, Eq. (1) is used to calculate the theoretical critical buckling stress for the specimens of type (1). The results of Eq. (1) and Eq. (2) are shown in Table (7). From Table (6) and Table (7), it can be observed that the experimental critical stress (�&w.) is, in general, lower than the value of theoretical critical stress (���) from Perry Robertson interaction formula. The difference between the experimentally and theoretically results (Perry Robertson critical buckling stress) is duo to: initial imperfection of columns, the accuracy of construction of test machine, the alignment of loads, and the details of support condition which are not perfect as Al-Khwarizmi Engineering Journal, Vol. 12 7 1.57/2 5.3 440 308 0.9/2 5 154 Long 1.55/2 5.6 2.6/2 5 2.2/2 4.7 2.25/2 5.8 � � ^# System used to control the deflection of columns during buckling test. experimental results of dynamic buckling test of 303 AISI column specimens without aluminizing (type 1). In Table (6) it can be observed that The critical buckling ) decreased with increasing in effective r both dynamic torsion load) and dynamic combined load (compression-bending- load). Also it can be seen that the bending ) is greater than the critical buckling stress for all slenderness ratio, but is also . In order to make a comparison between the experimental results and theoretical results, Eq. (1) is used to calculate the theoretical critical buckling stress for the specimens of type (1). The results of Eq. (1) and (2) are shown in Table (7). From Table (6) and Table (7), it can be observed that the ) is, in general, lower than the value of theoretical critical stress ) from Perry Robertson interaction formula. ence between the experimentally and theoretically results (Perry Robertson critical buckling stress) is duo to: initial imperfection of the accuracy of construction of test the alignment of loads, and the details of h are not perfect as assumed in theoretical consideration. formula (Eq. 8) is used to fit the experimental results of the specimen’s mathematical model that describes the buckling behavior of these specimens. Table ( values of k function that used to determine the fitted model, Fig. (5). The fitted model was in the form of k = 1/(-3.48777 + 3.40067/P the values of the predicated buckling load (P) are given in Table (9). The fitted model gives a good correlation between the experimental values and theoretical values for slenderness ratio (91 with maximum error of 5.757 % shows the experimentally results of dynamic buckling test of specimens type (2) (hot aluminized long columns) with constant slenderness ratio of �& dip conditions (dipping temperature and dipping time). From Table (10), it can be detected that there is enhancement in buckling resistance of long aluminized columns compression load (compression and torsion) and combined load (compression, bending, and torsion), but the results are approximately the same. Whatever, it appear that the aluminizing conditions at dipping time of ( dipping temperature of ( maximum enhancement of dynamic buckling resistance for the specimens of type (2). In order 2, No. 1, P.P. 1- 14 (2016) Combined System used to control the deflection of columns during buckling test. assumed in theoretical consideration. Greenhill ) is used to fit the experimental specimen’s type (1) to find a mathematical model that describes the buckling behavior of these specimens. Table (8) shows the values of k function that used to determine the The fitted model was in the 3.48777 + 3.40067/Pexp/��� � ) and the values of the predicated buckling load (P) are fitted model gives a good correlation between the experimental values and theoretical values for slenderness ratio (91-154) with maximum error of 5.757 %. Table (10) shows the experimentally results of dynamic buckling test of specimens type (2) (hot-dip aluminized long columns) with constant 154 and different hot- dip conditions (dipping temperature and dipping ), it can be detected that there is enhancement in buckling resistance of long aluminized columns under both dynamic compression load (compression and torsion) and combined load (compression, bending, and torsion), but the results are approximately the same. Whatever, it appear that the aluminizing conditions at dipping time of (���=3 min) and ng temperature of (���=820O) gives a maximum enhancement of dynamic buckling resistance for the specimens of type (2). In order Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 8 to show the improvement of dynamic buckling resistance of aluminized columns (type 2) compared with non-aluminized columns (type 1), Fig.