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1. Literature review

1.1 Introduction

This paper explains tests on bolt connections with cold formed steels. Different types of stainless steel are considered as test specimens for example austenite stainless steel, lean duplex stainless steel etc, and their material properties determined by tensile tests. Both single and double share connections with bolts of different diameters and arrangements are performed and the main failure modes observed in the connection tests. A comparison of nominal and test strengths is done and calculations performed using European codes, Australian standards, and American specifications. Comparison of failure modes observed from the experiments and those predicted shows that nominal strengths foreseen by the specifications are conservative. Numerical simulation of tests also ensures analysis of force distribution between bolts. Information on tests of similar connections is obtained from literature and when comparison is done there is great similarity with the experimental data.

1.2 Mechanical fasteners

According to Toma et al (1993), mechanical fasteners have different applications. Threaded fasteners such as bolts with nuts are assembled through materials to be joined, in preformed holes. Bolts threaded close to the head are usually used for thin materials and bolts have smaller diameters. The 8.8 and 10.9 are the most preferred class for use in thin walled elements. Furthermore, screws can be used effectively when fastening joints in the roof and steel framings and wall panels. Improvements on load bearing ability can be done when screws are combined with washers. There are many different types of screws and bolts and their use entirely depends on types of joints and strength properties required.

1.3 Design considerations

The current design specifications for bolted steel connections have a set of rules according to New Zealand standards, American specifications, and the European codes. Because the experimental work of steel bolted connections had many limitations, these design rules are mainly applicable to carbon steels. Researches on steel bolted connections were done by different researchers for instance Zadanfarrokh, Hancock, and Rogers etc. They investigated structural behaviours of austenite steels connected by bolts and noted that there existed a difference in stress and strain behaviours. Their conclusion was that the shear strength of a steel sheet depended on sheet thickness, tensile strength and the distance between the hole centre and the edge of the adjacent hole.

2. Material strengths

Generally, the attachment between the plates and the bolts are a result of improper establishments of perfections. The ratios of strengths between bolts and high speed steel plates when the connection is of high speed steels is different compared to that made of mild steel. With the mild steel, the material of the bolt is stronger than material for the plate. However, in case of high speed steel connections, the strength of the plate is same to that of the bolt material. It is therefore recommended to take into consideration the local ductility of the plate and shear capacity of the bolt during the design of high speed steel connections.

2.1 Types of failure modes

High strength steel and bearing bolts are used in this paper to analyze the behaviour of bolt connection with cold-formed steel. The contacts between the plates and the bolts together with the resistance of shear by the bolt ensure the transfer of loading between the steel plates. There exist more stresses on the bolts and plates making it very difficult to avoid the stress concentration. The clearance on the bolt hole also causes initial slip, a major character of connection of the bearing type. Experiments have shown that typical failures occur in the bolt connection with cold-formed steel as can be illustrated below.

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In bolt connections with cold — formed steel, a variety of failures normally occur. This includes but is not limited to; sheet tearing in the net section, bolt shearing, pilling of material in front of the bolt, and shearing of sheet longitudinally along parallel lines. However, a joint may experience different types of failures. Bolt rotations together with sheet material dishing often cause the sheet tearing leading to failure.

2.1.1 Shear strength method

The nominal shear strength on each bolt can be expressed according to the equation shown below.

PNo = T E Fu where;

PNo refers to nominal shear strength in lbs (per bolt)

E refers to distance from the hole centre to nearest edge of the adjacent in inches

T refers to thickness of sheet in inches (uncoated)

Fu refers to tensile strength of sheet in psi

2.1.2 Bearing strength method

Another test method that could be used is the bearing strength method especially in cases where there exist large distances in bolted connections. The design method for bearing strength in use today is focused on research that was conducted by Wallace and LaBoube (2001 — 2002) that led to development of Waterloo method, mainly used for connections on standard holes that do not have washers.

The nominal shear strength on each bolt can is expressed as shown below.

PNb = C D T Fu where;

PNb refers to nominal bearing strength of each bolt in lbf

C refers to bearing factor (value obtained from the first table)

D refers to nominal bolt diameter in inches

T refers
to sheet thickness inches (uncoated)

Fu refers to tensile strength of sheet in psi

Table 1: Bearing factor C, for waterloo method

Ratio of diameter of fastener to thickness of member, D/T

Bearing factor, C

D/T less than 10

10 less or equal to D/T less or equal to 16.5

22.5 / (D/T)

D/T greater than 16.5

The (NAS 2007) method for bearing strength is given by the equation shown below. It uses a linear equation for the bearing factor. Again, it employs the use of modification factor to take in to consideration the use of types of connections and washers.

