Abstract Agricultural and construction equipment are commonly implemented with rectangular tubing in their structural frame designs. A
typical joining method to fabricate these frames is by welding and the use of ancillary structural plating at the connections. This aids two continuous members to pass through an intersection point of the frame with some degree of connectivity, but the connections are highly unbalanced as the tubing centroids exhibit asymmetry. Due to the practice of welded continuous member frame intersections in current agricultural equipment designs, a conviction may exist that welded continuous member frames are superior in structural strength over that of structural frame intersections implementing welded non-continuous members where the tubing centroids lie within two planes of symmetry, a connection design that would likely fabricating a more fatigue resistant structural frame. Three types of welded continuous tubing frame intersections currently observed in the designs of agricultural equipment were compared to two non-continuous frame intersection designs. Each design was subjected to the same loading condition and then examined for stress levels using the Finite Element Method to predict fatigue life. Results demonstrated that a lighter weight, non-continuous member frame intersection design was two magnitudes superior in fatigue resistance than some current implemented frame designs when using Stress-Life fatigue prediction methods and empirical fatigue strengths for fillet welds. Stress-Life predictions were also made using theoretical fatigue strength calcula-tions for the fatigue strength at the welds for comparison to the empirical derived weld fatigue strength.
Fatigue failures account for about 90% of failure causation in welded structures [1]. Estimates are made that about 4% of the gross domestic product of both the USA and Europe are consumed by pre-mature failure of components by fatigue [2]. The U.S. market for the manufacturing of agriculture, con-struction and mining equipment was 89.2 billion dollars in 2001 [3]. Using the 4% cost of fatigue failures to this specific US market, the cost of fatigue failures are in the range of 3.5 billion dollars for agriculture, construction and mining equip-ment. With this magnitude of cost, there is always an eco-nomic drive to reduce fatigue failures in industry where possi-ble. Reducing fatigue failures will save raw materials, process energy and end of life scrap; concerns of sustainability engi-neering.
Welding is an effective, efficient and economical joining process but these superior benefits do not come without a
disadvantage. The disadvantage is a reduction of fatigue strength at the weld area as compared to the fatigue strength of the original or base material [4-8]. Several factors precipitate the reduction in fatigue strength at the weld as compared to the base material’s fatigue strength. A major factor is the change in the material’s microstructure at the heat affected zone (HAZ) of the weld. The typical pearlite microstructure in the base materials is transformed into un-tempered martensite during the welding process. Welding heats the parent and weld materials above the austenite temperature of the steel. The weld rapid cools below the critical cooling rate transform-ing the austenite to un-tempered martinsite. Un-tempered martensite exhibits a high susceptibility to fatigue induced cracking decreasing the by fatigue resistance in the HAZ by 40% over the non HAZ perlitle microstructure in the base material [4].
Another factor reducing the fatigue strength in the HAZ is the surface condition of the weld. As a result of forming from molten metal, a very rough finish occurs at the weld material. This rough surface condition promotes initiation sites for fa-tigue cracks to form, thus reducing fatigue strength. Fatigue literature suggests treating this welded surface condition as a casted or forged surface roughness [4]. This increase in sur-
† This paper was recommended for publication in revised form by Associate EditorJooho Choi
1176 M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183
face roughness would reduce the base material’s fatigue strength at the weld by factor of 1.6 for typical tubing materi-als such as ASTM A513 and A500 [4].
