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Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignAbstract:A cantilever support constructed of a column and a beam both made up of ½” ANSI 1020 HRsteel are being joined. Three methods of attachment were deemed acceptable after analysiscalculations were preformed. A welded connection was the first design. It is calculated for two6” long 3/16” fillet welds to be sufficient to bear the 6000 lb load in the specified weldingpattern. A bolted connection was the next option, this was found to be acceptable if two 3/8 in -16 UNC Grade 7 bolts were used in a vertical pattern. The final method of adjoining the twosteel parts is by using an adhesive. It is found through calculations and research that a specialtymixture of EPON Resin 580005 is capable of bearing the applied load. The recommendedmethod of joining the cantilever to the beam is by using the welded connection. This willprovide the strongest joint with the highest factor of safety which is 3.33 with just a 3/16” filletweld size.Mechanical and Aerospace EngineeringDepartmentiNC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignIt is determined to use a 3/16” weld for the most cost efficient weld while still maintaining asufficient safety factor of 3.33. All calculations can be seen in more detail in Appendix C.Bolted Connection AnalysisThe design of the bolted connection is intended to bear the 6000 lb load that is applied, as shownin Figure 1, yet not use more than 4 bolts. As you can see in Figure 6, the chosen designimplemented two bolts in a vertical pattern. The location and pattern of the bolts was selected inorder for the centroid of the bolt pattern to be located as close as possible to the line of action ofthe applied force to decrease the formed moment, all the while still maintaining ample columnand cantilever support material around the bolt holes for added strength. A safety factor ofn s = 1.2 was used throughout all calculations.yxFigure 6: Cantilever design with Bolt PatternThe primary and secondary shear forces must be accounted in the value for total shear for byusing Equation 12 and Equation 13 found in Shigley 1 .As seen in Figure 7, the forces act perpendicular to each other, therefore the sum of them will usethe Pythagorean Theorem, Equation 14. Both bolts have the same force on them, so forces inboth bolts will be critical to the design of this joint.(12)(13)Mechanical and Aerospace EngineeringDepartment5NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignF’F’’F’F’’yxFigure 7: Cantilever Design with Component Bolt Forces Shown(14)The length of the bolts are determined from equation 8-13 and from an equation found in Table8-7(Shigley 1 ) and are listed as Equation 15 and Equation 16, respectively.To determine the minimum diameter for the bolt, the bearing and bending in the members arecalculated using Equation 17 and 18 from Shigley 1 , respectively.After a standard bolt size of 3/8” is decided upon, the following equations implement that sizebolt into the calculations to determine what grade of bolt is required to maintain an adequatesafety factor throughout the entire joint connection. The bearing in the bolts, Equation 19, andthe shear of the bolts, Equation 20, from Shigley 1 , are used to determine the minimum proofstrength of the bolts.The final design was made with the bolts being 3/8 in – 16 UNC Grade 7 with nuts tightened to30 ft-lb. This is determined by using the recommended bolt torque specifications listed inEngineer’s Handbook 3 . The listed torque for the chosen bolts is 44 ft-lb, but the 30 ft-lb willallow a safety factor of 1.47. By using SAE Grade 7 bolts, the proof strength of these boltsoutweighs the necessary strength, therefore the factor of safety in the bolts is greater than thespecified n s = 1.2 used throughout the problem. The actual factor of safety using SAE Grade 7bolts is n s =1.46. All calculations are shown in Appendix D.(15)(16)(17)(18)(19)(20)Mechanical and Aerospace EngineeringDepartment6NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignAdhesive Connection AnalysisIn a connection bonded with adhesive, one of the most important variables is choosing thecorrect adhesive. That will bond to the materials present in the joint and also that will hold up tothe applied amount of stress. Figure 8 shows how the adhesive is planned to be laid out. It is acircle with a 4.6” diameter.yxFigure 8: Cantilever Design with Adhesive PatternThere will be aspects of both direct shear and shear produced by the moment, which will act onthe adhesively bonded joint. The primary shear acts on the joint due to the force that is appliedand the secondary shear results from the moment that the load causes on the joint. To calculatethese components of shear, Equation 21 and Equation 22 are used from Shigley 1 .To combine these components of shear, in order to calculate the total stress that is acting on thejoint, refer to Figure 9.(21)(22)yxFigure 9: Cantilever Design with Components of Stress ShownMechanical and Aerospace EngineeringDepartment7NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignThe primary shear, τ’, acts in the downward direction over the entire area of adhesive while thesecondary shear, τ’’, acts only tangent to the circular pattern in a clockwise direction. Therefore,as you can see at the point at the right most edge of the adhesive circle in Figure 9, the shearstresses will be a maximum and can be added directly since the will be acting in the samedirection. From this figure Equation 23 can be derived.