UNIVERSIDAD PERUANA UNIONFACULTAD DE INGENIERIA Y ARQUITECTURAESCUELA DE INGENIERA CIVIL

DETERMINACION DE PROPIEDADES DE ACERO A PARTIR DE LA CURVA ESFUERZO - DEFORMACIONTrabajo encargado en cumplimiento parcial del curso de Diseo en Acero y Madera

DOCENTE:Ing. Wilson Paredes Gmez.

Alumno:.Elvis Jhordy Mamani Uscamayta

Juliaca, 14 de septiembre del 20151. Se tiene datos de un ensayo en traccin de una varilla de 5/8" de calidad ASTM A615 Grado 60. Los datos locales, estn referidos a una longitud de 50 mm y los datos globales estn referidos a una longitud 200 mm. Se pide:

Determinar el esfuerzo de fluencia y la deformacin de fluencia. Determinar el mdulo de elasticidad. Determinar el esfuerzo ltimo. Determinar el porcentaje de elongacin o ductilidad por elongacin. Determinar el mdulo de resiliencia. Determinar el mdulo de tenacidad.

rea de una varilla de 5/8" = Av =

1.98Cm2

1.98E-04M2

Longitud inicial para datos locales = L= Longitud Inicial para datos globales = L =

50.00Mm

200.00Mm

Ahora tenemos la tabla de datos ya completos para graficar:

LVDTLVDTCargaDeform.Deform.Esfuerzo

GlobalLocalKNL/L, GlobalL/L, Local = Carga/Av

mmmm(Fuerza)(Adim.)(Adim.)MPa

0.0000000.4412870.4748470.5023170.5419870.5786070.6060770.6487970.7006770.7525570.7952870.8288570.8837870.9478771.1004671.2347371.3751171.5185571.6619871.7932071.9091772.0373472.1533172.2357172.3303172.3944072.4706972.5225772.5927672.6415970.0000000.0016480.0028680.0028680.0019530.0025630.0034790.0034790.0043940.0047000.0050050.0053100.0050050.0050050.0053100.0083620.0089720.0104980.0114130.0129390.0156860.0166010.0166010.0190430.0193480.0220950.0205690.0227050.0227050.0220950.0000001.6595541.8182342.0013342.1478342.3614542.5018342.6361142.8680343.1976343.3563343.5760543.8507144.1986144.9920745.9442146.8902547.7203348.5992349.78943410.55237411.54113412.43835413.31115414.01305414.75769415.17273415.88683516.13097416.6192540.0000000.0022060.0023740.0025120.0027100.0028930.0030300.0032440.0035030.0037630.0039760.0041440.0044190.0047390.0055020.0061740.0068760.0075930.0083100.0089660.0095460.0101870.0107670.0111790.0116520.0119720.0123530.0126130.0129640.0132080.0000000.0000330.0000570.0000570.0000390.0000510.0000700.0000700.0000880.0000940.0001000.0001060.0001000.0001000.0001060.0001670.0001790.0002100.0002280.0002590.0003140.0003320.0003320.0003810.0003870.0004420.0004110.0004540.0004540.0004420.008.389.1910.1110.8511.9312.6413.3214.4916.1616.9618.0719.4521.2125.2230.0334.8139.0043.4549.4653.3158.3162.8467.2570.8074.5676.6680.2681.5083.96

