CHAPTER FOUR 4.1 EXPERIMENTAL RESULTS AND DISCUSSIONS There were two specimens for each grade of steel and two loading capacities for these various grades of steel. The specimens were tested under the same constant load capacity as tabulated below: Table 4.1 Steel Grade Cyclic Load 1 Cyclic Load 2 300W 0.50P = 122 KN 0.75P = 184 KN 350W 0.50P = 122 KN 0.75P = 184 KN 460W 0.50P = 122 KN 0.75P = 184 KN 4.1.1 Grade 300W @ 0.50P Specimen 1 of Grade 300W was loaded with 122 KN at the midspan until failure. Moment determination: P = 122 KN KN KNP RA 612 122 2 === Maximum moment (moment @ midpoint), M300 = KNmmKNx 25.7625.161 = Stress determination: Considering the section at midspan directly under the point of loading where maximum stresses will be induced, as shown below. P RBRA 1.25 m 1.25 m 62 c I 100 16 mm Mmidspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen I = Cross-sectional moment of inertia ? ?= A Ay y ? =++= == == == 2 321 2 3 2 2 2 1 6688 160016100 348821816 160016100 mmAAAA mmxA mmxA mmxA mmy mmy mmy 8 2 16 12516 2 218 2428250 3 2 1 == =+= =?= 3 33211 32 33 32 2 32 11 836000 1280081600 4360001253488 3872002421600 mmyAyAyAAy mmmmxmmyA mmmmxmmyA mmmmxmmyA =++= == == == ? 16 mm 250 y1 218 16 mm y3 yy2 63 mm mm mm A Ay y 125 6688 836000 2 3 ===? ? ? ( ) ( ) 4 1 22 33 2 11 3 11 1 33.21936533 1252421600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 2 22 33 2 22 3 22 2 62.13813642 1251251600 12 21816 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 3 22 33 2 33 3 33 3 33.21936533 81251600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= 4 321 33.57686709 mmIIII =++=? NmmxMmidspan 61025.76= mmc 125= 2 46 6 max /1651069.57 1251025.76 mmN mmx mmNmmxx midspan ===? ?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 46 6 min /5.131069.57 1251025.6 mmN mmx mmNmmxx ==? 2 min 2 max /5.13 /165 mmN mmN = = ? ? ? 2minmax 2 minmax /25.89 2 5.178 2 , /5.151, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 64 2/75.75 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after every 100,000 cycles at a frequency of 1 Hz. 1 strain gauge was affixed at the top flange towards the support of the specimen while three strain gauges namely B, C and D were placed on the web within the zone of loading. Table 4.2 ? Strain gauge results Cycles to failure Top Flange (microstrain) Web - B (microstrain) Web - C (microstrain) Web -D (microstrain) Stress MPa 0 17380 14705 16400 18105 165 100000 16865 14830 16620 18365 165 200000 16980 14800 16660 18390 165 300000 16875 14780 16660 18370 165 400000 16855 14840 16630 18390 165 500000 16860 14840 16670 18395 165 600000 16860 14810 16665 18380 165 700000 16840 14850 16660 18410 165 800000 16865 14840 16645 18410 165 900000 16870 14835 16650 18390 165 1000000 16850 14830 16670 18395 165 1100000 16860 14850 16675 18395 165 At failure - 1200000 16750 14930 16720 18500 165 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until failure; the stress- strain curve yielded a straight line as shown below: 65 Stress vs Strain under cyclic loading @ constant stress 0 20 40 60 80 100 120 140 160 180 14500 15000 15500 16000 16500 17000 17500 18000 18500 19000 Strain S tr es s Flange Web - B Web - C Web - D Figure 4.1 ? Stress-strain curve Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at every 100,000 cycles of loading. Top flange Top Flange of 300W @ 122KN 0 17380 100000 16865 200000 16980 300000 16875 400000 16855 500000 16860 600000 16860 700000 16840 800000 16865 900000 16870 1000000 16850 1100000 16860 1200000 16750 16700 16800 16900 17000 17100 17200 17300 17400 17500 0 200000 400000 600000 800000 1000000 1200000 cycles to failure m ic ro s tr ai