(23)The next task is finding the correct adhesive, that will bond to the ANSI 1020 HR steel of whichboth pieces of the joint are constructed and bear the amount of stress that will be applied due tothe shear stress of τ = 2653.77 psi that was calculated.The most effective adhesive that was found for this application was made by Hexion SpecialtyChemicals 2 . The highest factor of safety was desired since adhesives can be very sensitive tomany types of user error. The adhesive that was chosen for the application is a mixture. Itcontains 75 parts by weight (pbw) of EPON Resin 828, 25 pbw EPON Resin 580005, and 6 pbwDicyandiamide for curing purposes. This adhesive is to cure for 2 hours at 93 o C and then for 2hours at 150 o C. After this process, the adhesive is rated at 5,230 psi when in shear. Thisprovides a safety factor of 1.89.Detailed calculations are shown in Appendix E and specifications on the chosen adhesive arelocated in Appendix F.Conclusions and RecommendationsIn order to meet and exceed the required strength of the cantilever joint there are three feasiblesolutions. The weld is determined to be suitable to connect the joint with any fillet size between3/16” and 1/2” while using the E6012 electrode. The bolted connection is found to be sufficientby using two 3/8 in – 16 UNC Grade 7 bolts. This provides a factor of safety of 1.46. Theconnection will be stable as well with an adhesively bonded joint by using the specializedmixture of EPON Resin 580005. The adhesively bonded joint will have a 1.89 safety factor.After all things are taken into account the welded connection, with a 3/16” fillet weld size, isrecommended due to the highest factor of safety of 3.33.Mechanical and Aerospace EngineeringDepartment8NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignReferences1. Budynas, Richard G., and Nisbett, J. Keith. Shigley's Mechanical Engineering Design.New York: McGraw-Hill, 2011. Print.2. "Hexion.com - EPON Resin 58005." Hexion.com - Binding, Bonding and Coating withThermoset Resins. Sept. 2001. Web. 28 Sept. 2010..3. "Steel Bolt Torque Specifications Table - Engineer's Handbook." MechanicalEngineering Design Guide - Engineer's Handbook. 2006. Web. 18 Oct. 2010..Appendix A – ConstantsS ut = 55ksi (Table A-20, Shigley 1 )S y(mem) = 30 ksi (Table A-20, Shigley 1 )S T = 62 ksi (Table 9-3, Shigley 1 )S Y = 50 ksi (Table 9-3, Shigley 1 )S P = 55 ksi (Table 8-9, Shigley 1 )H = 21/64” (Table A-31, Shigley 1 )Appendix B – NomenclatureS ut – ultimate strength of base metalS y(mem) – yield strength of base metalS T – ultimate strength of weld metalS Y – yield strength of weld metalA – weld areah – height (size) of fillet weldb – length of weldc – length of weld– component of centroid– component of centroidJ – polar moment of inertiaτ – shear stressτ all – allowable shear stressM – momentr – radiusd – diametert – thickness of plateV – shear forcen s – factor of safetyS P – proof strength of steel boltL T – threaded length of boltL – total length of boltH – height of nutMechanical and Aerospace EngineeringDepartment9NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignAppendix C – Welded Joint CalculationsThe allowable shear stress is 12 ksi since it is the minimum τ max value.Mechanical and Aerospace EngineeringDepartment10NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignAppendix D – Bolted Joint CalculationsMechanical and Aerospace EngineeringDepartment11NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignBolts 1.5” long were chosen so that the threaded length of the bolt would not be in shear.The minimum standard size bolt that is applicable in this base metal is 3/8”, therefore that sizewas chosen to minimize the size of the bolt.44100 psiMechanical and Aerospace EngineeringDepartment12NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignRefer to Table 8-9 (Shigley 1 ) to determine the SAE grade of bolt needed.Appendix E – Adhesively Bonded Joint CalculationsResearch was done in the internet to find an adhesive to bear this amount of shear stress. Moreinformation can be found in Appendix F for this adhesive.Mechanical and Aerospace EngineeringDepartment13NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignAppendix F – EPON Resin 580005 Technical Data Sheet (Hexion 2 )Re-issued September 2001EPON Resin 580005Product DescriptionEPON Resin 580005 is an elastomer modified epoxy functional adduct formed from thereaction of the diglycidyl ether of bisphenol A and a carboxyl terminated butadiene-acrylonitrileelastomer. Elastomer content is approximately 40% by weight. Primary use of EPON 58005 isthe modification of conventional epoxy systems to increase flexibility, adhesion properties andfatigue resistance.Application Areas/Suggested UsesHigh performance adhesives, featuring:BenefitsHigher peel and shear strengthsThermal shock resistanceGreater fatigue resistanceFatigue resistant composite structuresHigh elastomer content – convenient adjustment of elastomer contentCompatible with a wide range of liquid epoxy resinsImparts improved peel strength and fatigue resistance with minimal reduction of stiffnessand maximum operating temperatureSales SpecificationProperty Units Value Test Method/StandardEpoxide Equivalent Weight g/eq 325 – 375 ASTM D1652Viscosity at 25°C P 3,000 – 8,000 ASTM D2196Color Gardner 11 max. ASTM D1544AppearanceClear to SlightHazy LiquidMechanical and Aerospace EngineeringDepartment14NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignTypical PropertiesProperty Units Value Test Method/StandardDensity at 25°C lb/gal 9.0 ASTM D1475General InformationAs a result of a relatively high acrylonitrile content, EPON 580005 is compatible with mostepoxy resin types, including bisphenol F and novolac epoxies, within the typically used range ofconcentrations (