2.6721172.7148372.7545172.7941872.8460672.8613272.8796372.8918472.9101572.9284672.9742372.9742373.0017073.0291773.0718973.0932573.1054673.1268273.1390373.1542973.1909173.2427973.3099373.3618173.4167473.4594673.5235573.5876473.6181673.6334173.6669873.6975073.7371773.7799073.8226273.8653573.9233373.9721674.0454074.2010474.3933074.5672574.6557574.7320574.8266574.8815874.9304174.9761975.0402775.0769075.0952175.1104675.1409875.1745570.0242310.0239260.0242310.0251460.0254510.0260620.0257570.0263670.0263670.0260620.0260620.0281980.0291140.0275880.0275880.0285030.0278930.0288080.0288080.0294190.0294190.0315550.0306390.0321650.0312500.0330810.0346070.0346070.0349120.0355220.0364380.0364380.0367430.0373530.0382690.0382690.0385740.0410150.0401000.0431520.0474240.0480340.0498660.0510860.0510860.0520020.0526120.0532220.0550540.0550540.0553590.0556640.0559690.05657917.02819417.37609417.74841418.14513418.39539418.70055418.76769418.96911319.11559419.28039419.57337319.77477420.03113420.33631420.59265520.83679321.01989421.14197321.27013321.47155421.91101422.33215422.97301423.53455423.93737424.43787425.18859525.47547425.85999326.05529426.42151426.72669527.20885427.63001328.10607528.46007429.05823329.54041330.27283532.11609434.21569435.58289436.48009437.44445438.10973538.73841439.34875340.05065540.56335540.78919540.83191541.25915641.61925442.3028530.0133610.0135740.0137730.0139710.0142300.0143070.0143980.0144590.0145510.0146420.0148710.0148710.0150090.0151460.0153590.0154660.0155270.0156340.0156950.0157710.0159550.0162140.0165500.0168090.0170840.0172970.0176180.0179380.0180910.0181670.0183350.0184880.0186860.0189000.0191130.0193270.0196170.0198610.0202270.0210050.0219670.0228360.0232790.0236600.0241330.0244080.0246520.0248810.0252010.0253850.0254760.0255520.0257050.0258730.0004850.0004790.0004850.0005030.0005090.0005210.0005150.0005270.0005270.0005210.0005210.0005640.0005820.0005520.0005520.0005700.0005580.0005760.0005760.0005880.0005880.0006310.0006130.0006430.0006250.0006620.0006920.0006920.0006980.0007100.0007290.0007290.0007350.0007470.0007650.0007650.0007710.0008200.0008020.0008630.0009480.0009610.0009970.0010220.0010220.0010400.0010520.0010640.0011010.0011010.0011070.0011130.0011190.00113286.0387.7989.6791.6792.9494.4894.8295.8496.5897.4198.8999.91101.20102.74104.04105.27106.20106.81107.46108.48110.70112.83116.06118.90120.94123.47127.26128.71130.65131.64133.49135.03137.47139.59142.00143.79146.81149.24152.95162.26172.87179.77184.31189.18192.54195.72198.80202.34204.94206.08206.29208.45210.27213.72

5.2325475.2722175.3454575.4003875.4736275.5041475.5377175.5682375.5926475.6201175.6414775.6384275.6689475.6719975.7086175.7543975.7818575.7971175.8123775.8550975.9222375.9710676.0534676.1328076.2335176.3189676.4013676.5081776.6363476.7584176.8804877.0056177.1063177.2131377.3352077.4481177.5396677.5793477.6434277.7044677.8417977.9577578.1378178.3087178.5162378.6871378.8397178.9862079.1113279.2456079.3859879.4897479.5935079.7369370.0578000.0590210.0602420.0611570.0602420.0602420.0614620.0620730.0626830.0626830.0623780.0642090.0626830.0626830.0642090.0645140.0663450.0654290.0672610.0663450.0675660.0693970.0703120.0715330.0730590.0739740.0761110.0773310.0788570.0809930.0828250.0852660.0858760.0877070.0907590.0907590.0904540.0916750.0944210.0944210.0962520.0983880.1011350.1035760.1069330.1093750.1115110.1145630.1151730.1182250.1221920.1243280.1279910.13867242.68127543.32215444.03015244.64049445.18371245.60485446.02599246.26403446.45935646.79505447.09411247.11243247.17957647.33215448.31481548.63831648.70545548.96789649.35241349.84679350.56091451.20177452.19055353.10607554.22301455.01037256.04797457.39685658.91663660.33875561.44959562.73133463.98865365.29479666.62537267.77893668.51745269.04235469.92127570.75133472.41149573.87633475.47547477.17835579.20471380.78551482.15271183.33679384.53919585.55237986.93787787.57263388.37829789.0374760.0261630.0263610.0267270.0270020.0273680.0275210.0276890.0278410.0279630.0281010.0282070.0281920.0283450.0283600.0285430.0287720.0289090.0289860.0290620.0292750.0296110.0298550.0302670.0306640.0311680.0315950.0320070.0325410.0331820.0337920.0344020.0350280.0355320.0360660.0366760.0372410.0376980.0378970.0382170.0385220.0392090.0397890.0406890.0415440.0425810.0434360.0441990.0449310.0455570.0462280.0469300.0474490.0479680.0486850.0011560.0011800.0012050.0012230.0012050.0012050.0012290.0012410.0012540.0012540.0012480.0012840.0012540.0012540.0012840.0012900.0013270.0013090.0013450.0013270.0013510.0013880.0014060.0014310.0014610.0014790.0015220.0015470.0015770.0016200.0016570.0017050.0017180.0017540.0018150.0018150.0018090.0018340.0018880.0018880.0019250.0019680.0020230.0020720.0021390.0021880.0022300.0022910.0023030.0023650.0024440.0024870.0025600.002773215.64218.87222.45225.53228.28230.41232.53233.74234.72236.42237.93238.02238.36239.13244.10245.73246.07247.40249.34251.84255.45258.68263.68268.30273.95277.92283.17289.98297.66304.84310.46316.93323.29329.88336.61342.43346.17348.82353.26357.45365.84373.24381.32389.92400.16408.15415.05421.04427.11432.23439.23442.44446.51449.84

