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N f cd f yd E s b h d' A
Mechanical Characteristics Cross Section
kN N/mm N/mm N/mm mm mm mm mm
0 13,33 365 200000 300 700 50 12
C12-C25 C30 C35 C40 C45 C50
k 0,85 0,82 0,79 0,76 0,73 0,7
k 0,851
assume
mm/mm mm N/mm2
N/mm3
N/m
N ci c s1 E s x s s1 s2 E s x
0 0,00025 114,0 -1,18E-03 -235,09 -235,09 1,40E-04 2
0,0005 149,0 -1,68E-03 -336,24 -336,24 3,32E-04 6
, , - , - - , - , , -
0,0015 162,0 -4,52E-03 -903,70 -365,00 1,04E-03 20
0,0020 144,0 -7,03E-03 -1405,56 -365,00 1,31E-03 26
0,0025 127,0 -1,03E-02 -2059,06 -365,00 1,52E-03 30
0,0030 113,0 -1,43E-02 -2851,33 -365,00 1,67E-03 33
0,0035 103,0 -1,86E-02 -3717,48 -365,00 1,80E-03 36
0,0040 101,0 -2,17E-02 -4348,51 -365,00 2,02E-03 40
the given val
steel reinforc
CE3001 HW.I / Problem 1)
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positive:::: compression
kN kN kN kN kN kN rad/m kN
Fs1 Fs2 Fs3 Fs4 Fc total F k M
0 0
-282,105 33,684 -82,807 0,000 329,378 -1,850 2,19E-03 194
-403,490 79,732 -107,919 0,000 430,502 -1,176 3,36E-03 268
- , , - , , , - , , -
-438,000 248,889 -278,519 0,000 468,063 0,433 9,26E-03 337
-438,000 313,333 -292,000 0,000 416,056 -0,611 1,39E-02 345
-438,000 363,780 -292,000 0,000 366,938 0,718 1,97E-02 349
-438,000 401,416 -292,000 0,000 326,488 -2,096 2,65E-02 350
-438,000 432,233 -292,000 0,000 297,596 -0,171 3,40E-02 352
-438,000 438,000 -292,000 0,000 291,817 -0,183 3,96E-02 352
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hw11a
hw11b
350
400
hw11a
250
300
350
n t
( M -
k N . m
)
150
200
M o m e n t
( M -
0
50
100
0
0 0,005 0,01 0,015 0,02 0,025 0,03 0,035
Curvature (k - rad/m)
b denotes to case with two intermediate lev
reinforcement
a denotes to case with one intermediate le
reinforcement
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f ck f cd f yk f yd E s b h d' As1
N/mm2
N/mm3
N/mm2
N/mm3
N/mm2 mm mm mm mm
Mechanical Characteristics Cross Section
, ,
C12-C25 C30 C35 C40 C45 C50
k 0,85 0,82 0,79 0,76 0,73 0,7
k1
0,82
c 0,003
sy 0,001826 negative:::: tension
su 0,1 positive:::: compression
Nor 5197,487
bottom top int-1 int-2 int-3 concrete actual c Fs1 Fs2 Fs3 Fs4 Fs5 Fc N M
kN kN kN kN kN kN kN kN.m
, ,
800 -53,14 517,21 34,65 80,85 112,42 2788,00 3479,99 583,8
700 -182,19 517,21 13,20 66,00 112,42 2439,50 2966,14 697,2
600 -354,25 517,21 -15,40 46,20 107,80 2091,00 2392,56 799,7
500 -517,21 517,21 -55,44 18,48 92,40 1742,50 1797,94 870,2
- , , - , - , , , , ,
300 -517,21 517,21 -112,42 -92,40 30,80 1045,50 871,48 784,2
200 -517,21 517,21 -112,42 -112,42 -46,20 697,00 425,96 683,5
150 -517,21 517,21 -112,42 -112,42 -112,42 522,75 185,49 616,8
100 -517,21 425,10 -112,42 -112,42 -112,42 348,50 -80,87 519,4
50 -517,21 0,00 -112,42 -112,42 -112,42 174,25 -680,22 281,7
balanced 528 -517,21 517,21 -42,70 27,30 97,30 1840,08 1921,98 871,4
M f 111 -517,21 467,23 -112,42 -112,42 -112,42 386,84 -0,40 550,2
As3 x3 As4 x4 As5 x5
mm2 mm mm
2 mm mm2 mm
-
Steel Reinforcement
Intermediate - I Intermediate - II Intermediate - III
-
the given values
moment interacti
the cross-section
about x-x axis
CE 3001 HW I
Problem 2)
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c sb Esx s1 s1 s2 Esx s2 s2 s3 Esx s3 s3
800 -0,0001875 -37,5 -37,5 0,0028125 562,5 365,0 0,0005625 112,5 112,