Residual stress developed by the welding process is known to be a factor in fatigue strength reduction at the weld area. Residual stresses are frozen into the weld and near weld mate-rial as the result of non-uniform solidification of the weld due to various heat transfer rates occurring at the weld zone. This non-uniform solidification develops zones of tensile and com-pressive stresses [7, 8]. The regions of tensile residual stresses promote fatigue in a manner similar to the effect of mean ten-sile stresses under live load fatigue conditions [8, 9]. The con-trol of weld induced residual stresses are difficult and are lim-ited to joint design, pre-heating, post-heating and the welding process itself. Post-weld heat treatments and shot peening of welds can be conducted to counteract the effect of tensile re-sidual stresses on fatigue in the welds [10, 11], but these im-provement methods are costly and near impractical to incorpo-rate in large industrial tubing frame structures. Meaningful prediction of the magnitudes of residual weld stresses in struc-tural designs under various fabrication conditions in manufac-turing would be also difficult to determine at best. Thus, an exact effect on fatigue strength reduction due to residual stresses would be problematical in a real structure. The practi-cal method to consider the strength reduction effects of resid-ual stresses would be the use of published empirical welded fatigue strengths which inherently has the effects of residual stresses at the weld incorporated. Allowable weld fatigue strengths are published by several governing organizations such as the America Institute of Steel Construction (AISC) and American Society of Metals (ASM).
Fillet and J-groove welds are typically implemented in tu-bular frame structures. Fatigue reduction factors due to metal-lurgical and stress concentration effects in fillet welds report-edly range from 1.5 at the toe of a fillet weld to 2.7 at the end parallel fillet weld [4]. Multiplying the surface and fatigue reduction factors discussed above, it can be seen that the fa-tigue strength at the welds can be reduced by a factor of four as compared to the base material’s fatigue strength. This large reduction is supported by empirical testing of welded mild steels. The fatigue strength of parallel fillet welds at 1E6 cy-cles of tensile released loading was found to be 5.5 ksi (37.9 MPa), while the base material’s fatigue strength is 21 ksi (144.8 MPa) under the same loading condition, thus exhibiting a 3.8 fold reduction [7].
Fatigue strength for steels usually increases linearly with the steel’s ultimate strength until the ultimate strength reaches around 200 ksi (1,379 MPa). In contrast, the welded fatigue strength of steel is relatively independent of the ultimate strength of the base steel. The American Institute of Steel Construction stress allowable for the fatigue strength of fillet welds are equal for structural grades of steel regardless of ultimate strength [12]. Empirical fatigue strengths for butt welded 4130 steel were found to be in the range from 37 ksi (225.1 MPa) to 39 ksi (268.9 MPa) while the corresponding
ultimate strengths ranged from 113 ksi (779.1 MPa) to 172 ksi (1,186 MPa) based on the material’s heat treat condition [7].
With the resultant welded fatigue strength of steel relatively constant, the geometry of the frame connection is the only significant design parameter the designer can control to sig-nificantly influence the fatigue life. The implementation of connection designs which promote more efficient load trans-fers are required to produce increased fatigue resistant. A more efficient frame connection would be identified by a con-nection exhibiting lower stress magnitudes on a weight basis to normalize the effect of material usage differences in the connection designs. Even a modest decrease in stress levels can produce significant benefits in fatigue life. For example, a 25% reduction in stress level, results in a 225% increase in fatigue life for a typical welded tubing material [4, 5].
A review of the structural design of agriculture and con-struction equipment frames yields that a large amount of this equipment is designed with square and rectangular tubing. The most common method of joining the tubing at intersec-tions of these types of structures is by welding and use of an-cillary structural tie plates as shown in Fig. 1 as an example of agricultural implement. The use of tie plates allows for con-tinuous members to be used through the intersection point of the frame structure with some level of connectivity. Typical designs of continuous member connections are shown in Figs. 2-4. These connections, however, produce an unbalanced connection as the tubing centroids only lie within one plane of symmetry. This unbalanced design of welded tubular frames appears ad hoc as unbalanced frames would be expected to generate inefficient load transfer and thus poor fatigue per-formance. In contrast, as diagrammed in Figs. 5 and 6, the implementation of non-continuous members would allow the frame intersection connection to be balance as the centroids of the tubing members lie in two planes of symmetry. The pur-pose of this study is to examine and compare the fatigue resis-tance of tubing connections by finite element analysis method, employing continuous and non-continuous members through frame intersections.
