Giáo trình Strength of materials 1 - Nguyễn Hồng Mai

 string measuring machine, torsion testing table, plane bending 
testing table, axial compression testing table. Besides, there are measuring equipments: calipers, ruler, 
steel cutting pliers 
3.Progress and time to deploy experiments 
 After finishing the chapter “Torsion in round shaft”, students start experimenting the first three 
lessons. After finishing the chapter “Buckling of columns”, students experiment the last two lessons. 
4.The assessment of the experimental results of students 
 Theexperimental results of students are assessed by answering questions in class, observing 
students during the process of experiments and checking reports. 
5.Preparation of students 
Before experimenting, students have to carefully study experiments. The leader of class 
prepares list of students, divide students into small groups and sends it to lecturer two weeks before 
experiments. 
 Experimental curator 
Pham Thi Thanh 
 93 
PART II: DETAILED CONTENT OF EXPERIMENT 
LESSON 1 - DETERMINETHE MECHANICAL PROPERTIES OF MATERIALS 
1. The purpose of experiment: 
 Find out relation between force and deformation when pulling or pushing a steel sample, know 
the way to determine themechanical properties of steel in particular and materials in general. The 
above mechanical properties of materials are the necessary figures to calculate strength. 
2. Theoretical content 
 We prepare a steel sample as in the figure 1. 
Figure 1 
 lo-the initial length of sample 
 do - the initial diameter of sample 
Area of cross-section is: 
4
2
0
0
d
F

 
Carry out experiment pulling the sample on experimental machine until the sample is cut. We 
get the graph expressing relationship between P and l as shown in the figure 2. According to the 
graph, we can divide the load-resistant procedure of the sample into three stages: 
Figure 2 
 - Proportional stage (elastic stage): The diagram begins with a straight line from the origin O to 
point A,which means that the relationship between load P and deformation l in this initial region is 
not only linear but also proportional. Beyond point A, the proportionality between stress and strain no 
longer exists; hence the force at A is called the proportional force Ppr. The proportional stress is 
0F
Ppr
pr  
 - Yielding stage: With an increase in load beyond the proportional limit, the deformation 
begins to increase more rapidly for each increment in load. Consequently, the load-deformation curve 
has a smaller and smaller slope, until, at point B, the curve becomes horizontal. Beginning at this 
point, theconsiderable elongation of the test specimen occurs with no noticeable increase in the tensile 
force (from B to C). This phenomenon is known as theyielding stageof the material, and point B is 
called the yieldingpoint. The maximum load in this stage is signed Pyiel. The corresponding stress is 
 94 
known as the yielding stress of the steel 
0F
Pyiel
yiel  . In the region from B to C, the material becomes 
perfectly plastic, which means that it deforms without an increase in the appliedload. 
 - Ultimate stage: After undergoing the large deformations that occur during yielding stage in 
theregion BC, the steel begins to strain harden. During deformation hardening, thematerial undergoes 
changes in its crystalline structure, resulting in the increased resistance of the material to further 
deformation. The elongation of the test specimen in this region requires an increase in the tensile load, 
and therefore the load-deformation diagram has a positive slope from C to D. The load eventually 
reaches its maximum value, and the correspondingload (at point D) is called the ultimate load Pulti. The 
corresponding stress is known as the ultimate stress of the steel 
0F
Pulti
ulti  . Further stretching of the 
bar is actually accompanied by a reduction in the load, and fracture finally occurs at a point such as E 
in Fig. 2. 
 When a test specimen is stretched, lateral contraction occurs. The resulting decrease in cross-
sectional area is too small to have a noticeable effect on the calculated thevalues of thestresses up to 
about point C in Fig 2.2, but beyond that point the reduction in area begins to alter the shape of the 
curve. In the vicinity of the ultimate stress, the reduction in area of the bar becomes clearly visible and 
a pronounced necking of the bar occurs (see Figure 3). 
Figure 3 
 pr, yie, ultiare characteristics for ductility of materials. Besides, in case of ductile materials 
when pulled, we can find two characteristics forthe plasticity of materials  and . They are 
determined as below: 
The extension inthe length of the specimen after fracture to its initial gauge length: 
 %100.
0
01
l
ll 
 