- - -- , - , - , , , , , , ,
600 -0,0012500 -250,0 -250,0 0,0027500 550,0 365,0 -0,0002500 -50,0 -50,
500 -0,00 21000 -420,0 -365,0 0,0027000 540,0 365,0 -0,0009000 -180,0 -180
400 -0,00 33750 -675,0 -365,0 0,0026250 525,0 365,0 -0,0018750 -375,0 -3 65
300 -0,00 55000 -1100,0 -365,0 0,0025000 500,0 365,0 -0,0035000 -700,0 -365
200 -0,00 97500 -1950,0 -365,0 0,0022500 450,0 365,0 -0,0067500 -1350,0 -365
150 -0,01 40000 -2800,0 -365,0 0,0020000 400,0 365,0 -0,0100000 -2000,0 -365
100 -0,02 25000 -4500,0 - 365,0 0, 00150 00 300, 0 3 00,0 -0,01 65000 -3300,0 -365
50 -0,0480000 -9600,0 -365,0 0,0000000 0,0 0,0 -0,0360000 -7200,0 -365
balanced 528 -0,00 18295 -365,9 -365,0 0,0027159 543,2 365,0 -0,0006932 -138,6 -138
M f 111 -0,01 99730 -3994,6 - 365,0 0, 00164 86 329, 7 3 29,7 -0,0 145676 -2913,5 -365
s1 s2 s3 s4 s5
can not exceed f yd
s5 Esx s5 s5
0,0020625 412,5 365,0
, , ,0,0017500 350,0 350,0
0,0015000 300,0 300,0
0,0011250 225,0 225,0
0,0005000 100,0 100,0
- 0, 0007500 -150,0 - 150, 0
-0,0020000 -400,0 -365,0
-0,0045000 -900,0 -365,0
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6000
M-N interaction diagram
4000
5000hw12x
hw12y
design
3000
4000
N (
k N )
design
x
c N M
mm kN kN.m
Nor 5197,49 0,001000
2000
N
800 3479,99 583,8
700 2966,14 697,2
600 2392,56 799,7
500 1797,94 870,2
400 1327,78 848,7
0
1000
0 100 200 300 400 500 600 700 800 900 1000
300 871,48 784,2
200 425,96 683,5
150 185,49 616,8100 -80,87 519,4
-
M (kN.m)
- , ,
balanced 528 1921,98 871,4
Mf 111 -0,40 550,2
moment about x
axis
moment about y-yaxis
if the given design axial load-moment pair is given for a bending about
then, the cross-section is adequate. however, if the pair is given for a b
about y-y axis, then the cross-section can not carry the given design lo
N = 150 kN , M = 150kN.m
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f ck f cd f yk f yd E s b h d' As1
N/mm2
N/mm3
N/mm2
N/mm3
N/mm2 mm mm mm mm
Mechanical Characteristics Cross Section
, ,
C12-C25 C30 C35 C40 C45 C50
k1
0,85 0,82 0,79 0,76 0,73 0,7
k1
0,85
c 0,003
sy 0,001826 negative:::: tension
su 0,1 positive:::: compression
Nor 3727,536
bottom top int-1 int-2 int-3 concretec Fs1 Fs2 Fs3 Fs4 Fs5 Fc N M
kN kN kN kN kN kN kN kN.m
3727 54 0 00
actual
, ,
400 112,50 547,50 300,00 0,00 0,00 1926,67 2886,67 123,0
350 0,00 547,50 257,14 0,00 0,00 1685,83 2490,48 168,5
325 -69,23 547,50 230,77 0,00 0,00 1565,42 2274,46 189,3
300 -150,00 547,50 200,00 0,00 0,00 1445,00 2042,50 209,3
- , , , , , , , ,
250 -360,00 547,50 120,00 0,00 0,00 1204,17 1511,67 249,0
200 -547,50 547,50 0,00 0,00 0,00 963,33 963,33 275,0
150 -547,50 547,50 -200,00 0,00 0,00 722,50 522,50 262,6
100 -547,50 450,00 -365,00 0,00 0,00 481,67 19,17 225,4
50 -547,50 0,00 -365,00 0,00 0,00 240,83 -671,67 125,
balanced 217 -547,50 547,50 47,00 0,00 0,00 1045,22 1092,22 276,9
M f 98 -547,50 440,82 -365,00 0,00 0,00 472,03 0,35 222,9
As3 x3 As4 x4 As5 x5
mm2 mm mm
2 mm mm2 mm
Steel Reinforcement
Intermediate - I Intermediate - II Intermediate - III
CE3001 HW I
Problem 3)
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3500
4000M-N interaction diagram
2500
3000
3500
N )
-
hw13
1500
2000
N (
k N )
Nor
0
500
1000
0
0 50 100 150 200 250 300
M (kN.m)
balanc
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