(6) is plotted by using the experimental results of Table (6) for specimens type (1), and Table (10) for specimens type (2), whereas Table (7) gives the theoretical results from Perry Robertson interaction formula. The improvement, based on the average value of critical buckling stress, is as follow: (64.8 %) for long columns type (2), compared with columns type (1), under dynamic compression loading, and (56.6 %) for long columns type (2), compared with columns type (1), under dynamic combined loading, and (38.3 %) for long columns type (2) compared with Perry Robertson critical buckling stress. These enhancement ratios of buckling resistance are calculated by compared the values of critical buckling stress illustrated in Fig. (7). It should be noted that the effect of rotating of the column (torsional loading) during the applied of compression load and/or compression-bending loads was appear clearly first by a Spatial (non- planar) shape of column deformation until buckling is occur and second by reduced the value of the critical buckling load. The lateral loading (bending load) on rotating columns leads to a fast increasing in the lateral deflection of the column under combined loading conditions and a signification reduction in axial compressive load and as a result decrease the buckling resistance of the columns compared with the case without lateral loading . It experimentally noted that the effect of the lateral loading on the buckling resistance was much greater than the effect of the twisting or torsional loading for the same slenderness ratios. Table 6, Experimental results of dynamic buckling test of column specimen type (1). No. Symbol xayZ �z� PayZ �{Z|� }~ap. �z� P~ap. �{Z|� 1 1a 7422.0126 147.6563 --- --- 1b 4523.893 90 306 247.312 2 2a 6785.8401 135 --- --- 2b 4241.15 84.375 285.6 248.58 3 3a 6008.296 119.5313 --- --- 3b 3887.721 77.3438 265.2 247.312 4 4a 5301.4376 105.4688 --- --- 4b 3534.292 70.3125 244.8 243.507 5 5a 4948.0084 98.4375 --- --- 5b 3322.234 66.0938 224.4 237.166 6 6a 4665.2651 92.8125 --- --- 6b 3180.863 63.2813 204 228.288 7 7a 4241.1501 84.375 --- --- 7b 3039.491 60.4688 183.6 216.874 8 8a 3887.7209 77.34375 --- --- 8b 2827.433 56.25 163.2 202.923 9 9a 3534.2917 70.3125 --- --- 9b 2686.062 53.4375 142.8 186.435 10 10a 3180.8626 63.28125 --- --- 10b 2474.004 49.2188 122.4 167.411 11 11a 2827.4334 56.25 --- --- 11b 2120.575 42.1875 81.6 116.68 Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 9 Table 7, Theoretical values of critical load and critical stress using Perry Robertson interaction formula for specimen type (1). Table 8, Theoretical values of Greenhill formula for specimen type (1). * For motor power of 0.5 KW and N=17 r.p.m Fig. 5. Function k predicated using Greenhill formula results. No. ` (mm) `a (mm) 4a�`ad � xcd �z� Pcd �{Z|� 1 260 182 91 9764.33 194.2552 2 280 196 98 8602.489 171.1411 3 300 210 105 7625.835 151.7112 4 320 224 112 6800.153 135.2848 5 340 238 119 6097.662 121.3091 6 360 252 126 5496.088 109.3412 7 380 266 133 4977.642 99.02704 8 400 280 140 4528.094 90.08358 9 420 294 147 4136.02 82.28352 10 440 308 154 3792.199 75.44341 11 460 322 161 3489.142356 69.41429 No. ` (mm) `a (mm) 4a �`ad � xayZ �z� xcd � �N��N��N��N� xayZ/xcd� {S* (N.mm) k 1 260 182 91 7422.012644 12233.2698 0.606707182 209523 0.471332517 2 280 196 98 6785.840132 10548.07447 0.643325012 209523 0.533008048 3 300 210 105 6008.29595 9188.544868 0.65388982 209523 0.579730475 4 320 224 112 5301.437603 8075.869513 0.656454094 209523 0.620682717 5 340 