The percent reduction in area measuring the amount of necking that occurs: %100.
0
10
F
FF 
 
3. Experimenting machine 
 Use versatilely tensile (compressive) machine made in Germany. Its model is FM-1000. The 
maximum tensile force is 1000kG  10kN and it is driven by hydraulic power. Tensile (compressive) 
machine has two cantilevers used to keep sample during the process of tension. The upper cantilever is 
fixed while the lower cantilever can be mobile. Force measuring gauge and graph drawing equipment 
express relationship between P and l. 
4. The procedure of experiment 
- Measure initial diameter do and markthe initial length of sample lo = 10cm as the figure. 
 - Fix sample in two cantilevers of the machine, check thework of every part of the machine, 
control hand to return position “0”. 
 - Supply electric for the machine and control cantilever to the position marked on the sample. 
 - Begin pulling the sample, observe the process of pulling until the sample is cut, read thevalues 
Ppr, Pyiel, Pultion force measuring gauge. 
 95 
 - Take the sample out of two cantilevers of the machine, keep the line marked on the sample. 
Measure dimensions l1, d1 again after pulling. 
 + Measure l1: Attach two parts of the sample cut together and measure distance l1 among two lines 
marked. 
 + Measure d1: Diameter d1 is measured at the position which the sample is cut. Hence, we can 
calculate F1. 
5. Experimental result 
 After calculating, theexperimental result is written in the following table: 
Sample 
l1 
(cm) 
d1 
(cm) 
Ppr 
(kN) 
Pyiel 
(kN) 
Pulti 
(kN) 
pr 
(kN/cm
2
) 
yiel 
(kN/cm
2
) 
ulti 
(kN/cm
2
) 
 (%)  (%) 
Sample 1 
Sample 2 
Sample 3 
6. Comments 
 - Compare properties about the strength of the sample with the properties of steel CT3 when 
pulled. 
 - Comment the deformation and diameter of the sample after pulling in comparison with the 
initial sample. 
LESSON 2 - DETERMINE THE DEFORMATION OF THE ROUND SHAFT SUBJECTED TO 
TORSION 
1. The purpose of experiment: 
 Determine relative angle of twist of the round shaft subjected to torsion through experiment. 
Hence, we can evaluate the accuracy of theoretical formula. 
2. Theoretical content 
 When a round shaft is subjected to torsion, relative angle of twist among two cross-sections of 
shaft is determined by equation: 
* In general case: 
Shaft has many segments, Mz, GJp vary continuously on each segment. 
dz
GJ
M
i
n
i
l
p
z
i











1 0
 
In which: Mzis internal torque. 
 G is modulus of rigidity (shear modulus) of material. The sample is made from steel CT3 
having G = 8.10
6
kN/cm
2
 Jpis polar moment of inertia of cross-section. In case of hollow circular shaft, Jis determined:
)1(
32
4
4



D
J p 
 liis the length of segment i. 
* In particular case: 
Shaft has many segments, Mz, GJp are constant on each segment. 
 96 
i
n
i p
z
GJ
lM











1
 
4. Experimental layout 
 K1 
 K2 
1. Hollow circular shaft 
2. Gauge K1 
3. Gauge K2 
4. Arm 
5. Bracket to put load
Figure 4 
 Thanks tothe impact of the load P, shaft is deformed and cross-sections are rotated. At the 
section B and C, brackets e1, e2 are also rotated corresponding angles B và C. Hence, the gauges K1, 
K2 will point corresponding displacements h1 and h2. Angles of twist at the section B and C are 
determined through h1, h2, e1, e2. 
;
1
1
e
h
arctgB 
2
2
e
h
arctgC  
4. The procedure of experiment 
 - Assemble experimental layout. 
- Measure the dimensions of shaft: l1, l2, d, D, e1, e2, a. 
- Put loads in turn, read and write indexes on gauges. 
5. Experimental result 
 97 
li Pi (N) 
Mzi 
(Nmm) 
hi (mm) ith iex %100
ith
iexith