n Figure 4.2 ? Top flange 66 As can be seen from the figure above, there was a sharp contraction after the first 100,000 cycles and afterwards stabilization. This shows that the top flange was under compression. Web - B Web - B of 300W @ 122KN cyclic loading 0 14705 100000 14830 200000 14800 300000 14780 400000 14840 500000 14840 600000 14810 700000 14850 800000 14840 900000 14835 1000000 14830 1100000 14850 1200000 14930 14650 14700 14750 14800 14850 14900 14950 0 200000 400000 600000 800000 1000000 1200000 cycles to failure m ic ro s tr ai n Figure 4.3 ? Web B Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. Two other strain gauges were placed on the web and these yielded similar result as shown in figures 4.4 and 4.5 below. Web - C Web - C of 300W @ 122KN cyclic loading 0 16400 100000 16620 200000 16660 300000 16660 400000 16630 500000 16670 600000 16665 700000 16660 800000 16645 900000 16650 1000000 16670 1100000 16675 1200000 16720 16350 16400 16450 16500 16550 16600 16650 16700 16750 0 200000 400000 600000 800000 1000000 1200000 cycles to failure m ic ro s tr ai n Figure 4.4 ? Web C 67 Web - D Web - D of 300W @ 122KN cyclic loading 0 18105 100000 18365 200000 18390 300000 18370 400000 18390 500000 18395 600000 18380 700000 18410 800000 18410 900000 18390 1000000 18395 1100000 18395 1200000 18500 18050 18100 18150 18200 18250 18300 18350 18400 18450 18500 18550 0 200000 400000 600000 800000 1000000 1200000 cycles to failure m ic ro s tr ai n Figure 4.5 ? Web D Failure Cycle, time and shape: The beam failed by out-of-plane global buckling (figure 4.6a) at 1,200,000 cycles, which was approximately 333 hours of testing. The beam also showed a sign of in-plane local buckling at both the supports (figure 4.6b) and the point of loading (figure 4.6c). Figure 4.6a ? Specimen at failure (out-of-plane global buckling) 68 Figure 4.6b ? In-plane Local buckling at the support Figure 4.6c ? In-plane Local buckling at the point of loading 4.1.2 Grade 350W @ 0.50P Specimen 2 of Grade 350W was loaded with 122 KN at the midspan until failure. 69 Moment determination: P = 122 KN KN KNP RA 612 122 2 === Maximum moment (moment @ midpoint), M350 = KNmmKNx 25.7625.161 = Stress determination: Considering the section at midspan directly under the point of loading where maximum stresses will be induced, as shown below. c I M midspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen P RBRA 1.25 m 1.25 m 100 16 mm 16 mm 225 193 16 mm y3 y1 y2 y 70 I = Cross-sectional moment of inertia ? ?= A Ay y ? =++= == == == 2 321 2 3 2 2 2 1 6288 160016100 308819316 160016100 mmAAAA mmxA mmxA mmxA mmy mmy mmy 8 2 16 5.11216 2 193 2178225 3 2 1 == =+= =?= 3 33211 32 33 32 2 32 11 707400 1280081600 3474005.1123088 3472002171600 mmyAyAyAAy mmmmxmmyA mmmmxmmyA mmmmxmmyA =++= == == == ? mm mm mm A Ay y 5.112 6288 707400 2 3 ===? ? ? ( ) ( ) 4 1 22 33 2 11 3 11 1 33.17506533 5.1122171600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 2 22 33 2 22 3 22 2 33.9585409 5.1125.1121600 12 19316 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 3 22 33 2 33 3 33 3 33.17506533 85.1121600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= 4 321 99.44598475 mmIIII =++=? 71 NmmxMmidspan 61025.76= mmc 5.112= 2 46 6 /3.192 1060.44 5.1121025.76 mmN mmx mmNmmxx midspan ==?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 46 6 min /5.171060.44 1251025.6 mmN mmx mmNmmxx ==? 2 min 2 max /5.15 /3.192 mmN mmN = = ? ? ? 