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignTable 1 / Effect of EPON Resin 580005 concentration on properties of an epoxy systemMethod Units A B C D EEPON Resin 58005 pbw --- 12.5 25 37.5 50EPON Resin 828 pbw 100 87.5 75 62.5 50EPIKURE Curing Agent3072pbw 35 33 30 29 27Handling Properties @25°CInitial viscosity cP 4,000 7,720 13,700 21,200 32,200Gel Time, 100 gram mass minutes 43 48 51 61 73Cure Schedule wk/°C 1/25 1/25 1/25 1/25 1/25Cured State Properties 1Tensile StrengthASTMD638Aluminum/Aluminum psi 2,000 2,060 2,760 4,020 3,960Steel/Steel psi 2,600 3,700 3,880 4,290 3,91090° Peel StrengthAluminum/Aluminum lbs/inch 2-3 4-6 10-12 14-16 20-22Hardness Shore D 86 85 84 81 801 Determined at 23 °C following one week cure at 25 °C.Being epoxy functional, EPON 580005 can be cured with converters commonly used inconventional epoxy systems. Due to its higher weight per epoxide, adjustment of curing agentlevel should normally coincide with incorporation of this modifier resin. Effect of EPON 580005incorporation on the properties of standard systems cured with a representative aliphatic amine,aromatic amine, and a catalytic curative is indicated by Table 2 data. The high viscosity ofEPON 58005 will normally necessitate that this resin be heated in order to facilitate pumping orblending operations. Figure 2 provides guidance as to the reduction in product viscosity resultingfrom increasing temperatures within the 75 - 190 °F range.Mechanical and Aerospace EngineeringDepartment16NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignTable 2 / Effect of EPON Resin 580005 on adhesive properties of various systemsMethod Units A B C 1 DEPON Resin 828 pbw 100 62.5 100 75EPON Resin 58005 pbw --- 37.5 --- 25EPIKURE Curing Agent3234pbw 13 11 --- ---Dicyandiamide pbw --- --- 6 6Cure Schedule wk/°C 1/25 1/25 2hrs/93 +2hrs/1502hrs/93 +2hrs/150Cured State Properties 2Tensile StrengthASTM D638Aluminum/Aluminum psi 1,520 3,270 2,530 4,150Steel/Steel psi 2,610 4,100 5,100 5,23090° Peel StrengthAluminum/Aluminum lbs/inch 0.5-1.0 5.0 --- ---Hardness Shore D 88 70 --- ---1 System modified with 2 phr Cab-O-Sil M-5 to retain suspension of dicyandiamide throughgelation. Cab-O-Sil is a registered trademark of Cabot Corporation.2 Determined at 23 °C. Systems A and B cured one week at 25 °C. Systems C and D cured twohours at 93 °C plus two hours at 150 °C.Mechanical and Aerospace EngineeringDepartment17NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignFigure 2 / EPON Resin 580005 Viscosity vs. TemperatureSafety, Storage & HandlingPlease refer to the MSDS for the most current Safety and Handling information.Please refer to the Hexion web site for Shelf Life and recommended Storage information.Exposure to these materials should be minimized and avoided, if feasible, through theobservance of proper precautions, use of appropriate engineering controls and proper personalprotective clothing and equipment, and adherence to proper handling procedures. None of thesematerials should be used, stored, or transported until the handling precautions andrecommendations as stated in the Material Safety Data Sheet (MSDS) for these and allother products being used are understood by all persons who will work with them.Questions and requests for information on Hexion Specialty Chemicals, Inc. ("Hexion") productsshould be directed to your Hexion sales representative, or the nearest Hexion sales office.Mechanical and Aerospace EngineeringDepartment18NC STATE UNIVERSITY

Cantilever Support DesignDavid Bumgarner9-28-10MAE 415 Mechanical DesignInformation and MSDSs on non-Hexion products should be obtained from the respectivemanufacturer.PackagingAvailable in bulk and drum quantities.Contact InformationFor product prices, availability, or order placement, call our toll-free customer service number at:1-877-859-2800For literature and technical assistance, visit our website at: www.hexion.com® and Licensed trademarks of Hexion Specialty Chemicals, Inc.DISCLAIMERThe information provided herein was believed by Hexion Specialty Chemicals (“Hexion”) to beaccurate at the time of preparation or prepared from sources believed to be reliable, but it is theresponsibility of the user to investigate and understand other pertinent sources of information, tocomply with all laws and procedures applicable to the safe handling and use of the product andto determine the suitability of the product for its intended use. All products supplied by Hexionare subject to Hexion’s terms and conditions of sale. HEXION MAKES NO WARRANTY,EXPRESS OR IMPLIED, CONCERNING THE PRODUCT OR THEMERCHANTABILITY OR FITNESS THEREOF FOR ANY PURPOSE ORCONCERNING THE ACCURACY OF ANY INFORMATION PROVIDED BY HEXION,except that the product shall conform to Hexion’s specifications. Nothing contained hereinconstitutes an offer for the sale of any product.Mechanical and Aerospace EngineeringDepartment19NC STATE UNIVERSITY