 
l1 = 
P1 = 10 
... 
P5 = 50 
On 
P1=10 
... 
P5= 50 
6. Comments 
 - Commentthe accuracy of experimental result. 
 - Analyse reasons. 
LESSON3-DETERMINE THE DEFLECTION OF THE SPRING HELICAL, 
CYLINDRICAL, HAVING SMALL PITCH 
1. The purpose of experiment: 
 Determine the deflection of the spring helical, cylindrical, having small pitch through 
experiment. Hence, we can evaluate the accuracy of theoretical formula. 
2. Theoretical content 
Consider the spring helical, cylindrical, having small pitch, diameter of spring 
coil D, diameter of spring wire d and number of coils n. If we compress spring by a 
force P, deflection is determined by equation: 
4
38
Gd
nPD
 (mm, cm) 
3. Experimental layout 
 When load P cause compressive deformation for spring, gauge K measures 
corresponding value of deflection . Figure 54. The 
procedure of experiment 
- Determine the parameters of spring: D, d, n 
- Assemble and control hand to return to the position “0” of the gauge. 
- Put load P in turn, read and write the corresponding value of deflection on 
gauges. 
Figure 6 
5.Experimental result 
The process of calculating values  is written in the following table: 
 98 
Pi (N) 
th
i 
(mm) 


n
i
th
i
1
 
ex
i 
(mm) 


n
i
ex
i
1
 %100.
1
1 1

 

 