2minmax 2 minmax /9.103 2 8.207 2 , /8.176, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 2/4.88 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after every 100,000 cycles at a frequency of 1 Hz. 1 strain gauge was affixed at the top flange while another one was placed on the web within the zone of loading. Table 4.2 ? Strain gauge results Cycles to failure Web Flange Stress 0 17295 17050 192.3 100000 18450 16910 192.3 200000 18485 16900 192.3 300000 18490 16870 192.3 400000 18490 16885 192.3 500000 18480 16870 192.3 600000 18530 16900 192.3 700000 18010 17000 192.3 At failure 786000 17880 17400 192.3 72 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until failure; the stress- strain curve yielded a straight line as shown below: Stress Vs Strain under cyclic loading @ constant stress 0 50 100 150 200 250 16600 16800 17000 17200 17400 17600 17800 18000 18200 18400 18600 18800 Strain S tr es s Flange Web Figure 4.7 ? Stress-strain curve Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at every 100,000 cycles of loading. Top flange Flange of 350MPa @ 122KN under cyclic loading 0 17050 100000 16910 200000 16900 300000 16870 400000 16885 500000 16870 600000 16900 700000 17000 786000 17400 16800 16900 17000 17100 17200 17300 17400 17500 0 100000 200000 300000 400000 500000 600000 700000 800000 900000 cycles to failure m ic ro s tr ai n Figure 4.8 ? Top flange 73 As can be seen from the figure above, there was a sharp contraction after the first 100,000 cycles and afterwards stabilization. This shows that the top flange was under compression. Web Web 350 MPa @ 122KN under cyclic loading 0 17295 100000 18450 200000 18485 300000 18490 400000 18490 500000 18480 600000 18530 700000 18010 786000 17880 17200 17400 17600 17800 18000 18200 18400 18600 0 100000 200000 300000 400000 500000 600000 700000 800000 900000 cycles to failure m ic ro s tr ia n Figure 4.9 ? Web B Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. See figure 4.8 above. Failure Cycle: The beam failed by fracture at 786,000 cycles, which was approximately 218 hours of testing. The fracture occurred a small distance away from the point of loading. But since there was a carton packing of 120 mm long at the point of loading to help distribute the load, it can be said that failure occurred within the zone of loading. 1.10 m 1.40 m Figure 4.10a 74 Figure 4.10b ? Specimen at failure 4.1.3 Grade 460W @ 0.50P Specimen 3 of Grade 460W was loaded with 122 KN at the midspan until failure. Moment determination: P = 122 KN KN KNP RA 612 122 2 === Maximum moment (moment @ midpoint), M460 = KNmmKNx 25.7625.161 = 1.25 m P 1.25 m RA RB 75 Stress determination: Considering the section at midspan directly under the point of loading where maximum stresses will be induced, as shown below. c I M midspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen I = Cross-sectional moment of inertia ? ?= A Ay y ? =++= == == == 2 321 2 3 2 2 2 1 5680 160016100 248015516 160016100 mmAAAA mmxA mmxA mmxA mmy mmy mmy 8 2 16 5.9316 2 155 1798187 3 2 1 == =+= =?= 100 16 mm 16 mm 187 155 16 mm y3 y1 y2 y 76 3 33211 32 33 32 2 32 11 531080 1280081600 2318805.932480 2864001791600 mmyAyAyAAy mmmmxmmyA mmmmxmmyA mmmmxmmyA =++= == == == ? mm mm mm A Ay y 5.93 5680 531080 2 3 ===? ? ? ( ) ( ) 4 1 22 33 2 11 3 11 1 33.11730533 5.931791600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 2 22 33 2 22 3 22 2 67.4965166 5.935.931600 12 15516 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= ( ) ( ) 4 3 22 33 2 33 3 33 3 33.11730533 85.931600 12 16100 12 mmI mmmmmm mmmmx yyA db I = ?+= ?+= 4 321 33.28426233 mmIIII =++=? NmmxMmidspan 61025.76= mmc 5.93= 2 46 6 /251 1043.28 5.931025.76 mmN mmx mmNmmxx midspan ==?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 46 6 min /5.271043.28 1251025.6 mmN mmx mmNmmxx ==? 77 2 min 2 max /5.27 /251 mmN mmN = = ? ? ? 