9.88647710.00854710.08483710.14587710.22826710.35338710.50597710.70129710.92406711.16210611.40014711.58935711.78161711.94335612.11425712.23937712.24853712.27294712.26379712.26684812.26073712.25463712.26073712.26684812.26073712.26684812.26989712.26073712.25463712.26379712.26684812.25463712.26684812.26684812.26989712.26073712.26989712.26684812.24547712.12035711.99218711.83959711.65038611.43066711.22008710.98815710.62499710.33813710.16723710.0512679.9749779.9230979.8773179.8681670.1487420.1710200.1954340.2183230.2497560.2763060.2930910.3181150.3477170.3791500.4044800.4288940.4548340.4743650.4951170.5097650.5115960.5125120.5125120.5122070.5119020.5128170.5112910.5122070.5125120.5119020.5134280.5128170.5125120.5125120.5125120.5122070.5128170.5137330.5122070.5131220.5122070.5134280.5091550.4914550.4746700.4575800.4438470.4343870.4243160.4169920.3995970.3864740.3788450.3757930.3724360.3715210.3684690.36724888.83605189.14733088.95203789.33655889.64173490.46569090.83191091.79015293.04749694.13391294.61609095.59265296.39221396.87439097.76549497.15515296.42883496.08093395.85509495.69031895.54993795.43395195.34241895.29357095.18371795.14709695.09215495.05553395.01281894.94567094.90905894.88465494.85413694.80529994.77477294.76867894.73815094.68933290.93567077.48351263.75671549.98107541.26525534.64295529.09485423.48571414.8614539.2523146.2860144.5465143.4661942.8558342.4713142.1844540.0494320.0500430.0504240.0507290.0511410.0517670.0525300.0535060.0546200.0558110.0570010.0579470.0589080.0597170.0605710.0611970.0612430.0613650.0613190.0613340.0613040.0612730.0613040.0613340.0613040.0613340.0613490.0613040.0612730.0613190.0613340.0612730.0613340.0613340.0613490.0613040.0613490.0613340.0612270.0606020.0599610.0591980.0582520.0571530.0561000.0549410.0531250.0516910.0508360.0502560.0498750.0496150.0493870.0493410.0029750.0034200.0039090.0043660.0049950.0055260.0058620.0063620.0069540.0075830.0080900.0085780.0090970.0094870.0099020.0101950.0102320.0102500.0102500.0102440.0102380.0102560.0102260.0102440.0102500.0102380.0102690.0102560.0102500.0102500.0102500.0102440.0102560.0102750.0102440.0102620.0102440.0102690.0101830.0098290.0094930.0091520.0088770.0086880.0084860.0083400.0079920.0077290.0075770.0075160.0074490.0074300.0073690.007345448.82450.39449.41451.35452.89457.05458.90463.74470.10475.59478.02482.96487.00489.43493.93490.85487.18485.42484.28483.45482.74482.15481.69481.44480.89480.70480.43480.24480.03479.69479.50479.38479.22478.98478.82478.79478.64478.39459.43391.46322.11252.52208.48175.02146.99118.6675.0846.7431.7622.9717.5114.4312.4911.04