Fig. 1. Agricultural implement utilizing the rectangular tubing welded and tie plates as supports.
M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183 1177
2. Methodology
Five different connection designs of square tubing at a frame intersection were examined for stress levels and fatigue resistance when imposed with an identical loading condition. The first three connection designs were observed to be im-plemented into agricultural frame structures incorporating
continuous members through the intersection at the expense of structural efficiency by offsetting the connection member’s centroids as shown in Figs. 2-4. Two connection designs in-corporating alignment the connecting member’s centroids at the expense of increase manufacturing cost by using non-continuous members were equally compared for fatigue resis-tance as shown in Figs. 5 and 6.
The size of rectangular tubing examined in this paper was a 6 × 6 × 0.25 inch (152.4 × 152.4 × 6.3 mm) square tube, typical of the stronger members in these types of the larger frame structures. The material type examined was ASTM A500 grade C, a structural grade of tubing with an ultimate strength of 62 ksi (427.5 MPa), yield strength of 50 ksi (345 MPa) and an elongation of fracture of 21%. Joining of tubing of this size is done by partial penetration fillet and J welds. A compatible in strength weld material would be ER70S-6 weld-ing wire possessing an ultimate strength of 75 ksi (517 MPa), yield strength of 63 ksi (434 MPa) with a fracture elongation of 28%.
Fig. 2. Basic continous member framing connection design.
Fig. 3. Half-tie plate continuous member framing connection design.
Fig. 4. Full-tie plate continuous member framing connection design.
Fig. 5. Non-continuous member framing connection design with con-tinuous torsional member (CT).
Fig. 6. Non-continuous member framing connection design with non-continuous torsional member (NCT).
1178 M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183
The torsional load developed on the transverse member represents the main loading from the soil. In a plow or tillage implement, the disk or tine drags through the soil. The soil imparts a drag force Fsoil on the tine or disk. This load is transmitted through the attachment feature connecting the tine or disk with the transverse member. The transverse member carries this torque load developed by the tine soil load Fsoil times the distance L from the soil bed to the centerline of the transverse member. This has been diagrammed on figure one to explain the load path. To simplify the model, the moment L×Fsoil was modeled as a couple at the end of the transverse members to study the welded connection efficiencies.
To load the joint, a 16.8 kip-inches (1,898 N-m) torque was applied to the transverse tube of the connection as a force couple, 18 inches (457.2 mm) away from the nearest welded area of the frame connection. The torsional load transfers into the longitudinal tube as a bending moment through the welds of the connection. This loading path scenario is typical of soil loading the tines of agricultural equipment or the blades of construction equipment. For the purpose of the analysis, the 16.8 kip-inches loading is a reversing load providing a con-stant amplitude fatigue loading with zero mean stress. The basic continuous member framing connection and loading scenario described above is shown in Fig. 2.
To compare the fatigue merit of the various framing con-nection designs, Finite Element Analyses (FEA) were con-ducted to determine stress levels that were required for each connection design to transfer the 16.8 kip-inches (1,898 N-m) of torque into the longitudinal. The goal of the FEA analyses was to provide relative measurements between the designs for fatigue resistance and not absolute fatigue lives. Thus, mesh refinement and convergence effects were not incorporated in this study, as each connection design was directly ranked against each negating these effects. However, as in any final design analysis using FEA, convergence and mesh studies should be considered.
Each design was meshed with 8-node 24 DOF solid brick elements exhibiting a uniform mesh density of 0.5 inches (12.7 mm). Each design was given identical boundary condi-tions as the longitudinal tube exhibited boundary conditions of a fixed-fixed beam as the connection design is under study and not the entire implement. The length of each beam in-volved in the connection was such that the Saint Venant ef-fects of the boundary conditions and torsional loading were attenuated at the weld connection area. The finite element code used in the analysis was ALGOR, a displacement based FEA typical of a design office for a medium sized manufac-turer and is quality certified by the Nuclear Regulatory Com-mission for use in this industry [14].