2minmax 2 minmax /25.139 2 5.278 2 , /5.223, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 2/75.111 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after every 100,000 cycles at a frequency of 1 Hz. 1 strain gauge was affixed at the top flange while another one was placed on the web within the zone of loading. Table 4.3 ? Strain gauge results Cycles to failure Web Flange Stress 0 17400 23975 251 50000 18100 21855 251 100000 18060 22035 251 150000 18000 22610 251 At Failure 182400 19300 18290 251 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until failure; the stress- strain curve yielded a straight line as shown below: 78 Stress vs Strain under cyclic loading @ constant stress 0 50 100 150 200 250 300 0 5000 10000 15000 20000 25000 Strain S tr es s Flange Web Figure 4.11 ? Stress-strain curve Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at every 50,000 cycles of loading. Top flange Flange 460W @ 122KN cyclic loading 0 23975 50000 21855 100000 22035 150000 22610 182400 18290 0 5000 10000 15000 20000 25000 30000 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 cycles to failure m ic ro s tr ai n Figure 4.12 ? Top flange 79 As can be seen from the figure above, there was a sharp contraction after the first 50,000 cycles and afterwards stabilization. This shows that the top flange was under compression. Web Web 460W @ 122KN cyclic loading 0 17400 50000 18100 100000 18060 150000 18000 182400 19300 17000 17500 18000 18500 19000 19500 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000 cycles to failure m ic ro s tr ai n Figure 4.13 ? Web B Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. See figure 4.11 above. Failure Cycle: The beam failed by fracture at 182,400 cycles, which was approximately 51 hours of testing. Fracture at a distance slightly away from the centre of the beam but still within the zone of loading as shown below. Figure 4.14a 1.21 m 1.29 m 80 Figure 4.14b ? Specimen at failure 4.1.4 Grade 300W @ 0.75P Specimen 4 of Grade 300W was loaded with 184 KN at the midspan until failure. Moment determination: P = 184 KN KN KNP RA 922 184 2 === Maximum moment (moment @ midpoint), M300 = KNmmKNx 11525.192 = Stress determination: 1.25 m P 1.25 m RA RB 81 Considering the section at midspan directly under the point of loading where maximum stresses were induced, as shown below. c I M midspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen I = Cross-sectional moment of inertia As previously determined, 433.57686709 mmI =? NmmxMmidspan 61025.76= mmc 125= 2 46 6 /249 1069.57 12510115 mmN mmx mmNmmxx midspan ==?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 min /5.13 mmN=? 100 16 mm 16 mm 250 218 16 mm y3 y1 y2 y 82 2 min 2 max /5.13 /249 mmN mmN = = ? ? ? 2minmax 2 minmax /25.131 2 5.262 2 , /5.235, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 2/75.117 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after every 100,000 cycles at a frequency of 1 Hz. 1 strain gauge was affixed at the top flange while another one was placed on the web within the zone of loading. Table 4.4 ? Strain gauge results Cycles to failure Web Flange Stress 0 16455 18330 249 100000 16600 16600 249 200000 16630 16640 249 300000 16610 16590 249 At failure 322023 16590 249 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until failure; the stress- strain curve yielded a straight line as shown below: 83 Stress vs Strain under cyclic loading @ constant stress 0 50 100 150 200 250 300 16000 16500 17000 17500 18000 18500 Strain S tr es s Flange Web Figure 4.15 ? Stress-strain curve Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at every 100,000 cycles of loading. Top flange