Giáo trình Strength of materials 2 - Nguyễn Hồng Mai

the cross-section of curved bar subjected to complicated load, which stress exits? 
Write formula to calculate. Present the condition of strength of curved bar subjected 
to complicated load and the way to solve three basic problems. 
Numerical problems 
Exercise 1: 
Draw bending moment diagram, longitudinal force diagram and shear force diagram of 
the following curved bars. 
 78 
Exercise 2: 
Determine the maximum tensile stress and the maximum compressive stress at 
dangerous section and the normal stress at the point A of dangerous section. 
Exercise 3: 
A cast iron ring has circular section as in the figure. 
Determine allowable load. Know that []tens = 6 kN/cm
2
; []comp = 10 kN/cm
2
; cho R = 
16 cm; d = 8 cm. 
M
 =
 P
r
r
45°
P
(a)
P
a
P
(b)
P
a= 12 cm
(c)
q = 200 N/m
P
P= 2.10 N 
3
a
a a
60
40
5
A
8
0
120
2
0
P
P
A B
A - B
r1 = 60 mm
d
P
A B
R
 79 
Exercise 4:A curved bar has rectangular section and it is subjected to load as in the figure. 
Know that P = 6 kN; q = 12 kN/m; a = 16 cm; 
4
3
h
b
 ; [] = 200 
MN/m
2
. 
Determine the dimension of cross-section. 
P
a
a
q
h
b
 80 
APPENDIX 1 – LABORATORY MANUAL 
TABLE OF CONTENTS 
The number of experiments: 05. The number of lessons: 05 
Ordi
nal 
No. 
EXPERIMENT PLACE 
THE 
NUMBER 
OF 
LESSONS 
PAGES NOTE 
1 
Determine the deflection of 
straight bar subjected to planely 
horizontal flexure 
118 - B5 01 
2 
Determine the critical load of 
straight bar subjected to axial 
compressive load 
118 - B5 01 
3 
Determine the displacement of 
the beam subjected to oblique 
bending 
118 – B5 01 
 81 
PART I - INTRODUCTION 
1. The general target of experiments of the subject 
Strength of materials as a basic subject in engineering field is defined as a branch of 
mechanics of deformable solids that deals with the behaviours of solid bodies subjected to 
various types of loadings. It provides the future civil engineers with the means of analyzing 
and designing so that all types of structures operate safely. 
The method to study Strength of materials is association between theory and 
experiments. The study by experiments not only decreases or replaces some complicated 
calculations but also raises assumptions to establish formulas and checks the accuracy of the 
results found by theory. 
The laboratory manual of Strength of materials is compiled in order to instruct 
students the most basic experiments of the subject. Hence, it helps students to get used to 
research method relying on experiments and understand the importance of experiments in 
study. 
2. General introduction about equipment in the laboratory 
The laboratory of Strength of materials has: versatilely tensile (compressive) machine, 
tensile (compressive) machine FM1000, torsion testing machine K5, two fatigue testing 
machines, two impact testing machines, deflection of 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 
 The experimental results of students are assessed by answering questions in class, 
observing students during the process of experiments and checking reports. 
5. The 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. 
 Experimen
tal curator 
Pham Thi Thanh 
 82 
PART II: DETAILED CONTENT OF EXPERIMENT 
LESSON 4 -DETERMINE THE DEFLECTION OF STRAIGHT BAR SUBJECTED 
TO PLANELY HORIZONTAL FLEXURE 
1.Thepurpose of experiment: 
 Determine the deflection and slope of the straight bar subjected to planely horizontal 
flexure by experiments. Hence, we can evaluate the accuracy of the deflection and slope 
calculated by theoretical methods. 
2. Theoretical content 
 To determine the deflection and slope of the beam subjected to planely horizontal 
flexure, we have the following methods: 
 - Indefinite integration method 
 - Initial parameter method 
 - Artificial load method 
 - Morh’s integration method associated with multiplying Veresaghin’s diagram. 
Use Morh’s integration method associated with multiplying Veresaghin’s diagram to calculate 
the deflection at B and the slope at A for the simple beam subjected to loads as in the figure 7. 
It is carried out by the following steps: 
 - Draw diagram Mx
m
 caused by the load. 
- Establish state “k” and draw diagram 
k
xM 
- Use Morh’s integration method associated 
with multiplying Veresaghin’s diagram, we 
have: 
x
3
x J48
2.
4
.
3
2
.
2
.
4
.
2
1
.
J
1
E
PlllPl
E
yB 





 
x
2
x
J16
3
1
.
2
.
4
.
2
1
3
2
.
2
.
4
.
2
1
J
1
E
Pl
lPllPl
E
A








Figure 7 
3. Experimental layout 
The gauge K1 determines the deflection at B. 
The gauge K2 measures the displacement a. 
The slope at A is calculated by a, e. 
e
a
arctgA  
4. Theprocedure of experiment 
- Assemble experimental layout. 
- Measure the dimensions of the bar: l, b, h, e. 
- Put loads P in turn, read and write indexes on 
gauges. 
Figure 8 
5. Experimental result 
The experimental result is written in the table below: 
 83 
Pi (N) 
th
By 
ex
By
th
A 
ex
A
%100
th
B
ex
B
th
B
y
yy
y

 %100th
A
ex
A
th
A




 
P1 = 4 
.... 
P5 = 20 
6. Comments 
 - Comment the accuracy of experimental result. 
 - Analyse reasons. 
LESSON5-BUCKLING OF COLUMNS 
1.Thepurpose of experiment: 
Determine critical load by experiments and observe the stability of the column 
subjected to axial compressive load. Compare and check again the formula to calculate 
critical load by theory. 
2. Theoretical content 
 Assume that there is the bar subjected to axial compressive load. The bar will be lost 
its stability as compressive load reaches critical load or compressive load is larger than critical 
load. Critical load is determined by Euler’s formula: 
2
min
2
)(
J
l
E
Pcr