9.8467979.8498479.8498479.8467979.8437479.8498479.8437479.8559579.8406979.8498479.8498479.8437479.8437479.8437479.8529079.8467979.8437479.8559579.8803679.9047879.9475079.99328710.02074710.05126710.07567710.08788610.10009710.11230710.12145710.12755710.13366610.13671710.14892610.15502810.14892610.19775710.29540710.37170710.43578710.53344710.60668710.66161710.72570710.78673710.82641710.86608710.89660710.91796710.90880710.93322710.94237710.95458710.96068711.0095170.3675540.3693850.3669430.3681640.3672480.3675540.3672480.3669430.3672480.3669430.3672480.3672480.3663330.3672480.3657220.3675540.3678590.3693850.3721310.3776240.3828120.3834230.3864740.3867800.3876950.3886110.3895260.3898310.3907470.3910520.3907470.3913570.3913570.3919680.3922730.3947140.3983760.4020380.4053950.4093630.4111940.4145510.4191280.4212640.4246210.4261470.4276730.4273680.4285890.4298090.4298090.4295040.4291990.4334712.2271742.2576942.2882142.2943142.3126142.3309342.3431342.3248342.3492342.3248342.3187342.2759942.2515942.1661342.1783542.1722343.1915344.7113146.97571410.94299414.34265516.39953518.04137419.31091420.23865320.87341421.49597522.00257422.57629522.83875322.99133423.23547423.58337523.69323323.78479325.91491328.94225431.90247434.53307537.71911539.75159542.41883444.65271646.80725248.41247249.46839450.56091451.02477651.39709651.87927352.50183252.46521652.59339455.1995950.0492340.0492490.0492490.0492340.0492190.0492490.0492190.0492800.0492030.0492490.0492490.0492190.0492190.0492190.0492650.0492340.0492190.0492800.0494020.0495240.0497380.0499660.0501040.0502560.0503780.0504390.0505000.0505620.0506070.0506380.0506680.0506840.0507450.0507750.0507450.0509890.0514770.0518590.0521790.0526670.0530330.0533080.0536290.0539340.0541320.0543300.0544830.0545900.0545440.0546660.0547120.0547730.0548030.0550480.0073510.0073880.0073390.0073630.0073450.0073510.0073450.0073390.0073450.0073390.0073450.0073450.0073270.0073450.0073140.0073510.0073570.0073880.0074430.0075520.0076560.0076680.0077290.0077360.0077540.0077720.0077910.0077970.0078150.0078210.0078150.0078270.0078270.0078390.0078450.0078940.0079680.0080410.0081080.0081870.0082240.0082910.0083830.0084250.0084920.0085230.0085530.0085470.0085720.0085960.0085960.0085900.0085840.00866911.2511.4111.5611.5911.6811.7811.8411.7511.8711.7511.7111.5011.3810.9411.0110.9716.1223.8035.2455.2972.4682.8591.1597.56102.25105.46108.60111.16114.06115.39116.16117.39119.15119.70120.17130.93146.22161.18174.47190.57200.83214.31225.60236.48244.59249.93255.45257.79259.67262.11265.25265.07265.71278.88