238 119 4948.00843 7153.711403 0.691670121 209523 0.696118496 6 360 252 126 4665.265091 6380.933936 0.731125747 209523 0.789296097 7 380 266 133 4241.150083 5726.932397 0.740562275 209523 0.848162555 8 400 280 140 3887.720909 5168.556489 0.752186983 209523 0.913503038 9 420 294 147 3534.291735 4688.033096 0.753896498 209523 0.962503809 10 440 308 154 3180.862562 4271.534288 0.744665113 209523 0.989941795 11 460 322 161 2827.433388 3908.171258 0.723467116 209523 0.994481029 Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 10 Table 9, Theoretical results of fitted model (k = 1/(-3.48777 + 3.40067/Pexp/���� )). Table 10, Experimental results of dynamic buckling test of column specimen type (2). symbol No. xayZ �z� PayZ �{Z|� symbol No. xayZ �z� PayZ �{Z|� }~ �z� P~a �{Z|� A1 1 5655 112.5 A2 26 3534.292 70.3125 163.2 357.1437 2 6362 126.5625 27 3534.292 70.3125 204 446.4297 3 5655 112.5 28 3534.292 70.3125 183.6 401.7867 4 4948 98.4375 29 4241.15 84.375 163.2 357.1437 5 4948 98.4375 30 4241.15 84.375 204 446.4297 B1 6 4948 98.4375 B2 31 3534.292 70.3125 204 446.4297 7 4241 84.375 32 3534.292 70.3125 183.6 401.7867 8 4948 98.4375 33 4241.15 84.375 183.6 401.7867 9 5655 112.5 34 4241.15 84.375 204 446.4297 10 5655 112.5 35 3534.292 70.3125 163.2 357.1437 C1 11 4948 98.4375 C2 36 4241.15 84.375 204 446.4297 12 5301 105.4688 37 3534.292 70.3125 183.6 401.7867 13 5655 112.5 38 4241.15 84.375 183.6 401.7867 14 5301 105.4688 39 2827.433 56.25 163.2 357.1437 15 4948 98.4375 40 2827.433 56.25 204 446.4297 D1 16 5655 112.5 D2 41 4241.15 84.375 183.6 401.7867 17 7069 140.625 42 4241.15 84.375 204 446.4297 18 4948 98.4375 43 4948.008 98.4375 183.6 401.7867 19 4948 98.4375 44 4241.15 84.375 204 446.4297 20 5301 105.4688 45 4241.15 84.375 204 446.4297 E1 21 5655 112.5 E2 46 4241.15 84.375 204 446.4297 No. ` (mm) `a (mm) k ���� (N.mm) x (fitted model) �z� xayZ �z� Error% 1 260 182 0.472287209 334774.5823 7441.032476 7422.012644 0.296 2 280 196 0.556076439 366012.6571 7091.215227 6785.840132 4.500 3 300 210 0.583802725 358644.7718 6052.238726 6008.29595 0.731 4 320 224 0.590809751 340265.0296 5013.515634 5301.437603 -5.431 5 340 238 0.699870006 379365.7378 4971.40402 4948.00843 0.472 6 360 252 0.859468903 439994.5612 4933.861242 4665.265091 5.757 7 380 266 0.905599535 439210.0157 4423.530637 4241.150083 4.300 8 400 280 0.967798059 445907.1091 4027.305436 3887.720909 3.590 9 420 294 0.977496457 428929.1311 3569.315935 3534.291735 0.990 10 440 308 0.926835156 388212.4536 3027.175305 3180.862562 -4.831 11 460 322 0.824573802 330362.9546 2336.029801 2827.433388 -17.3798 Ahmed Naïf Al-Khazraji 22 4948 98.4375 23 4948 98.4375 24 4241 84.375 25 4241 84.375 Fig. 6. Critical stress- slenderness ratio relation for stainless steel 303 AISI columns under dynamic compression and combined loads compared with theoretical results (Perry Robertson formula). Fig. 7. Critical buckling stress for the specimens of type (1) and type (2) at the same effective slenderness ratio. 5. Conclusions 1. The experimental values of the critical buckling loads and/or stresses for non aluminized long columns, (�& > ��,�&�91 �� 161��, are less than the theoretical values predicated by Perry Robertson interaction formula , and this differences in results is duo to effect of initial imperfection of columns, the accuracy of Al-Khwarizmi Engineering Journal, Vol. 12 11 47 4241.15 84.375 183.6 48 4241.15 84.375 204 49 3534.292 70.3125 163.2 50 2827.433 56.25 204 slenderness ratio relation for stainless steel 303 AISI columns under dynamic compression and combined loads compared with formula). Critical buckling stress for the specimens of type (1) and type (2) at the same effective The experimental values of the critical buckling loads and/or stresses for non- aluminized long columns, , are less than the theoretical values predicated by Perry Robertson interaction formula , and this differences in results is duo to effect of initial the accuracy of construction of test machine, loads, and the details of support condition. 