Flange 300W @ 184KN cyclic loading 0 18330 100000 16600 200000 16640 300000 16590 16400 16600 16800 17000 17200 17400 17600 17800 18000 18200 18400 18600 0 50000 100000 150000 200000 250000 300000 350000 cycles to failure m ic ro s tr ai n Figure 4.16 ? Top flange 84 As can be seen from the figure above, there was a sharp contraction after the first 100,000 cycles and afterwards stabilization. This shows that the top flange was under compression. Web - B Web 300W @ 184KN cyclic loading 0 16455 100000 16600 200000 16630 300000 16610 322023 16590 16440 16460 16480 16500 16520 16540 16560 16580 16600 16620 16640 0 50000 100000 150000 200000 250000 300000 350000 cycles to failure m ic ro s tr ai n Figure 4.17 ? Web B Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. Failure Cycle: The beam failed by fracture at 322,023 cycles, which was approximately 89 hours of testing. Fracture occurred approximately at the middle of the beam within the zone of loading. 1.24 m 1.26 m Figure 4.18a 85 Figure 4.18b ? Specimen at failure 4.1.5 Grade 350W @ 0.75P Specimen 5 of Grade 350W was loaded with 184 KN at the midspan until failure. Moment determination: P = 184 KN KN KNP RA 922 184 2 === Maximum moment (moment @ midpoint), M350 = KNmmKNx 11525.192 = Stress determination: 1.25 m P 1.25 m RA RB 86 Considering the section at midspan directly under the point of loading where maximum stresses will be induced, as shown below. c I M midspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen I = Cross-sectional moment of inertia As already determined earlier, 499.44598475 mmI =? NmmxM midspan 610115= mmc 5.112= 2 46 6 /290 1060.44 5.11210115 mmN mmx mmNmmxx midspan ==?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 min /5.17 mmN=? 100 16 mm 16 mm 225 193 16 mm y3 y1 y2 y 87 2 min 2 max /5.17 /290 mmN mmN = = ? ? ? 2minmax 2 minmax /25.153 2 5.307 2 , /5.272, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 2/25.136 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after 60 cycles at a frequency of 1 Hz when the structure deformed in its global axis. 1 strain gauge was affixed at the top flange while another one was placed on the web within the zone of loading. Table 4.4 ? Strain gauge results Cycles to failure Flange Web Stress 0 17610 17050 290 At failure 60 17185 19370 290 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until deformation occurred; the stress-strain curve yielded a straight line as shown below: Stress vs Strain under cyclic loading @ constant stress 0 50 100 150 200 250 300 350 16500 17000 17500 18000 18500 19000 19500 Strain S tr es s Flange Web Figure 4.19 ? Stress-strain curve 88 Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at the end of the 60 cycle deformation. Top flange Flange 350W @ 184KN cyclic loading 17150 17200 17250 17300 17350 17400 17450 17500 17550 17600 17650 0 10 20 30 40 50 60 7 c 0 ycles to failure M ic ro st ra in Figure 4.20 ? Top flange As can be seen from the figure above, there was a sharp reduction after the 60 cycles of loading. This shows that the top flange was under compression. Web - B Web 350W @ 184KN cyclic loading 16500 17000 17500 18000 18500 19000 19500 0 10 20 30 40 50 60 7 Cycles to failure S tr ai n 0 Figure 4.21 ? Web B 89 Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. Failure Cycle: The beam failed by deformation at 60 cycles, which was approximately 1 minute of testing. Deformation of 30 mm maximum occurred at the centre of the beam. Figure 4.22 ? Specimen at failure 4.1.6 Grade 460W @ 0.75P Specimen 6 of Grade 350W was loaded with 184 KN at the midspan until failure. Moment determination: P = 184 KN P RBRA 1.25 m 1.25 m 90 