11.10717711.19262811.24450711.27807711.31774711.36352711.45202711.52221711.65649711.78161711.92809612.05321712.16918712.29125712.40417712.54150712.68188712.82836712.95043713.09081713.28918813.43871713.53942713.59435713.68896713.78356813.97582714.16503714.40917714.64416714.91271715.13549715.34301715.53222715.68481715.87096816.06017716.21581716.34704716.53930716.71935716.89330616.99096717.10387717.21374717.37243717.57995717.82714718.09569718.39477718.66027718.90136719.13024719.3286070.4395750.4429320.4450680.4475100.4496460.4523920.4578860.4627680.4673460.4768060.4859620.4938960.5015260.5128170.5219720.5369260.5555420.5720210.5897210.6089480.6327510.6538080.6660150.6751710.6861570.7026370.7264400.7520750.7835080.8125000.8454590.8729250.8988650.9217530.9434200.9660030.9928591.0120851.0313111.0572511.0813601.1021121.1158451.1286621.1439211.1704711.1970211.2336421.2684321.3065791.3432001.3743281.4063721.43322758.32459561.04065562.85949363.77503565.45349267.10143270.25085572.91199376.78161280.96863885.88805389.68445992.85827795.84899097.62511399.126597100.182496100.512095101.171275102.214976102.501832103.069449103.276978103.502818103.856812105.028697105.315553106.554576107.451774108.141471109.209596109.673453110.631715111.242076111.766978112.468873113.128053113.408814114.208375114.849234115.734254115.929576115.740357116.552134116.808473118.132935118.596793119.573375120.440074121.123658122.075816122.472535123.339234123.7420760.0555360.0559630.0562230.0563900.0565890.0568180.0572600.0576110.0582820.0589080.0596400.0602660.0608460.0614560.0620210.0627080.0634090.0641420.0647520.0654540.0664460.0671940.0676970.0679720.0684450.0689180.0698790.0708250.0720460.0732210.0745640.0756770.0767150.0776610.0784240.0793550.0803010.0810790.0817350.0826970.0835970.0844670.0849550.0855190.0860690.0868620.0879000.0891360.0904780.0919740.0933010.0945070.0956510.0966430.0087920.0088590.0089010.0089500.0089930.0090480.0091580.0092550.0093470.0095360.0097190.0098780.0100310.0102560.0104390.0107390.0111110.0114400.0117940.0121790.0126550.0130760.0133200.0135030.0137230.0140530.0145290.0150420.0156700.0162500.0169090.0174590.0179770.0184350.0188680.0193200.0198570.0202420.0206260.0211450.0216270.0220420.0223170.0225730.0228780.0234090.0239400.0246730.0253690.0261320.0268640.0274870.0281270.028665294.67308.39317.58322.21330.69339.01354.92368.37387.92409.07433.93453.11469.14484.25493.22500.81506.14507.81511.14516.41517.86520.73521.78522.92524.71530.63532.08538.34542.87546.36551.75554.09558.94562.02564.67568.22571.55572.97577.01580.24584.72585.70584.75588.85590.14596.83599.18604.11608.49611.94616.75618.76623.14625.17

19.52392619.72838719.92675720.10680720.28991820.51879720.69579720.85754720.97961721.11693721.26647821.44652721.45263721.45873621.49230821.48620721.47399721.48009621.47704721.48009621.48315721.48620721.48009621.48925621.48620721.59911721.61437821.61437821.62353821.62658821.63268621.63268621.62658821.62963721.63573821.62047721.62963721.72423721.88293821.99279622.09350622.20031822.35900722.53295722.71911722.91137823.09753723.28368723.43932723.58886823.73229823.87878724.00695624.1381771.4616091.4915161.5168461.5424801.5720821.6038211.6297611.6538691.6706541.6926271.7164301.7387081.7426761.743286124.389029125.206910125.255738126.000377126.848756127.184459127.440797127.819215128.203736128.472291129.284058128.344117127.355357126.867076123.882457123.864137123.851930123.827515123.815318123.815318123.796998123.809214123.784791123.766471123.784791128.881236128.045054127.642213127.385875127.208854127.037974126.976930126.873170126.812135126.683951126.592418126.513053130.199595130.639029130.486451131.212769131.463014131.896354132.213755132.738658132.994996133.684693133.837272134.191295134.246217134.472056134.710074135.271617135.3936780.0976200.0986420.0996340.1005340.1014500.1025940.1034790.1042880.1048980.1055850.1063320.1072330.1072630.1072940.1074620.1074310.1073700.1074000.1073850.1074000.1074160.1074310.1074000.1074460.1074310.1079960.1080720.1080720.1081180.1081330.1081630.1081630.1081330.1081480.1081790.1081020.1081480.1086210.1094150.1099640.1104680.1110020.1117950.1126650.1135960.1145570.1154880.1164180.1171970.1179440.1186610.1193940.1200350.1206910.0292320.0298300.0303370.0308500.0314420.0320760.0325950.0330770.0334130.0338530.0343290.0347740.0348540.034866628.44632.57632.82636.58640.87642.56643.86645.77647.71649.07653.17648.42643.43640.96625.88625.79625.73625.60625.54625.54625.45625.51625.39625.30625.39651.14646.91644.88643.58642.69641.82641.52640.99640.68640.04639.57639.17657.80660.02659.25662.92664.18666.37667.97670.63671.92675.41676.18677.96678.24679.38680.59683.42684.04