2. Using of hot- dip aluminizing surface treatment has make double benefit one of them is to develop protection layer for substrate material from environment conditions and the other is the improvement of dynamic buc resistance of long aluminized columns under dynamic compression loading and under dynamic combined loading. 3. The improvement in the dynamic buckling resistance were (64.8 %) for long columns type (2), compared with columns type (1), under dynamic compression loading only, and ( %) for long columns type (2), columns type (1), under dynamic combined loading, and (33.3 %) for long columns type (2) compared with Perry Robertson critical buckling stress. 4. The optimum hot-dip aluminizing co that give a maximum enhancement of dynamic buckling resistance for the specimens of type (2), are: dipping time of ( dipping temperature of ( 5. torsional loading during the applied of compression load and/or compression loads was appear clearly first by a Spatial (non-planar) shape of column deformation until buckling is occur and second by reduced the value of the critical buckling load. 6. The lateral loading (bending load) on rotating columns leads to a fast increas deflection of the column under combined loading conditions and a signification reduction in axial compressive load (critical buckling load). 2, No. 1, P.P. 1- 14 (2016) 401.7867 446.4297 357.1437 446.4297 construction of test machine, the alignment of ads, and the details of support condition. dip aluminizing surface treatment has make double benefit one of them develop protection layer for substrate material from environment conditions and the other is the improvement of dynamic buckling resistance of long aluminized columns under dynamic compression loading and under dynamic combined loading. The improvement in the dynamic buckling (64.8 %) for long columns type (2), compared with columns type (1), under pression loading only, and (56.6 %) for long columns type (2), compared with under dynamic combined loading, and (33.3 %) for long columns type (2) compared with Perry Robertson critical dip aluminizing conditions, a maximum enhancement of dynamic buckling resistance for the specimens of type (2), are: dipping time of (t��=3 min) and dipping temperature of (T��=820O). during the applied of compression load and/or compression-bending loads was appear clearly first by a Spatial planar) shape of column deformation until buckling is occur and second by reduced the value of the critical buckling load. The lateral loading (bending load) on rotating columns leads to a fast increasing in the lateral deflection of the column under combined loading conditions and a signification reduction in axial compressive load (critical Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 12 Notation ℃ Dipping temperature ��� s (second) Dipping time t�� N (newton) Theoretical and experimental critical buckling load P��, P��� ��M The cross-sectional area of the column A ��� Modulus of elasticity E dimensio nless Effective length factor(depends on column ends support) K mm Unsupported and effective length of the column L,L� �� Smallest radius of gyration of the column r ��� Moment of inertia of the column cross sectional area I � critical load for buckling without torque (Euler formula) ��� � �.�� Applied torque 67 �.�� critical torque for buckling without axial force 6�� � � Bending load F� Greek letters ��� Theoretical and experimental critical buckling stress Pcd,PayZ dimension less The reduction factor accounting for buckling ��� the yield strength �� dimension less The imperfection factor defined in table (3-1). " dimension less The limiting and non-dimensional slenderness ratio �#,� dimension less Effective and critical slenderness ratio �&,�� ��� Ultimate and proportional limit of column’s material � /7,�./ �� Initial and critical deflection of the column ^#,^�� ��� Bending stress= F�/A �u 6. References [1] T. H. G. MEGSON,”Structural and Stress Analysis”, Butterworth-Heinemann, 2000. [2] Jianqiao Ye,” Structural and Stress Analysis Theories, tutorials and examples”, Taylor & Francis, 2008. [3] R. C. Hibbeler, SI