PNb = Mf C D T Fu where

PNb refers to nominal bearing strength of each bolt in lbf

Mf refers to modification factor

C refers bearing factor (value obtained from the second table)

D refers to nominal bolt diameter in inches

T refers to sheet thickness inches (uncoated)

Fu refers to tensile strength of sheet in psi

Table 2: Bearing factor C, for NAS 2007 method

Ratio of diameter of fastener to thickness of member, D/T

Bearing factor, C

D/T less than 10

10 less or equal to D/T less or equal to 22

4 – 0.1 (D/T)

D/T greater than 22

2.2 Desirable qualities of steel

The stainless steel has desirable qualities for example resistance to corrosion and fire, good in appearance, high strength and durability etc that can be easily exploited in various applications. A cold formed connection on steel structures has many types but the most common is bolted connections. These steel structures are used in constructions in commercial and residential buildings more so because they are light in weight. This study involved specimens fabricated from austenite stainless steels and lean duplex stainless steels. Lean duplex stainless steel has a high strength and a nominal yield stress of approximately 450 MPa. No tests have been carried on this material and the design specifications do not include their design. The tensile coupon test is carried on these materials and focus majored on tests strengths and nominal strengths. The size, number and arrangement of bolts are varied and both single and double share bolted connections conducted on the steels and final comparison done. It involved installation and tightening of bolts in order to obtain the desired performance of connections under the conditions.

2.3 Connections for thin – walled structures

Thin walled structures can be joined by a variety of methods. According to Davies (1991), connections in thin walled structures are characterized by little plate stiffness as compared to thicker connections of greater than 3 mm. Many design procedures have been developed for cold formed connections although the procedures are different for thicker materials. Connections for thin — walled elements are mainly used for connecting steel sheets on to support structures, assembling linear connections, and sheets interconnections. According to Yu (2000) and Toma et al. (1993) three types of connections mainly used on thin walled structures include the use of mechanical fasteners, adhesive bonding, and use of welds.

3. Theoretical analysis

3.1 Shear lag effect

The load of one element to the other is transmitted by a bolted connection (Johnson and Salmon, 1996). The transfer of load occurs through the bolt hence stresses are strangle close to the bolt and increases the shear lag effect, preventing a complete loading of the transversal section especially when there is no connection with its elements. There is increase in tension failure of the sheet hence reduced ability to those members that are subjected to tension, a phenomenon considered in the codes through reduction in net area.

Studies by Munse and Chesson (1963) revealed more about the shear lag, according to AISC/93 specification. They argued that length and eccentricity are the main factors that affect effective net section. The structural behaviours of these connections always show dissimilarity in connection to hot rolled shapes. This is due to the fact that the smaller the thickness of the joined elements, the more their chances of failure. However, the research conducted by LaBoube & Yu (1998) and Holcomb et al. (1995) demonstrated that the formulation shown by the AISC/93 specification is never applies to cold formed shapes. The results of the studies led to the development of equations that can be useful to find out the effective net area of shapes connected by more bolts in the line of power.

3.2 Equations for finding U factor

  1. In case of channel members having more bolts in the line of load.

U = 1.00 — 0.36 * X / L less or equals 0.9, with U greater or equals 0.50

  1. In case of angle members having more bolts in the line of force.

U = 1.00 — 1.20 * X / L less or equals 0.9 with U greater or equals 0.40

  1. When all there is connection to all elements.

X refers to as the eccentricity of attachment

L refers to as length of the attachment

The same procedures were adopted by the Brazilian code to develop the equation of the U factor to be equivalent to; U = 2.S (D/S) less or equals to 1.00

This implies that The U factor entirely depends on the ratio (D/S).

3.3 Tests for material properties

This analysis involved evaluation of the connections with the equations in order to calculate the U factor. Some factors such as friction between the parts are not factored in calculations and the bolts fitted in tight conditions. It is also assumed that the bolts in the connection are loaded equally. High strength bolts are used without washers to reduce chances of shear failure. The bolts are set at a distance equals to 3D between hole centres and position of the hole to the edge.