 
In which: 
 E - modulus of elasticity about tension or compression 
 Jmin-the minimum moment of inertia 
 l -the length of bar 
 - the factor depending on supports 
 = 0.7  = 2 
3. Experimental layout 
Figure 9 
4. Theprocedure of experiment 
- Measure the dimensions of the bar:l1, b1, h1, l2, 
b2, h2. 
- Put loads P in turn until the bar is lost its stability. 
Write the value of the critical load of bar. 
5. Experimental result 
The experimental result is written in the table 
below: 
Layout ex
crP (N) 
th
crP (N) %100th
cr
ex
cr
th
cr
cr
P
PP
P

 
1 
2 
6. Comments 
 - Comment the accuracy of experimental result. 
 84 
 - Analyse reasons. 
LESSON 6-DETERMINE THE DEFLECTION OF THE BEAM SUBJECTED TO 
OBLIQUE BENDING 
1. ThePurpose of experiment: 
Determine the total deflection of the bar subjected to oblique bending by experiments. 
On that basis, we evaluate the accuracy of the total deflection determined by theory. 
2. Theoretical content 
 Consider the cantilever beam subjected to oblique bending as in the figure 10. 
Consider section at free end A: 22 Ay
A
xA fff  . Use the methods of determining the 
displacement (deflection) of the beam subjected to plane flexure, we get: 
y
3
J3
.sin.
E
lP
f Ax

 
.
J3
.cos.
x
3
E
lP
f Ay

 
In which: 
fyis the deflection at A following the direction y. 
f 
A
is the total deflection at A.Figure 10 
3. Experimental layout 
Figure 11 
The gauge K1 measures the deflection following the direction x. The gauge K2 measures the 
deflection following the direction y. After measuring fx, fy by experiments,we determine the 
value of total deflection: 
22
yx fff  
4.The Procedure of experiment 
- Measure the dimensions of cross-section: l, b, h. 
- Put loads P in turn, read and write indexes on gauges. 
5. Experimental result 
The experimental result is calculated and written in the table below: 
 85 
Pi (N) 
th
xf
ex
xf 
th
yf
exf y
th
totf 
ex
totf %100th
tot
ex
tot
th
tot
f
ff
f

 
P1 = 4 
.... 
P5 = 20 
6. Comments 
 - Comment the accuracy of experimental result. 
 - Analyse reasons. 
The sample of laboratory report 
The cover of laboratory report is published the same sample. The content of report is 
handwritten and framed. The content of report needs to present purpose, content, internal 
force diagram, used methods to calculate theory clearly. The layout of experiment, necessary 
dimensions, the methods of calculation and the results of experiments, comments about the 
accuracy of theoretic formula are presented obviously in the report. 
 86 
APPENDIX 02 
 VIETNAM MARITIME UNIVERSITY 
 Subject of Strength of materials 
PROPERTIES OF SHAPED STEEL 
I -Section 
OCT 8239-56 
The 
sign 
numb
er of 
secti
on 
Gravity 
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 
 87 
 VIETNAM MARITIME UNIVERSITY 
 Subject of Strength of materials 
PROPERTIES OF SHAPED STEEL 
C -Section 
OCT 8240-56 
The 
sign 
numb
er of 
secti
on 
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 
Z o 
 88 
1. THE INDEX OF 
The 
slenderness 
ratio 
Trị số  đối với 
Steel CT 
2,3,4 
Steel CT5 Alloy steel Cast iron Timber 
10 0,99 0,98 1 1 1 
20 0,96 0,95 0,95 0,91 0,97 
30 0,94 0,92 0,91 0,81 0,93 
40 0,92 0,89 0,87 0,69 0,87 
50 0,89 0,86 0,83 0,54 0,80 
60 0,86 0,82 0,79 0,44 0,71 
70 0,81 0,76 0,72 0,34 0,6 
80 0,75 0,7 0,65 0,26 0,48 
90 0,69 0,62 0,55 0,2 0,38 
100 0,6 0,51 0,43 0,16 0,31 
110 0,52 0,43 0,35 0,25 
120 0,45 0,36 0,3 0,22 
130 0,4 0,33 0,26 0,18 
140 0,36 0,29 0,23 0,16 
150 0,32 0,26 0,21 0,14 
160 0,29 0,24 0,19 0,12 
170 0,26 0,21 0,17 0,11 
180 0,23 0,19 0,15 0,10 
190 0,21 0,17 0,14 0,09 
200 0,19 0,16 0,13 0,08 
2. THE MATERIAL INDEX ( a, b) 
Material  
E 
( KN/cm
2
) 
a 
( KN/cm
2
) 
b 
( KN/cm
2
) 
Steel CT2, CT3, CT4 100 70 2.10
4
 31 0,114 
Steel CT5 100 72 2.10
4
 46,4 0,326 
Timber 70 40 10
3
 3,68 0,0265 
Cast iron 80 30 1,5.10
4
 77,6 0,415 
 THE INDEX OF 
 89 
 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 
5 6.13 48.1 23.1 1.94 36.6 2.44 9.52 1.25 41.5 1.74 
Z
o
b
b
d
xx
y
y
xo
xo
R
yo
yo
 90 
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 
 91 
12 32.5 255 602 4.21 957 5.43 248 2.76 1097 3.9 
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 
 92