1 Introduction
2 Provisions for Flexural Design
2.1 Design Format and Material Strength
AISC 360-10 | KBC 2014 | Eurocode 4 | JSCE 2009 | |
---|---|---|---|---|
Design format | Load and resistance factor design | Load and resistance factor design | Partial factor method | Partial factor method |
Design moment strength M
d
|
M
d
= ϕM(f
k
) |
M
d
= ϕM(f
k
) |
f
d
= f
k
/γ and M
d
= M(f
d
) |
f
d
= f
k
/γ and M
d
= M(f
d
)/γ
b
(1)
|
Resistance factor ϕ or Safety factor γ for materials |
ϕ = 0.9 |
ϕ = 0.9 | Concrete γ
c
= 1.5 Steel γ
s
= 1.0(2)
Reinforcing bar γ
r
= 1.15 | Concrete γ
c
= 1.3 Steel γ
s
= 1.0 Reinforcing bar γ
r
= 1.0 |
Characteristic material strength f
k
(MPa) | Concrete 21 ≤ f
ck
≤ 70 Steel F
yk
≤ 525 | Concrete 21 ≤ f
ck
≤ 70 Steel F
yk
≤ 650 | Concrete 20 ≤ f
ck
≤ 60 Steel F
yk
≤ 460 | Concrete 18 ≤ f
ck
≤ 80 Steel –
(3)
|
2.2 Design Moment Strength
AISC 360-10 and KBC 2014 | Eurocode 4 | JSCE 2009 | |
---|---|---|---|
PSDM(1)
| |||
Plastic stress | Conc. 0.85f
ck
, steel F
yk
, and reinforcing bar f
yrk
| Conc. 0.85f
cd
, steel F
yd
, and reinforcing bar f
yrd
| Conc. 0.85f
cd
, steel F
yd
, and reinforcing bar f
yrd
|
Stress distribution | |||
Design strength M
d
|
M
d
= ϕM
pl
and ϕ = 0.9 |
M
d
= M
pl
or βM
pl
(2)
|
M
d
= M
pl
/γ
b
and γ
b
= 1.1 |
SCM(1)
| |||
Conc. σ–ɛ curve | Not specified(3)
Maximum compressive strain = 0.003 | Parabola-rectangle(4)
| Parabola-rectangle(5)
|
Steel σ–ɛ curve | Not specified(3)
| Elastic-perfectly plastic | Bilinear with 0.01E
s
hardening |
Stress and strain distributions (positive bending) | |||
Design strength M
d
|
M
d
= ϕM
nl
and ϕ = 0.9 |
M
d
= M
nl
|
M
d
= M
nl
/γ
b
and γ
b
= 1.1 |
3 KSSC–KCI Provisions for Flexural Design
4 Design Resistance by Plastic Stress Distribution Method
4.1 Positive Bending
f
ck
(MPa) |
F
yk
(MPa) | AISC 360-10 | KSSC–KCI | Eurocode 4 | JSCE 2009 | |||
---|---|---|---|---|---|---|---|---|
M
pl
|
M
d
(1)
|
β
|
M
d
(1)
|
β
|
M
d
(1)
|
M
d
(1)
| ||
21 | 235 | 1268 | 1141 | 0.957 | 1138 | –(2)
| 1196 | 1123 |
315 | 1648 | 1483 | 0.952 | 1422 | –(2)
| 1501 | 1407 | |
355 | 1803 | 1623 | 0.951 | 1564 | –(2)
| 1653 | 1545 | |
450 | 2167 | 1950 | 0.934 | 1868 | 0.949 | 1907 | 1871 | |
650 | 2920 | 2628 | 0.782 | 2097 | –(3)
| –(3)
| –(3)
| |
30 | 235 | 1301 | 1171 | 1.000 | 1287 | –(2)
| 1293 | 1203 |
315 | 1709 | 1538 | 0.958 | 1550 | –(2)
| 1628 | 1516 | |
355 | 1907 | 1716 | 0.956 | 1694 | –(2)
| 1783 | 1677 | |
450 | 2354 | 2119 | 0.949 | 2025 | 0.961 | 2062 | 2010 | |
650 | 3122 | 2810 | 0.881 | 2539 | –(3)
| –(3)
| –(3)
|
f
ck
(MPa) |
F
yk
(MPa) | AISC 360-10 | KSSC–KCI | Eurocode 4 | JSCE 2009 | |||
---|---|---|---|---|---|---|---|---|
M
pl
|
M
d
(1)
|
β
|
M
d
(1)
|
β
|
M
d
(1)
|
M
d
(1)
| ||
21 | 235 | 1082 | 974 | 0.901 | 907 | –(2)
| 1004 | 939 |
315 | 1377 | 1239 | 0.866 | 1089 | –(2)
| 1265 | 1185 | |
355 | 1514 | 1363 | 0.854 | 1181 | –(4)