The J welds were modeled into each design with both 6-node 18 DOF and 8-node 24 DOF solid brick elements. Fillet welds were modeled with weld modeling feature called WELD in ALGOR which bonds the nodes along the edges of adjoining surfaces with multi-point constraint (MPC) equa-tions to simulate the fillet weld. Remaining nodes on the sur-
faces between the edges were free to translate, thus the load must be transferred by the multi-point constraint equation producing the stress concentration effect of the weld in the base material. Use of MPC equations to simulate fillet welds in FEA models is an accepted analysis methodology.
The efficiency of the frame connection was determined by examining the predicted fatigue life of the connection based on a pure reversal of the maximum stress level observed in each design due to the 16.8 kip-inches (1,898 N-m) torsional load. The predicted fatigue life was based on the empirical fatigue strength of fillet welds which accounts for the strength reduction effects due to HAZ, surface finish, stress concentra-tion and residual stress. This fillet fatigue weld empirical strength relation was for reverse loading with a zero mean stress, given by Ref. [8] as diagramed in Fig. 7:
8
3.3f
7.3973 10N=
S (1)
where N is the predicted fatigue life in cycles of reversed load-ing of the frame connection design, and Sf is the maximum stress (in ksi) observed in the weld zone of the connection from the FEA analysis. The constant coefficient in Eq. (1) changes to 4.33×1011 for the stress in SI unit (in MPa). The S-N curve from Eq. (1) did not exhibit an endurance limit or knee at 1E6 cycles as shown in Fig. 7 which is typical of welded ferrous materials. However, data points for Eq. (1) were taken to 1E8 cycles. Von-Mises stress was used as the method to compute the maximum stress as it is the accepted method of analyzing for both uni-axial stress and in-phase multi-axial stress conditions in the fatigue analysis of ductile materials such as A500 tubing [4, 7, 9, 10, 13]. Using Von-Mises stresses allows the stress magnitude to be directly com-pared to the fatigue strength value. From Eq. (1), the fatigue life N of each connection design was ranked and assessed for efficiency by examining the number of loading cycle the con-nection was predicted to endure.
For comparison to the empirical fatigue strength from Eq. (1), the theoretical fatigue strengths at the welds were com-
Fig. 7. S-N curves and test results for specimens containing partial penetration fillet welds for narrow-band random loading at zero mean stress [8].
M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183 1179
puted analytically from knowledge of ultimate strength of the base materials [4]. The corrected theoretical endurance limit Se is calculated by:
e a b c d e f eS k k k k k k S′= (2)
where S'e is the uncorrected endurance limit of the material based on the material’s ultimate strength. For 50% confidence level, this uncorrected endurance limit for steel is given by the minimum of 50% of the material’s ultimate strength Sut or 100 ksi (689.5 MPa):
(0.5 ,100 (689.5 )) .e utS min S ksi MPa′ = (3)
The uncorrected endurance limit S'e is corrected by several
correction factors which consider surface finish ka, size factor kb, loading conditions kc, temperature effects kd, reliability factor ke and stress concentration factor kf. For the given con-ditions of the materials examined in this study, the theoretical endurance limit is calculated as:
1
0.32364
521.873fS
N
−
⎛ ⎞= ⎜ ⎟⎝ ⎠
(4)
where N is the predicted fatigue life in cycles of reversed load-ing of the frame connection design, and Sf is the maximum alternating stress (in ksi) observed in the weld zone of the connection from the FEA analysis. The denominator in Eq. (4) changes to 3,598.2 for stress in MPa. The S-N curve from Eq. (4) exhibits an endurance limit or knee at 1E6 cycles at stress level of less than endurance limit stress; however data points for Eq. (4) are taken to 1E8 in this study to show the differ-ence between each design as welded ferrous materials do not exhibit a knee [4, 8, 15]. Computation of the theoretical fa-tigue strength can be found in the appendix.