24.26025724.38842624.53185624.66003724.76073824.84313824.93468625.04150725.16662725.30089725.45348725.57860725.73730825.86547725.98449826.08214726.18896826.28356826.39037726.48803826.57348726.68334826.77184626.86950726.93664627.01293827.06786727.15636827.26623627.38219827.49816727.61718827.74230827.83996627.94067728.02611728.09630728.19396828.27636828.35876828.42589728.51745728.58459828.68224728.72802828.78600728.82567728.90197828.98131729.06066729.14916829.24071629.34753729.432977135.387574135.875855135.820914136.193238136.058951136.290894136.419078136.931754136.950074137.413932137.670298137.804576138.067017138.018189138.262330138.219615138.482056138.549195138.732291138.787232138.970338139.354850139.202271139.269410138.982554139.379273139.446412139.891978139.952994140.270396140.276490140.545054140.697633140.520631140.728150140.636598140.850211140.752574140.935670140.892955141.045533141.484996141.265250141.301871141.015015141.155396141.112672141.680299141.643678142.058717142.003795142.168570142.186890142.1197520.1213010.1219420.1226590.1233000.1238040.1242160.1246730.1252080.1258330.1265040.1272670.1278930.1286870.1293270.1299220.1304110.1309450.1314180.1319520.1324400.1328670.1334170.1338590.1343480.1346830.1350650.1353390.1357820.1363310.1369110.1374910.1380860.1387120.1392000.1397030.1401310.1404820.1409700.1413820.1417940.1421290.1425870.1429230.1434110.1436400.1439300.1441280.1445100.1449070.1453030.1457460.1462040.1467380.147165684.01686.48686.20688.08687.40688.57689.22691.81691.90694.25695.54696.22697.55697.30698.53698.32699.64699.98700.91701.18702.11704.05703.28703.62702.17704.18704.51706.77707.07708.68708.71710.07710.84709.94710.99710.53711.61711.11712.04711.82712.59714.81713.70713.89712.44713.15712.93715.80715.62717.71717.44718.27718.36718.02

29.50622629.57641729.63134629.68322829.75036729.79919729.86022829.90905629.97924630.03722730.07079730.11352630.13488630.18066730.23559630.29967630.38512830.45531830.54687830.62316730.70556730.77880730.83678830.89477630.94359731.00768631.05346731.09618731.15722731.21825831.26708831.31286731.34948831.38000831.42577731.46850631.53258631.61498631.69433731.78283831.84692731.92931731.98424632.04528632.08495732.13988632.21313832.25280632.29247632.36266732.42065732.46032832.51525732.545777142.119752141.997672141.997672142.107554142.351695142.150269142.058717142.418834142.327271142.315074142.192994141.906138141.887818142.357798142.589713142.992555143.041373143.120738143.242799143.206178143.114634143.004752142.962037143.053590143.023072143.139029142.962037143.010875143.364879143.255015143.157349142.919312142.894898142.846070143.291636143.407594143.865357143.920298143.999635143.981334143.926392143.853150143.761598143.645631143.792115143.712769143.847056143.657838143.810435144.072877143.975211143.798219143.602916143.5906900.1475310.1478820.1481570.1484160.1487520.1489960.1493010.1495450.1498960.1501860.1503540.1505680.1506740.1509030.1511780.1514980.1519260.1522770.1527340.1531160.1535280.1538940.1541840.1544740.1547180.1550380.1552670.1554810.1557860.1560910.1563350.1565640.1567470.1569000.1571290.1573430.1576630.1580750.1584720.1589140.1592350.1596470.1599210.1602260.1604250.1606990.1610660.1612640.1614620.1618130.1621030.1623020.1625760.162729718.02717.40717.40717.96719.19718.18717.71719.53719.07719.01718.39716.94716.85719.22720.40722.43722.68723.08723.69723.51723.05722.49722.28722.74722.58723.17722.28722.52724.31723.76723.26722.06721.94721.69723.94724.53726.84727.12727.52727.43727.15726.78726.32725.73726.47726.07726.75725.79726.56727.89727.40726.50725.51725.45