KN KNP RA 922 184 2 === Maximum moment (moment @ midpoint), M460 = KNmmKNx 11525.192 = Stress determination: Considering the section at midspan directly under the point of loading where maximum stresses will be induced, as shown below. c I M midspan midspan =? Where: midspan? = maximum stress at midspan Mmidspan = Applied bending moment at midspan C = Distance from neutral axis to surface of the specimen I = Cross-sectional moment of inertia As already determined earlier, 433.28426233 mmI =? NmmxM midspan 610115= mmc 5.93= 100 16 mm 16 mm 187 155 16 mm y3 y1 y2 y 91 2 46 6 /378 1043.28 5.9310115 mmN mmx mmNmmxx midspan ==?? For minimum stress applied at midspan with P = 10 KN: Minimum moment @ midspan, Mmin = KNmmKNx 25.625.15 = 2 min /5.27 mmN=? 2 min 2 max /5.27 /378 mmN mmN = = ? ? ? 2minmax 2 minmax /75.202 2 5.405 2 , /5.350, mmNStressMean mmNRangeStress m ==+= =?=? ??? ??? 2/25.175 2 , mmNAmplitudeStress a =?= ?? Strain gauge results The strain values obtained during the experiment is shown below. The strain values were measured after 50 cycles at a frequency of 1 Hz when the structure deformed in its global axis. 1 strain gauge was affixed at the top flange while another one was placed on the web within the zone of loading. Table 4.4 ? Strain gauge results Cycles to failure Flange Web Stress 0 18310 17780 378 At failure 50 17420 19650 378 Since there were no changes in stresses, i.e. a constant stress was applied to the structure throughout the testing until deformation occurred; the stress-strain curve yielded a straight line as shown below: 92 Stress vs Strain under cyclic loading @ constant stress 0 50 100 150 200 250 300 350 400 17000 17500 18000 18500 19000 19500 20000 Strain S tr es s flange Web Figure 4.23 ? Stress-strain curve Relationship between Strain and cycles to failure The changes in strain were monitored periodically using the strain gauges during the experiment. Microstrains were read off at the end of the 50 cycle deformation. Top flange Flange 460W @ 184KN cyclic loading 17300 17400 17500 17600 17700 17800 17900 18000 18100 18200 18300 18400 0 10 20 30 40 50 6 cycle to failure M ic ro st ra in 0 Figure 4.24 ? Top flange 93 As can be seen from the figure above, there was a sharp reduction after the 60 cycles of loading. This shows that the top flange was under compression. Web - B Web 460W @ 184KN cyclic loading 17500 18000 18500 19000 19500 20000 0 10 20 30 40 50 6 Cycles to failure S tr ai n 0 Figure 4.25 ? Web B Also, there was a sharp increment of the specimen at the web as measured using the strain gauges. This shows that the web was under tension. Failure Cycle: The beam failed by deformation at 50 cycles, which was approximately 1 minute of testing. Deformation of 70 mm maximum occurred at the centre of the beam. Figure 4.26 ? Specimen at failure 94 4.2 FURTHER DISCUSSIONS 4.2.1 Cycles to failure It is observed that as the steel grades increase in yield stress with lower web depth, their cycle to failure reduces. As a summary, the tables below show the points and mode of failure for the various steel grades tested under the same load factor. Under 0.5P = 122KN Table 4.5 Steel Grades Failure Cycle Testing Time Comment 300W 1,200,000 333 hours Buckling 350W 786,000 218 hours Fracture 460W 182,400 51 hours Fracture Under 0.75P = 184KN Table 4.6 Steel Grades Failure Cycle Testing Time Comment 300W 322,023 89 hours Fracture 350W 60 1 minute Buckling 460W 50 50 seconds Buckling As already been indicated, all the beams have the same moment capacity but varies in section dimension. The thickness and the flange dimension of all the specimen were kept constant, only the depth of flanges were changed in other to achieve equal capacity. 