3. Results and discussion
3.1 Comparison of tubular frame connection designs
3.1.1 Basic continuous member framing connection design
Fig. 2 presents the basic continuous member frame connec-tion design. The top flange of transverse tube is welded to bottom flange of longitudinal tube forming four 6 inches (152.4 mm) long J-groove welds. The weight of the material involved at the connection was measured at 19.52 lbf (8.85 kg). This frame connection design was the basis to which the other four connections designs will be compared to for fatigue improvement.
3.1.2 Half-tie plate continuous member framing connection
design
Fig. 3 presents the half-tie plate design with intent to lower stress levels in the weld area by the addition of two tie plates.
The top flange of transverse tube is welded to the bottom flange of longitudinal tube forming four 6 inches (15.2 mm) of J-groove welds. In addition, two plates 0.25 inches (6.3 mm) in thickness were added in symmetry to connect the longitudi-nal and transverse tubes in order to assist in transferring loads from the transverse tube into the longitudinal tube. The plates extend to the neutral axes of each tubing member in the con-nection. Full welding of the plates to the beams was modeled. The weight of the material involved at the connection of this design was 25.34 lbf (11.47 kg).
3.1.3 Full-tie plate continuous member framing connection
design
Fig. 4 presents the full-tie plate design to lower stress levels even further. The top flange of transverse tube was welded to bottom area of longitudinal tube forming four 6 inch long J-groove welds. Again, two plates 0.25 inches (6.3 mm) in thickness are added in symmetry to connect the longitudinal and transverse tubes in order to assist in transferring loads from the transverse tube into the longitudinal tube; however, these plates extend around the transverse tube and up to the top flange of the longitudinal tube. Full welding of the plates on the beam was modeled. The weight of the material in-volved at the full-tie plate connection design was 32.18 lbf (14.71 kg).
3.1.4 Non-continuous framing connection design with con-
tinuous torsional member (CT)
Fig. 5 presents a non-continuous member design. The hori-zontal tube which is the bending member is sectioned and welded flange to flange to the transverse member, which is loaded by torsion. This allows the centroids of the connection members to lie within the same geometric plane and promote load transfer efficiency. The transverse member remains a continuous element through the framing connection. Material usage in this connection is efficient as less of the 6” × 6” tubing material is required to make the connection. As the tubes’ flanges meet flush for welding, the need for tie plates is eliminated. Full fillet welds were modeled running down the tube web while J-groove welds tied the tube flanges on the connecting members. The weight of the material involved at the CT connection design was 9.76 lbf (4.42 kg). This connec-tion was the most economical design in terms of material us-age.
3.1.5 Non-continuous member framing connection design
with non-continuous torsional member (NCT) Fig. 6 presents the intersected connection design with non-
continuous torsional member design. This connection design is equivalent with the above CT design with the exception that the torque is inputted through the transverse member which non-continuous while the bending member is continuous through the frame connection. This connection would exhibit the same weight of material in the connection as the CT de-
1180 M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183
sign weighing 9.76 lbf (4.42 kg).
3.2 Comparison of fatigue resistance of connection designs
FEA analyses were conducted the above five connection designs to evaluate the efficiency of each design. A design with lower stress levels in the weld area would exhibit a greater fatigue life or fatigue resistance.
3.2.1 Basic continuous member framing connection design
Fig. 2 diagrams the base connection design while Fig. 8 presents the stress levels of the connection due to the torsional input load. A peak stress of 17.630 ksi (121.5 MPa) was ob-served in the weld area located in the corner radii of the tor-sional member. Using Eq. (1) with an alternating stress Sf equal to 17.630 ksi (121.5 MPa), the predicted fatigue life N of the base connection design would be 5.707E4 cycles based on the empirical fatigue strength of Eq. (1) and 3.721E4 cycles based on the theoretical fatigue strength based on Eq. (4).