32.56408832.61291832.65868732.72887832.80212732.87841632.96386833.04626833.10424633.17138733.22326733.28124633.31481833.38195633.44298733.48571633.54064833.59862633.65661733.68102633.72069733.75121733.79699833.85192733.89770833.97399734.05334834.12658834.20898734.27611734.33715634.39818734.45006734.50500834.56908834.60570634.65758634.71557734.77660734.81933734.86510834.89562834.93529634.97497635.02379735.09093635.17638735.24963735.33202735.41747635.48766735.56090735.62194635.670777143.511353144.005738144.030152144.518433144.524537144.634391144.603873144.567252144.390250144.371959144.243775144.347535144.335338144.414674144.274293144.335338144.689332144.451295144.365855144.140015144.103394144.017955144.426871144.542857144.890757144.994517144.970094145.116578144.994517144.915152144.786998144.756471144.738150144.683238144.860230144.664918144.719849144.957896144.872437144.744254144.585572144.463492144.420777144.854136144.963990145.342418145.342418145.440074145.501090145.440074145.293570145.208131145.086051145.1165780.1628200.1630650.1632930.1636440.1640110.1643920.1648190.1652310.1655210.1658570.1661160.1664060.1665740.1669100.1672150.1674290.1677030.1679930.1682830.1684050.1686030.1687560.1689850.1692600.1694890.1698700.1702670.1706330.1710450.1713810.1716860.1719910.1722500.1725250.1728450.1730290.1732880.1735780.1738830.1740970.1743260.1744780.1746760.1748750.1751190.1754550.1758820.1762480.1766600.1770870.1774380.1778050.1781100.178354725.05727.55727.67730.14730.17730.73730.57730.39729.49729.40728.75729.28729.21729.62728.91729.21731.00729.80729.37728.23728.04727.61729.68730.26732.02732.54732.42733.16732.54732.14731.50731.34731.25730.97731.87730.88731.16732.36731.93731.28730.48729.86729.65731.84732.39734.30734.30734.80735.10734.80734.06733.62733.01733.16

35.72265735.79284735.84777735.89049635.95153636.03088736.08886836.15600636.18957636.23839736.26891736.32384636.39403636.45507636.54662736.63512836.71142636.81213736.87011836.94030637.00439837.06847737.13256737.20580637.26684637.33703737.38891737.46520637.52624837.58117737.63000837.67577737.71850637.79479837.84667837.94433738.02672738.12743738.20983738.29833838.38378738.45397838.51501838.58214738.66454738.73778638.80187838.87206638.94836739.02465639.08263739.13756739.19555739.244388145.055533145.293570145.177613145.092154145.391236145.397330145.281373145.128795144.829713144.927379144.915152145.372935145.324098145.629273145.659791145.739137145.733033145.641471145.519410145.470572145.348512145.488892145.397330145.501090145.379039145.458375145.690318145.531617145.421754145.214234145.177613145.079957145.464478145.519410145.836793145.824595145.879517145.916139145.836793145.617076145.726930145.568238145.562135145.586558145.757457145.641471145.501090145.678092145.745231145.580455145.464478145.202037145.336314145.2996740.1786130.1789640.1792390.1794520.1797580.1801540.1804440.1807800.1809480.1811920.1813450.1816190.1819700.1822750.1827330.1831760.1835570.1840610.1843510.1847020.1850220.1853420.1856630.1860290.1863340.1866850.1869450.1873260.1876310.1879060.1881500.1883790.1885930.1889740.1892330.1897220.1901340.1906370.1910490.1914920.1919190.1922700.1925750.1929110.1933230.1936890.1940090.1943600.1947420.1951230.1954130.1956880.1959780.196222732.85734.06733.47733.04734.55734.58733.99733.22731.71732.21732.14734.46734.21735.75735.91736.31736.28735.81735.20734.95734.33735.04734.58735.10734.49734.89736.06735.26734.70733.65733.47732.98734.92735.20736.80736.74737.02737.20736.80735.69736.25735.44735.41735.54736.40735.81735.10736.00736.34735.51734.92733.59734.27734.09