Zinc coated steel is used to prepare the samples and the nominal thickness maintained at 1.50 mm and carbon steel at 3.70 mm. Punching of holes is done at 15.00 mm and 17.00 mm for the 12.5 mm and 16.5 mm bolts respectively. The test samples with thickness of 1.50 mm is prepared with 15.00 mm holes but the samples with thickness of 3.70 mm had holes of diameter 17.00 mm. When tensile tests are carried out on mechanical properties of the materials, the following result is obtained.

Tn in (mm)

Fy in (MPa)

Fu in (MPa)

Carbon — steel (SAE 1008)

Zinc — coated steel (ZAR 345)

More than one hundred samples are tested to represent different shapes and testing done in duplicate and the number of bolts varied. A servo — hydraulic instron machine is used to investigate the experiment results with a tension load being applied to displacement of the machines piston at rate of two millimetres per minute. Both extension and loads readings are automatically taken after every second. The extension curves are then plotted on a graph from the data collected.

4. Comparison of failures

If experimental values calculated from the equation U = PU / (AN / FU) and theoretical values obtained from the Brazilian Code and AISI/96 of the U factor are compared, there occur some differences. For the connections that had all bolts in one section, the procedure of equivalent sheet is taken in to consideration despite the fact that failure mode is piling up of steel sheet. Every test shows bearing as a failure mode possibly because of more concentration of stress at such points. Theoretical bearing strengths are also compared to experimental results. When the graphs are plotted, it is evident that theoretical value is less than the ultimate load. This means that the procedure of equivalent sheet provides a good evaluation of capacity of members in areas of connection even if the mode of failure is bearing.

If more bolts are placed in the line of force, the mode of failure is tearing in the net section. This means that there is a tension failure on the sheet due to strains in front of the bolts. But for the angles, it is noted that theoretical values are slightly higher than those from experiment but the difference in value tend to decrease with the increase in the value of X/L. In case of the channels, theoretical values are significantly higher than experimental values but when only the web connections are made, bearing is the mode of failure.

4.1 Comparison of strengths

The strengths of tests are compared with nominal strengths predicted by the various specifications. There is an indication that nominal strengths envisaged by the European specifications are less conservative compared to those of Australian and American specifications.

The test samples with all bolts in one section experiences piling up of the sheet in front of the bolts and bearing as the mode of failures. There is no tearing of sheet in net section as witnessed in other cases. Theoretical values from the calculations are less than experimental values that are also scattered. This means that the AISI/96 procedure confirmed accurate from the analysis (Holcomb, B. et al. 1995 pg 23).

The equivalent sheet procedure used for the calculation of the U factor for cases where the bolts are in one section is presented by the Brazilian code. There is an agreement between theoretical and experimental results, an indication that the procedure used is good for evaluation of capacity of members in areas of connection (Kouhi J, and Kortesmaa M. 1990 pg 67).

If there is connection of all the elements, the theoretical value of one is more than the experimental value. It is therefore recommended that a value of U = 0.9 should be adopted for sheet thickness of up to 3.70 mm. more tests should be carried out to determine the limit thickness where the U factor can be considered to be equals to one.

In case of samples with more bolts in the line of force, tearing of sheet is witnessed as the major mode of failure but coupled with some bearing and tearing. Theoretical values obtained from the equation are higher than experimental values although the difference reduces as the value of X/L increases.

4.2 Conclusion

In conclusion, the AISI/96 and new Brazilian Code procedures, should further be analyzed and other sheet thickness and connection configurations be used to carry new tests for a better analysis and modification on terms used to obtain U factor.

5. Bibliography

Holcomb, B. et al. 1995. Tensile and bearing capacities of bolted connections. Summary Report. University of Missouri: Rolla.

Kouhi J, and Kortesmaa M. 1990. Strength tests on bolted connections using high strength steels as a base material. Espoo: Technical Research Centre of Finland.

Munse and Chesson 1963. Riveted and bolted joints: net section design. Journal of the Structural Division. pg. 107 — 126,

Salmon, G. and Johnson, E. 1996. Steel structures: design and behaviour (4th ed.). New York, Harper Collins Inc.

LaBoube, R., Wallace, J., and Schuster, R. 2001. Calibrations of Bolted Cold-Formed steel Connections in Bearing. Final Report, American Iron and Steel Institute. Washington, DC.

Dubina and Zaharia. 2000. Behaviour of cold — formed steel truss bolted joints. In: The 4th international workshop on connections in steel structures.