conversion by S. C. Fan,” Statics and Mechanics of Materials”, Prentice-Hall, Inc., 2004. [4] N. R. Baddoo,” A Comparison of Structural Stainless Steel Design Standards”, the Steel Construction Institute, p.p. 131-149, (2003). [5] L. Gardner and D. A. Nethercot, “Experiments on Stainless Steel Hollow Sections-Part 2: Member Behaviour of Coloumns and Beams”, Journal of Constructional Steel Research, Vol. 60, p.p. 1319-1332, (2004). [6] Kifah Hameed Al-Jubori, “Columns Lateral Buckling Under Combined Dynamic Loading”, PhD. Thesis, University of Technology, Department of Technical Education, 2005. [7] Hamed Ali Hussein,”Buckling of Square Columns Under Cycling Loads for Nitriding Steel DIN (CK45, CK67, CK101)”, PhD. Thesis, University of Technology, Department of Mechanical Engineering, 2010. [8] Al-Alkhawi H. J. M., Al-Khazraji A. N., and Essam Zuhier Fadhel, “Determination the Optimum Shot Peening Time for Improving the Buckling Behavior of Medium Carbon Steel”, Eng. & Tech. Journal, Vol. 32, Part (A), No. 3, 2014. [9] Sung-Ha Hwang, Jin-Hwa Song, and Yong- Suk Kim, “Effects of carbon content of carbon steel on its dissolution into a molten aluminum alloy”, Materials Science and Engineering A 390, pp. 437–443, 2005. Ahmed Naïf Al-Khazraji Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 1- 14 (2016) 13 [10] Hishamuddin Hj. Husain, Muhamad Daud, Anasyida Abu Seman and Abdul Razak Daud, “Preliminary Study on Metallic Coating of Steel Substrates through Hot Dip Aluminizing by Using Energy Dispersive X-Ray Spectroscopy (EDX) Technique”, Journal of Nuclear and Related Technologies, Vol. 6, No. 2,pp. 63-69, December, 2009. [11] Rajab Mohammed Hussein, “Improvement of Stainless Steel (316L) Hot Corrosion and Oxidation Resistance by Aluminizing- Siliconizing”, PhD. Thesis, University of Technology, Department of Production Engineering and Metalluragy, 2007. [12] G. H. Awan, F. Ahmed, L. Ali, M. S. Shuja, and F. Hasan, “Effect of Coating- Thickness on the Formability of Hot Dip Aluminized Steel”, Pak. J. Engg. & Appl. Sci., Vol. 2, p.p. 14-21, Jan 2008. [13] N. R. Baddoo and B. A. Burgan, “Structural Design of Stainless Steel”, The Steel Construction Institute, SCI Publication P291 2001, 2001. [14] Euro Inox and The Steel Construction Institute, “Structural Design of Stainless Steel”, 3rd edition, 2006. [15] L. Gardner and D. A. Nethercot, “Designers’ Guide to EN 1993-1-1. Eurocode 3: Design of Steel Structures. General Rules and Rules for Building”, The Steel Construction Institute, Thomas Telford Ltd., 2005. [16] James M. Gere, “Mechanics of Materials”, 6th Ed, Thomson Learning, Inc., 2004. [17] Zdeněk P. Bažant and Luigi Cipolin”Stability of Structures Elastic, Inelastic, Fracture, and Damage theories”, Dover Puplications, Inc., 2003. [18] ASM Handbook,”Surface Engineering”, ASM International, Vol. 5, 1994. ا���ر�� �� �� 1، ا�� د12 ��� ا���ارزم� ا��� ��� ا����ما���� ،14 -1 )2016( 14 �.�& م$�وم� ا-�,��ج �*(� ة ا�'� �� م& ا�!�% ا��$�وم ��! أ /AISI 303 ����0ا�� )4'2 $� ا�2�3 ا�.�1& HDA( ا���ر���� ���5 ��24 ا���(�� **���2 (�� ا����42 *ا�����*** *،** �����������'&�� / %$# ا�"! �� ا'!�(� .- اد/ ا�+�*(� ا �( ات * **����12 وا� .- اد/ ا�+�*(� ا�)6!�� ا�'�45 / *(" ا�)�!3'&�� / %$# ا dr_ahmed53 @yahoo.com : ا�;8: ا9��)8و�7 * alrabiee202@yahoo.com :8;�: ا9��)8و�7 ا ** hameedshamkhi@yahoo.com : ا��� رو�� ا��ر�د*** ا��*�� <3���6وم ��>!'?� *1 ا�>3< ا��!� ا�@���!� و8�A ا�@��� ة ا�5':�3 ا?C� 7��*�!: ��$3'ك ا�9;(�ج ا 73�)�. AISI 303أ 7K #L ھIا ا�;HG ا�)F6G ا ،7��*�!: ��N ا�9;(�ج اO8�P�L QGL ة ��!� QX8���N اG �N ا�G!�ء(O 2ط زا�-Zا� N�O .( �-�d e* f2�(!��-8ض LGreenhill# ا�)[ ام LPerry Robertson interaction formula . �-�d# *�6ر�� ا 7��*�!: ��N ا�9;(�ج اO 8�P^L QGL 3'ك ا�9;(�ج� h<: 7i�:ر N:ل ?43 *'د'$!��)'�m ا&"�د ا�9;(�ج ا�8Gج، وھIه ا� �:'n* >$!. HG;�� ة ا�5':�3 �'ع) % 64.8( :ا?C�و8�P^L QGL ) ١(*�6ر�� .�9?� ة �'ع ) ٢( ،7��*�!: ���N اZ�9-�ط7 اG(�� ة ا�5':�3 �'ع ) % 56.6(و ا?C��X8<، و ) ١(*�6ر�� .�9?� ة �'ع ) ٢(���N ا� :!�*��7 اG(�) %33.3(و8�P^L QGL ا � ة �'ع ?C�)٢ (�-�d 1* ب'$G�� .Perry Robertson *�6ر�� .�6�� ا&"�د ا�9;(�ج ا�8Gج ا