39.30846839.37560639.47021839.55871639.67162739.76623639.86083839.93713740.02257640.09887540.17821640.24840740.33996940.39794740.48949540.55358740.65124840.73058940.80077540.85570640.92284540.97167841.04796741.12426641.22192741.32567741.44164941.55150741.64916841.74682941.82921741.92382642.01537942.10998842.19848942.28088742.35412942.44872942.53722542.62572642.71117542.77831942.84850942.91869542.99804543.09569743.19640943.31237643.42528643.55346543.67553543.79150743.88915843.995965145.617076145.647574145.830689145.989371145.885611145.964976145.751334145.751334145.635377145.580455145.586558145.519410145.678092145.592652145.482798145.665894145.592652145.470572145.458375145.128795145.208131145.195914145.537711145.446177145.745231145.757457145.781852145.617076145.513316145.391236145.385133145.238658145.330191145.189811145.324098145.147096145.067750145.189811145.098277145.006715144.945670144.603873144.640494144.677134144.854136144.823609144.945670144.970094144.872437144.738150144.524537144.323111144.097291143.9080720.1965420.1968780.1973510.1977940.1983580.1988310.1993040.1996860.2001130.2004940.2008910.2012420.2017000.2019900.2024470.2027680.2032560.2036530.2040040.2042790.2046140.2048580.2052400.2056210.2061100.2066280.2072080.2077580.2082460.2087340.2091460.2096190.2100770.2105500.2109920.2114040.2117710.2122440.2126860.2131290.2135560.2138920.2142430.2145930.2149900.2154780.2159820.2165620.2171260.2177670.2183780.2189580.2194460.219980735.69735.84736.77737.57737.05737.45736.37736.37735.78735.51735.54735.20736.00735.57735.01735.94735.57734.95734.89733.22733.62733.56735.29734.83736.34736.40736.52735.69735.17734.55734.52733.78734.24733.53734.21733.32732.91733.53733.07732.61732.30730.57730.76730.94731.84731.68732.30732.42731.93731.25730.17729.15728.01727.06

`

a) GRAFICA DE ESFUERZO-DEFORMACION DEL ACERO GLOBAL.

Diagrama Esfuerzo-Deformacin Global

800

700

600

500

400

300

200

100

00.00 0.05 0.10 0.15 0.20 0.25

700

Diagrama Esfuerzo-Deformacin Local

600

500

400

300

200

100

00.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

Para hallar el esfuerzo y la deformacin de fluencia se trazar una lnea offset paralela al tramo elstico en el diagrama de esfuerzo-deformacin local del elemento.

El inicio del offset ser a partir de una deformacin de 0.002 en el eje de las abscisas:

700

Diagrama Esfuerzo-Deformacin Local

600

500f prop400

300

200

100 0.002 f0

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

Graficando una lnea paralela, se tienen los siguientes puntos aproximados del offset:

MPa MPa MPa

MPa

De la grfica se tiene que:Esfuerzo de Fluencia = y =450.00MPa

Deformacin de Fluencia = y =0.0042

Hallamos el lmite de proporcionalidad por inspeccin visual:Lmite de Proporcionalidad = prop = 420.00 MPa

Ahora el mdulo de elasticidad est definido por: = Modulo de Elasticidad = E = 200000.00 MPaPara hallar el esfuerzo ltimo se tiene en el diagrama global:

Diagrama Esfuerzo-Deformacin Global

800

u700

600

500

400

300

200

100

0r

0.00 0.05 0.10 0.15 0.20 0.25

Entonces tenemos:

Esfuerzo ltimo = u = 720.00

MPa

Del grfico anterior se puede extraer que la deformacin unitaria de ruptura es igual a:Deformacin Unitaria de Ruptura = r = 0.2310

Entonces el porcentaje de elongacin o ductilidad por elongacin ser calculado en base al anterior resultado obtenido:% de Elongacin = 100 x r = 23.10 %

Ahora para calcular el mdulo de resilencia debemos hallar el rea bajo la curva del diagrama esfuerzo- deformacin local en el intervalo elstico de la siguiente manera:

Diagrama Esfuerzo-Deformacin Local

700

600

500prop400

300

200100

0

UR

0.00230.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

El grfico anterior tenemos un rea triangular a calcular:Mdulo de Resiliencia = rea Bajo Curva Elstica = UR = 0.483 MPa

Finalmente para calcular el mdulo de tenacidad necesitaremos calcular el rea bajo la curva del diagrama esfuerzo-deformacin global completo de la siguiente manera:

Diagrama Esfuerzo-Deformacin Global

800

700

600

500

400

300

200

100

0

UT 0.00 0.05 0.10 0.15 0.20