n
i
th
i
n
i
n
i
ex
i
th
i


 
P1 = 5 
... 
P8 = 40 
6. Comments 
 - Commentthe accuracy of experimental result. 
 - Analyse reasons. 
 99 
APPENDIX 
 VIETNAM MARITIME UNIVERSITY 
 Subject of Strength of materials 
PROPERTIES OF SHAPED STEEL 
I -Section 
OCT 8239-56 
The 
sign 
numb
er of 
sectio
n 
Gravit
y 
N/m 
Dimensions ( mm ) 
The 
area 
of 
sectio
n cm
2
The properities of area 
h 
b 
d 
t 
R 
r 
x-x y-y 
Jx 
cm
4
Wx 
cm
3
ix 
cm 
Sx 
cm
3
Jy 
cm
4
Wy 
cm
3
iy 
cm 
10 111 100 70 4,5 7,2 7,0 3,0 14,2 244 48,8 4,15 28,0 35,3 10 1,58 
12 130 120 75 5,0 7,3 7,5 3,0 16,5 403 67,2 4,94 38,5 43,8 11,7 1,63 
14 148 140 82 5,0 7,5 8,0 3,0 18,9 632 90,3 5,78 51,5 58,2 14,2 1,75 
16 169 160 90 5,0 7,7 8,5 3,5 21,5 945 118 6,63 67,0 77,6 17,2 1,90 
18 187 180 95 5,0 8,0 9,0 3,5 23,8 1330 148 4,47 83,7 94,6 19,9 1,99 
18a 199 180 102 5,0 8,2 9,0 3,5 25,4 1440 160 5,53 90,1 119 23,3 2,06 
20 207 200 100 5,2 8,2 9,5 4,0 26,4 1810 181 8,27 102 112 22,4 2,17 
20a 222 200 110 5,2 8,3 9,5 4,0 28,3 1970 197 8,36 111 148 27,0 2,29 
22 237 220 110 5,3 8,6 10,0 4,0 30,2 2530 230 9,14 130 155 28,2 2,26 
22a 254 220 120 5,3 8,8 10,0 4,0 32,4 2760 251 9,23 141 203 33,8 2,50 
24 273 240 115 5,6 9,5 10,5 4,0 34,8 3460 289 9,97 163 198 34,5 2,37 
24a 294 240 125 5,6 9,8 10,5 4,0 37,5 3800 317 10,1 178 260 41,6 2,63 
27 315 270 125 6,0 9,8 11,0 4,5 40,2 5010 371 11,2 210 260 41,5 2,54 
27a 339 270 135 6,0 10,2 11,0 4,5 43,2 5500 407 11,3 229 337 50,0 2,80 
30 365 300 135 6,5 10,2 12,0 5,5 46,5 7080 472 12,3 268 337 49,9 2,69 
30a 392 300 145 6,5 10,7 12,0 5,5 49,9 7780 518 12,5 292 346 60,1 2,95 
33 422 330 140 7,0 11,2 13,0 5,5 53,8 9840 597 13,5 339 419 59,9 2,79 
36 486 360 145 7,5 12,3 14,0 6,0 61,9 13380 743 14,7 423 516 71,1 2,89 
40 561 400 155 8,0 13,0 15,0 6,0 71,9 18930 974 16,3 540 666 75,9 3,05 
45 652 450 160 8,6 14,2 16,0 7,0 83,0 27450 1220 18,2 699 807 101 3,12 
50 761 500 170 9,3 15,2 17,0 7,0 96,9 39120 1560 20,1 899 1040 122 3,28 
55 886 550 180 10,0 16,5 18,0 7,0 113 54810 1990 20,2 1150 1350 150 3,46 
60 1030 600 190 10,8 17,8 20,0 8,0 131 75010 2500 23,9 1440 1720 181 3,62 
65 1190 650 200 11,7 19,2 22,0 9,0 151 100840 3100 25,8 1790 2170 217 3,79 
70 1370 700 210 12,7 20,8 24,0 10,0 174 133890 3830 27,7 2220 2730 260 3,76 
70a 1580 700 210 15,0 24,0 24,0 10,0 202 152700 4360 27,5 2550 3240 309 4,01 
70b 1840 700 210 17,5 28,2 24,0 10,0 234 175350 5010 27,4 2940 3910 373 4,09 