3.2.2 Half-tie plate continuous member framing connection
design
Fig. 3 diagrams the mid-plate connection design while Fig. 9 illustrates the stress levels in the connection. A peak stress of 6.961 ksi (48.0 MPa) was found in a weld area. This peak stress was located at the toe of the tie plate on the inside wall of the torsional tube. The predicted fatigue life N of the base connection design would be 1.225E6 cycles based on the em-pirical fatigue strength of Eq. (1) and 6.878E5 cycles based on the theoretical fatigue strength based on Eq. (4).
3.2.3 Full-tie plate continuous member framing connection
design
Fig. 4 illustrates the full-tie plate connection design. Fig. 10 displays the stress levels of the connection. A peak stress of 3.907 ksi (26.9 MPa) was found in a weld area. This stress was located at the corner radii of the torsion tube and tie plate. The predicted fatigue life N of the base connection design would be 8.241E6 cycles based on the empirical fatigue strength of Eq. (1) and 4.214E6 cycles based on the extended theoretical fatigue strength based on Eq. (4).
3.2.4 Non-continuous member framing connection design
with continuous torsional member (CT)
Fig. 5 diagrams the CT connection design while Fig. 11 shows the stress levels in the connection due to the 16.8 kips-inch (1898 N-m) torsional load. A peak stress of 2.160 ksi (14.9 MPa) was found in a weld area of this design located at the top midline of the longitudinal tube. The predicted fatigue life N of the base connection design would be 5.826E7 cycles based on the empirical fatigue strength of Eq. (1) and 2.708E7 cycles based on the extended theoretical fatigue strength based on Eq. (4).
Fig. 8. Von Mises stress in basic continuous member framing connec-tion design.
Fig. 9. Von Mises stress in half-tie Plate continuous member framingconnection design.
Fig. 10. Von Mises stress in full-tie plate continuous member framing connection design.
M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183 1181
3.2.5 Non-continuous member framing connection design with non-continuous torsional member (NCT)
Fig. 6 diagrams the NCT connection design. Fig. 12 shows the stress levels of the connection. A peak stress of 3.68 ksi (26.7 MPa) was found in a weld area of this design. This peak stress was located at the corner of the transverse tube at the weld. The predicted fatigue life N of the base connection de-sign would be 1.003E7 cycles based on the empirical fatigue strength of Eq. (1) and 5.081E6 cycles based on the extended theoretical fatigue strength based on Eq. (4).
3.3 Comparative results
Fig. 13 presents the fatigue life N of the five welded fram-ing connection designs. As seen, the geometry of connection design has a significant impact on the fatigue resistance of the connection. Both of the non-continuous member designs are predicted to perform significantly better than the three indus-try-used continuous member welded frame connection designs
of Figs. 2-4. The increase in fatigue resistance can be easily understood by examine the stress levels in various connection designs for balance and symmetry. The non-continuous de-signs are balanced allowing stresses to flow in both the top and bottom fibers of each framing member through the frame connection. This results in reduced stress concentrations and lower stress levels producing the increased fatigue resistance which is vital in welded connections. The CT non-continuous design of Fig. 5 was superior to the other four designs. The CT design exhibited 1000 fold increase fatigue resistance over the basic continuous member design of Figs. 2 and 7 fold in-creases in fatigue resistance of the best performing continuous member design of Fig. 4. The CT design, Fig. 5 which incor-porates a continuous torsion member through the framing connection was 5.8 fold superior to NCT design which uses a non-continuous torsion member. This can be understood as the CT design’s continuous torsional member has four webs to carry the torsional load into the longitudinal member while the NCT design only effectively uses two webs to carry torsion into the bending member. Thus, in welded framing connec-tions, torsional carrying members should be continuous through the connection while the bending member is the non-continuous member.