4.2.2 Determination of stresses at the point of failure Stresses will be determined for 300W @ 184 KN, 350 @ 122 KN and 460W @ 122 KN which were the beams that failed by fracture. 95 300W @ 184 KN KNmmKNxM KN KN RR KNP BA 08.11424.192 92 2 184 184 24.1 == === = c I M 24.1 24.1 =? From previous calculations, 2 46 6 24.1 46 /2.247125 1069.57 1008.114 125 1069.57 mmNmmx mmx Nmmx mmc mmxI ==? = = ? 350W @ 122 KN KNmmKNxM KN KN RR KNP BA 1.6710.161 61 2 122 122 10.1 == === = 1.24 m 1.25 m 1.25 m 1.26 m P RB RA 1.10 m 1.25 m 1.25 m 1.40 m P RB RA 96 c I M 10.1 10.1 =? From previous calculations, 2 46 6 10.1 46 /3.1695.112 106.44 101.67 5.112 106.44 mmNmmx mmx Nmmx mmc mmxI ==? = = ? 460W @ 122 KN KNmmKNxM KN KN RR KNP BA 81.7321.161 61 2 122 122 21.1 == === = c I M 21.1 21.1 =? From previous calculations, 2 46 6 21.1 46 /2435.93 1043.28 1081.73 5.93 1043.28 mmNmmx mmx Nmmx mmc mmxI ==? = = ? Summarily, the moment and stress at the point of fracture as compared to the maximum moment and stresses applied at midspan are represented in the table below: 1.21 m 1.25 m 1.25 m 1.29 m P RB RA 97 Table 4.5 Specimen Maximum Moment @ midspan Moment at point of failure Maximum Stress @ midspan Stress at point of failure 300 @ 184 KN 115 KNm 114.08 KNm 249 N/mm2 247.2 N/mm2 350 @ 122 KN 76.25 KNm 67.1 KNm 192.3 N/mm2 169.3 N/mm2 460 @ 122 KN 76.25 KNm 73.81 KNm 251 N/mm2 243 N/mm2 Stress Table: Table 4.6 ? Stress Table Specimen Maximum Stress, ?max (N/mm2) Minimum Stress, ?min (N/mm2) Stress Range, ?? (N/mm2) Mean Stress, ?m (N/mm2) Stress Amplitude, ?m (N/mm2) 300@122KN 165 13.5 151.5 89.25 75.75 350@122KN 192.3 15.5 176.8 103.9 88.4 460@122KN 251 27.5 223.5 139.25 111.75 300@184KN 249 13.5 235.5 131.25 117.75 350@184KN 290 17.5 272.5 153.25 136.25 460@184KN 378 27.5 350.5 202.75 175.25 4.2.3 Relationship of graph curves As can be seen in the above graphs plotted, the behaviour of the strain gauge is similar to each other. All the strain measurements were similar (see figures 4.2, 4.8, 4.12, 4.16, 4.20 and 4.24), i.e. there was a visible contraction in length after the first 100,000 cycles of testing, then stabilization. This notably shows that the flanges were subjected to initial compression. The stabilization was a fluctuation between contractions and expansions as the beam was been dynamically loaded. This shows that the beam was experiencing both strain hardening and softening as it was been loaded. Also, all the strain gauges placed on the web, figures 4.3, 4.4, 4.5, 4.16, 4.9, 4.13, 4.17, 4.21 and 4.25 showed similar behaviour, i.e. there was 98 a visible expansion in length after the first 100,000 cycles of testing, then stabilization. This notably shows that the webs were subjected to initial tension. The stabilization was a fluctuation between contractions and expansions as the beam was been dynamically loaded. In other words, the beam was experiencing both strain hardening and softening as it was been loaded. The values of the strain gauges after failure seem outrageous and should be neglected in design analysis since they were obtained after failure. This was caused by a snap of the strain gauges since the failure instantaneously. 4.2.4 Relationship of the zone of failure As can be seen from the failure modes, all the specimens failed, whether fracture or deformation, within the zone of loading. The stresses induced at the point of failure where close to the maximum stresses induced at the midspan of the specimens. Even the specimen 1 (300W @ 122 KN) which failed by global buckling, the maximum deformation occurred at the zone of loading. 99