t 
R r 
x 
y 
h 
b 
d 
 100 
 VIETNAM MARITIME UNIVERSITY 
 Subject of Strength of materials 
PROPERTIES OF SHAPED STEEL 
C -Section 
OCT 8240-56 
The 
sign 
numbe
r of 
section 
Gravity 
 N/m 
Dimensions ( mm ) The 
area of 
section
s cm
2
The properties of area 
 Z0 
h 
b 
d 
t 
R 
r 
x-x y-y 
Jx 
cm
4
Wx 
cm
3
ix 
cm 
Sx 
cm
3
Jy 
cm
4
Wy 
cm
3
iy 
cm 
 6 54,2 50 37 4,5 7,0 6,0 2,5 6,90 26,1 10,4 1,94 6,36 8,41 3,59 1,10 1,36 
6,5 65,0 65 40 4,5 7,4 6,0 2,5 8,28 54,5 16,8 2,57 10,0 11,9 4,58 1,20 1,40 
8 77,8 80 45 4,8 7,4 6,5 2,5 9,91 99,9 25,0 3,17 14,8 17,8 5,89 1,34 1,48 
10 92,0 100 50 4,8 7,5 7,0 3,0 11,7 187 37,3 3,99 21,9 25,6 7,42 1,48 1,55 
12 108,0 120 54 5,0 7,7 7,5 3,0 13,7 313 52,2 4,78 30,5 34,4 9,01 1,58 1,59 
14 123,0 140 58 5,0 8,0 8,0 3,0 15,7 489 69,8 5,59 40,7 45,1 10,9 1,70 1,66 
14a 132,0 140 62 5,0 8,5 8,0 3,0 16,9 538 76,8 5,65 44,6 56,6 13,0 1,83 1,84 
16 141,0 160 64 5,0 8,3 8,5 3,5 18,0 741 92,6 6,42 53,7 62,6 13,6 1,87 1,79 
16a 151,0 160 68 5,0 8,8 8,5 3,5 19,3 811 101 6,48 58,5 77,3 16,0 2,00 1,98 
18 161,0 180 70 5,0 8,7 9,0 3,5 20,5 1080 120 7,26 69,4 85,6 16,9 2,04 1,95 
18a 172,0 180 74 5,0 9,2 9,0 3,5 21,9 1180 131 7,33 75,2 104 19,7 2,18 2,13 
20 184,0 200 76 5,2 9,0 9,5 4,0 23,4 1520 152 8,07 87,8 113 20,5 2,20 2,07 
20a 196,0 200 80 5,2 9,9 9,5 4,0 25,0 1660 166 8,15 95,2 137 24,0 2,34 2,57 
22 209,0 220 82 5,3 9,9 10,0 4,0 26,7 2120 193 8,91 111 151 25,4 2,38 2,24 
22a 225,0 220 87 5,3 10,2 10,0 4,0 28,6 2320 211 9,01 121 186 29,9 2,55 2,47 
24 240,0 240 90 5,6 10,0 10,5 4,0 30,6 2900 242 9,73 139 208 31,6 2,60 2,42 
24a 258,0 240 95 5,6 10,7 10,5 4.0 32,9 3180 265 9,84 151 254 37,2 3,78 2,67 
27 277,0 270 95 6,0 10,5 11 4,5 35,2 4160 308 10,9 178 262 37,3 2,73 2,47 
30 318,0 300 100 6,5 11,0 12 5,0 40,5 5810 387 12,0 224 327 43,6 2,84 2,52 
33 365,0 330 105 7,0 11,7 13 5,0 46,5 7980 484 13,1 281 410 51,8 2,97 2,59 
36 419,0 360 110 7,5 12,6 14 6,0 53,4 10820 601 14,2 350 513 61,7 3,10 2,68 
40 483,0 400 115 8,0 13,5 15 6,0 61,5 15220 761 15,7 444 642 73,4 3,23 2,75 
y 
x 
r 
R 
t 
d 
b 
h 
o Z 
 101 
 VIETNAM MARITIME UNIVERSITY 
 Subject of Strength of materials 
 PROPERTIES OF SHAPED STEEL 
 Equal angle steel 
OCT 8240-56 
The sign 
number 
of 
section 
Dimensions, mm 
The area 
of 
section 
cm
2
Gravity 
per 
meter 
N 
The properties of area 
b d r R 
x - x y - y yo - yo x0 – x0 