Fig. 14 presents the fatigue resistance of the framing con-nection designs when considering the weight of the material involved in making the connection. On a weight basis, the CT design is even further superior to the other connection designs. The CT design which is the lightest of the designs was nearly 24 fold superior in weight basis fatigue resistance over the heaviest full-tie plate design. Table 1 identifies the peak stress, location of the peak stress, whether it occurs in the parent or weld material and the largest stress magnitude found in the weld area used to determine fatigue life.
4. Conclusion
Five designs of framing connections of rectangular tubing which are used in the structural frames of construction and agricultural equipment were examined for their fatigue resis-tance to help resolve any issues concerning the strength of
Fig. 11. Von Mises stress in CT connection design torque input from continuous member.
Fig. 12. Von Mises stress in NCT connection design torque input from non-continuous member.
1182 M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183
welded continuous versus non-continuous connections. Each of these different design connections were observed in current framing designs in the agricultural industry. The designs were evaluated using finite element analysis to predict fatigue life under the same loading conditions. In general, the following results concluded from this study.
(1) The research conducted on the various tubing connec-tions designs identified that a simple CT connection would exhibit a fatigue resistance that at least 4 fold superior while using less materials. The increase performance would circum-vent the increase preparation of fitting tubing for the CT con-nection design. These results can be extended to other users of welded tubing when making connections to increase fatigue life and decrease warranty costs.
(2) Life predictions were made with both empirical weld fa-tigue strengths and theoretical weld fatigue strengths. The theoretical method was found to be on the average 2 times more conservative on the number of fatigue cycles.
(3) Lastly, the finite element method was demonstrated as a common sense front-end design tool providing a great deal of insight to alternative competing designs with minimal tempo-ral and monetary costs even before any steel is cut and welded.
References
[1] J. Lapido, Fatigue failure and improvement in welded struc-ture (2004).
[2] J. Draper, Machine design, machine design.com: new ideas in fatigue analysis (2004).
[3] Size of US Market by Industry. http://www.bizstat.com/ marketsizes.htm. Retrieved (2009).
[4] J. Shigley, Mechanical engineering design, McGraw-Hill (1983).
[5] O. Blodgett, Design of weldments, the james lincoln arc welding foundation (1976).
[6] Proceedings of the conference of welded structures, Vol. I and II, The welding institute, Cambridge, England (1971).
[7] J. Collins, Failure of materials in mechanical design (1993). [8] N. E. Frost, Metal fatigue, Dover publications (1974). [9] R. Juvinall, Stress, strain and strength, McGraw-Hill (1963). [10] Anon, Fatigue strength of steel welds tripled, National
Institute of Metals, UK (1998). [11] J. Faubel, Design engineering, John Wiley & Sons (1981). [12] K. Kirthop, Weld detail fatigue improvement techniques
(1996). [13] G. Sines, Failure of materials under combined repeated
stresses superimposed with static stresses, Technical Note 3495, NACA (1955).
[14] Algor, Inc., Users manual, Pittsburg, PA (2008). [15] H. Boyer, Atlas of stress of fatigue curves, ASME (1986).
Appendix
A. The calculation of theoretical fatigue strength and life
ASTM A500 Grade, C Shape: Ultimate strength; 62utS ksi= Yield strength; 50ytS ksi= Maximum temperature; max 80T F= Cross-sectional area to calculate the area of 95% for
Equivalent shaft diameter; 2(36 30.25)A in= −
Equivalent diameter of shaft;
0.050.0766
Ad = , then:
1.937d in= Uncorrected endurance limit, Eq. (3);
(0.5 , 100 (689.5 )) 31e utS min S ksi MPa ksi′ = = Surface finish conditions for weld effected material;
In which: (T in F ), then: dk =1 Reliability factor for 50% or mean value; 1ek = Weld stress concentration factor of fillet weld; 1/ 2.7fk =
Table 1. Comparison of connection design for peak stress and maxi-mum stress in weld zones.
Connection Design Peak Stress Location Peak
Stress Max Stress at
Weld
Base Connection 17.63 ksi (121.5 MPa) Weld Material 17.63 ksi
(121.5 MPa)
Mid Gusset 6.96 ksi (48.0 MPa) Weld Material 6.96 ksi
(48.0 MPa)
Full Gusset 5.06 ksi (34.8 MPa) Parent Material 3.91 ksi
(26.9 MPa)
CT-Connection 3.58 ksi (24.7 MPa) Parent Material 2.16 ksi
(14.9 MPa)
NCT-Connection 4.75 ksi (32.7 MPa) Parent Material 3.68 ksi
(26.7 MPa)
Fig. 14. Fatigue resistance of welded rectangular tubing frame connec-tion per lbf of material in connection.
M. L. McCoy et al. / Journal of Mechanical Science and Technology 25 (5) (2011) 1175~1183 1183
∴ Corrected endurance limit, Eq. (2); 6.178e a b c d e f eS k k k k k k S ksi′= =
Fatigue strength fraction at 1000 cycles; 0.9f = 1000 cycles life strength; .m utS f S= , 55.8mS ksi= S-N curve equation;
log( ) .log( ) logfS b N a= + ,
in which: 2
503.988m
e
Sa ksiS
= = , 1 log( ) 0.318593
m
e
SbS
= − = −
Alternating stress in case five, non-continuous member framing connection design with non-continuous torsional member (NCT); 3.681a ksiσ =
Mean stress; 0.0m ksiσ = Equivalent reversed stress which is less than Endurance
limit;
.3.681a yt
ECR ayt m
Sksi
Sσ
σ σσ
= = =−
So according to the theoretical equation, the structure has the infinite life but according to the extension of Eq. (4) to 1E8 cycle, N is:
1b
ECRNa
σ⎛ ⎞= ⎜ ⎟⎝ ⎠
; 65.081 10N = × , which is finite cyclic life
from Eq. (4) for fillet weld fatigue life From Eq. (1) and Fig. 7, the welded structure has the infi-
nite life of: 8
3.3
(7.3973) 10
f
NS
×= ; 71.003 10N = ×
Mike McCoy is a practicing engineer with twenty-five years experience spe-cializing in product development for the transportation, aerospace and engineer-ing consulting industries. His current position is a Senior Technical Fellow for Electromech Technologies developing flight controls. He has held other posi-
tions with the Boeing Company and Spirit Aerosystems. He also is an adjunct professor of mechanical engineering at Wichita State University. Dr. McCoy has multiple patents and has been of author of several journals. Dr. McCoy holds a PhD in mechanical engineering and a MBA, both from Wich-ita State University and is a Licensed Professional Engineer.
Rasoul Moradi is a PhD candidate in mechanical engineering at Wichita State University, Wichita, KS, USA started on Spring 2009. His research interests include impact and crash dynamics, automotive and aviation crashworthi-ness, and injury biomechanics of occu-pants. He received his BSc (1997) and
MSc (2000) degrees in mechanical engineering from Univer-sity of Tehran, Iran. He has worked as a chief engineer of vehicle dynamics, vehicle passive safety, and homologation department of ITRAC, IKCO, Iran for about 10 years and has served as a type approval consultant for several vehicle manu-facturers in Iran.
Hamid Lankarani is a professor of mechanical engineering and a senior fellow of the National Institute for Avia-tion Research, at Wichita State Univer-sity. He is one of the world’s leading researchers and educators in the field of impact dynamics, automotive and air-craft crashworthiness, occupant protec-
tion, and injury biomechanics. Dr. Lankarani has directed over 250 graduate student MS theses and PhD dissertations, and has been the author of over 300 articles in journals, book chapters and conference proceedings. Dr. Lankarani has served as a Technical Editor or a member of Editorial Board for several international journals, and is an ASME fellow.