Jx 
cm
4
ix 
 cm 
Jxomax 
 cm
4
ixomax 
 cm 
Jxomin 
 cm
4
ixomin 
 cm 
Jxomax 
 cm
4
Zo 
cm 
2 20 
3 
3.5 1.2 
1.13 8.9 0.4 0.59 0.63 0.75 0.17 0.39 0.81 0.6 
4 1.46 11.5 0.5 0.58 0.78 0.73 0.22 0.38 1.09 0.64 
2.5 25 
3 
3.5 1.2 
1.43 11.2 0.81 0.75 1.29 0.95 0.34 0.49 1.57 0.73 
4 1.86 14.6 1.03 0.74 1.62 0.93 0.44 0.48 2.11 0.76 
2.8 28 3 4 1.3 1.62 12.7 1.16 0.85 1.84 1.07 0.48 0.55 2.2 0.8 
3.2 32 
3 
4.5 1.5 
1.86 14.6 1.77 0.97 2.8 1.23 0.74 0.63 3.26 0.89 
4 2.43 19.1 2.26 0.96 3.58 1.21 0.94 0.62 4.39 0.94 
3.6 36 
3 
4.5 1.5 
2.1 16.5 2.56 1.1 4.06 1.39 1.06 0.71 4.64 0.99 
4 2.75 21.6 3.29 1.09 5.21 1.38 1.36 0.7 6.24 1.04 
4 40 
3 
5 1.7 
2.35 18.5 3.55 1.23 5.63 1.55 1.47 0.79 6.35 1.09 
4 3.08 24.2 4.58 1.22 7.26 1.53 1.9 0.78 8.53 1.13 
4.5 45 
3 
5 1.7 
2.65 20.8 5.13 1.39 8.13 1.75 2.12 0.89 9.04 1.21 
4 3.48 27.3 6.63 1.38 10.05 1.74 2.74 0.89 12.1 1.26 
5 4.29 33.7 8.03 1.37 12.7 1.72 3.33 0.88 15.3 1.3 
5 50 
3 
5.5 1.8 
2.96 23.2 7.11 1.55 11.3 1.95 2.95 1 12.4 1.33 
4 3.89 30.5 9.21 1.54 14.6 1.94 3.8 0.99 16.6 1.38 
5 4.8 37.7 11.2 1.53 17.8 1.92 4.63 0.98 20.9 1.42 
5.6 56 
3.5 
6 2 
3.66 30.3 11.6 1.73 18.4 2.18 4.8 1.12 20.3 1.5 
4 4.38 34.4 13.1 1.73 20.8 2.18 5.41 1.11 23.3 1.52 
5 5.41 42.5 16 1.72 25.4 2.16 6.59 1.1 29.2 1.57 
6 63 4 7 2.3 4.96 39 18.9 1.95 29.9 2.45 7.81 1.25 33.1 1.69 
Z
o
b
b
d
xx
y
y
xo
xo
R
yo
yo
 102 
5 6.13 48.1 23.1 1.94 36.6 2.44 9.52 1.25 41.5 1.74 
6 7.28 57.2 27.1 1.93 42.9 2.43 11.2 1.24 50 1.78 
7 70 
4.5 
8 2.7 
6.2 48.7 29 2.16 46 2.72 12 1.39 51 1.88 
5 6.86 53.8 31.9 2.16 50.7 2.72 13.2 1.39 56.7 1.9 
6 8.15 63.9 37.6 2.15 59.6 2.71 15.5 1.38 68.4 1.94 
7 9.42 73.9 43 2.14 68.2 2.69 17.8 1.37 80.1 1.99 
8 10.7 83.7 48.2 2.13 76.4 2.68 20 1.37 91.9 2.02 
7.5 75 
5 
9 3 
7.39 58 39.5 2.31 62.6 2.91 16.4 1.49 69.6 2.02 
6 8.78 68.9 46.6 2.3 73.9 2.9 19.3 1.48 83.9 2.06 
7 10.1 79.6 53.3 2.29 84.6 2.89 22.1 1.48 98.3 2.1 
8 11.5 90.2 59.8 2.28 94.9 2.87 24.8 1.47 113 2.15 
9 12.8 101 66.1 2.27 105 2.86 27.5 1.46 127 2.18 
8 80 
5.5 
9 3 
8.63 67.8 52.7 2.47 83.6 3.11 21.8 1.59 93.2 2.17 
6 9.38 73.6 57 2.47 90 3.11 23.5 1.58 102 2.19 
7 10.8 85.1 65.3 2.45 104 3.09 27 1.58 119 2.23 
8 12.3 96.5 73.4 2.44 116 3.08 30.3 1.57 137 2.27 
9 90 
6 
10 3.3 
10.6 83.3 82.1 2.78 130 3.5 34 1.79 1.45 2.43 
7 12.3 96.4 94.3 2.77 150 3.49 38.9 1.78 1.69 2.47 
8 13.9 109 106 2.76 168 3.48 43.8 1.77 1.94 2.51 
9 15.6 122 118 2.75 186 3.46 48.6 1.77 2.19 2.55 
10 100 
6.5 
12 4 
12.8 101 122 3.09 193 3.88 50.7 1.99 214 2.68 
7 13.8 108 131 3.08 207 3.88 54.2 1.98 231 2.71 
8 15.6 122 147 3.07 233 3.87 60.9 1.98 265 2.75 
10 19.2 151 179 3.05 284 3.84 74.1 1.96 330 2.83 
12 22.8 179 209 3.03 331 3.81 86.9 1.95 402 2.91 
14 26.3 206 237 3 375 3.78 99.3 1.94 472 2.99 
16 29.7 233 264 2.98 416 3.74 112 1.94 542 3.06 
11 110 
7 
12 4 
15.2 119 176 3.4 279 4.29 72.7 2.19 308 2.96 
8 17.2 135 198 3.39 315 4.28 81.8 2.18 353 3 
12.5 125 
8 
14 4.6 
19.7 155 294 3.87 467 4.87 122 2.49 516 3.36 
9 22 173 327 3.86 520 4.86 135 2.48 582 3.4 
10 24.3 191 360 3.85 571 4.84 149 2.47 649 3.45 
12 28.9 227 422 3.82 670 4.82 174 2.46 782 3.53 
14 33.4 262 482 3.8 764 4.78 211 2.45 916 3.61 
16 37.8 296 539 3.78 853 4.75 224 2.44 1051 3.68 
14 140 
9 
14 4.6 
24.7 194 466 4.34 739 5.47 192 2.79 818 3.78 
10 27.3 215 512 4.33 814 5.46 211 2.78 914 3.82 
12 32.5 255 602 4.21 957 5.43 248 2.76 1097 3.9 
 103 
16 160 
10 
16 5.3 
31.4 247 774 4.96 1229 6.25 319 3.19 1356 4.3 
11 34.4 270 844 4.95 1341 6.24 348 3.18 1494 4.35 
12 37.4 294 913 4.94 1450 6.23 376 3.17 1633 4.39 
14 43.3 340 1046 4.92 1662 6.2 431 3.16 1911 4.47 
16 49.1 385 1175 4.89 1866 6.17 485 3.14 2191 4.55 
18 54.8 430 1299 4.87 2061 6.13 537 3.13 2472 4.63 
20 60.4 474 1419 4.85 2248 6.1 589 3.12 2756 4.7 
18 180 
11 
16 5.3 
38.8 305 1216 5.6 1933 7.06 500 3.59 2128 4.85 
12 42.2 331 1317 5.59 2093 7.04 540 3.58 2324 4.89 
20 200 
12 
18 6 
47.1 370 1823 6.22 2896 7.84 749 3.99 3182 5.37 
13 50.9 399 1961 6.21 3116 7.83 805 3.98 3452 5.42 
14 54.6 428 2097 6.2 3333 7.81 861 3.97 3722 5.46 
16 62 487 2326 6.17 3755 7.78 970 3.96 4264 5.54 
20 76.5 601 2871 6.12 4560 7.72 1182 3.93 5355 5.7 
25 94.3 740 3466 6.06 5494 7.63 1432 3.91 6733 5.89 
30 111.5 876 4020 6 6351 7.55 1688 3.89 8130 6.07 
22 220 
14 
21 7 
60.4 474 2814 6.83 4470 8.6 1159 4.38 4941 5.93 
16 68.6 538 3157 6.81 5045 8.58 1306 4.36 5661 6.02 
25 250 
16 
24 8 
78.4 615 4717 7.76 7492 9.78 1942 4.98 8286 6.75 
18 87.7 689 5247 7.73 8337 9.75 2158 4.96 9342 6.83 
20 97 761 5765 7.71 9160 9.72 2370 4.94 10401 6.91 
22 116.1 833 6270 7.69 9961 9.69 2579 4.93 11464 7 
25 119.7 940 7006 7.65 11125 9.64 2887 4.91 13064 7.11 
28 133.1 1045 7717 7.61 12244 9.59 3190 4.89 14674 7.23 
30 142 1114 8117 7.59 12965 9.56 3389 4.89 15753 7.31 
 104 
 105