| –(4)
| 1302 | |
450 | 1826 | 1643 | –(4)
| –(4)
| –(4)
| –(4)
| 1570 | |
650 | 2443 | 2199 | –(4)
| –(4)
| –(3)
| –(3)
| –(3)
| |
30 | 235 | 1164 | 1048 | 0.949 | 1014 | –(2)
| 1073 | 1001 |
315 | 1468 | 1321 | 0.911 | 1237 | –(2)
| 1364 | 1274 | |
355 | 1619 | 1457 | 0.894 | 1334 | –(2)
| 1499 | 1403 | |
450 | 1967 | 1770 | 0.866 | 1556 | 0.861 | 1555 | 1693 | |
650 | 2631 | 2368 | –(4)
| –(4)
| –(3)
| –(3)
| –(3)
|
4.2 Negative Bending
Type |
F
yk
(MPa) | AISC 360-10 | KSSC–KCI | Eurocode 4 | JSCE 2009 | |
---|---|---|---|---|---|---|
M
pl
|
M
d
(1)
|
M
d
(1)
|
M
d
(1)
|
M
d
(1)
| ||
Exterior beam | 235 | 799 | 719 | 787 | 784 | 726 |
315 | 1031 | 928 | 1019 | 1015 | 937 | |
355 | 1147 | 1032 | 1134 | 1130 | 1041 | |
450 | 1420 | 1278 | 1407 | 1403 | 1290 | |
650 | 1994 | 1795 | 1981 | 1977 | 1812 | |
Interior beam | 235 | 940 | 846 | 919 | 912 | 855 |
315 | 1184 | 1066 | 1161 | 1153 | 1077 | |
355 | 1304 | 1174 | 1279 | 1272 | 1185 | |
450 | 1586 | 1427 | 1558 | 1550 | 1440 | |
650 | 2168 | 1951 | 2139 | 2130 | 1970 |
5 Design Resistance by Strain-Compatibility Method
5.1 Rotational Capacity and Resistance Factor for Bending
f
ck
(MPa) |
F
yk
(MPa) | KSSC–KCI | Eurocode 4 | JSCE 2009 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
| ||
21 | 235 | 1282 | 1221 | 0.952 | 9.36 | 1282 | 1232 | 0.961 | 10.7 | 1461 | 1245 | 0.852 | 11.0 |
315 | 1674 | 1534 | 0.916 | 5.73 | 1675 | 1544 | 0.921 | 6.17 | 1778 | 1504 | 0.845 | 6.70 | |
355 | 1841 | 1684 | 0.914 | 4.51 | 1847 | 1695 | 0.917 | 4.93 | 1916 | 1629 | 0.850 | 5.44 | |
450 | 2223 | 2008 | 0.903 | 2.99 | 2226 | 2023 | 0.908 | 3.30 | 2265 | 1920 | 0.847 | 3.58 | |
650 | 2914 | 2497 | 0.856 | 1.68 | 2915 | 2537 | 0.870 | 1.78 | 2874 | 2398 | 0.834 | 1.88 | |
30 | 235 | 1310 | 1274 | 0.972 | 14.9 | 1311 | 1277 | 0.974 | 15.4 | 1575 | 1352 | 0.858 | 15.1 |
315 | 1726 | 1655 | 0.958 | 8.30 | 1726 | 1667 | 0.965 | 8.76 | 1915 | 1652 | 0.862 | 8.80 | |
355 | 1928 | 1814 | 0.940 | 6.54 | 1928 | 1827 | 0.947 | 7.37 | 2085 | 1792 | 0.859 | 7.38 | |
450 | 2377 | 2189 | 0.920 | 4.51 | 2378 | 2204 | 0.926 | 4.81 | 2460 | 2107 | 0.856 | 4.82 | |
650 | 3194 | 2844 | 0.890 | 2.19 | 3200 | 2873 | 0.897 | 2.43 | 3195 | 2692 | 0.842 | 2.77 |
f
ck
(MPa) |
F
yk
(MPa) | KSSC–KCI | Eurocode 4 | JSCE 2009 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
|
M
k
(1)
|
M
d
(1)
|
ϕ
|
μ
d
| ||
21 | 235 | 1109 | 1020 | 0.919 | 4.37 | 1110 | 1024 | 0.922 | 4.38 | 1145 | 986 | 0.861 | 4.73 |
315 | 1392 | 1271 | 0.913 | 2.79 | 1394 | 1281 | 0.918 | 2.96 | 1405 | 1208 | 0.859 | 3.08 | |
355 | 1519 | 1377 | 0.906 | 2.31 | 1524 | 1393 | 0.914 | 2.52 | 1524 | 1309 | 0.858 | 2.59 | |
450 | 1782 | 1581 | 0.887 | 1.67 | 1782 | 1604 | 0.900 | 1.76 | 1769 | 1506 | 0.851 | 1.86 | |
650 | 2078 | 1789 | 0.860 | 1.00(2)
| 2134 | 1821 | 0.853 | 1.00(2)
| 2099 | 1703 | 0.811 | 1.00(2)
| |
30 | 235 | 1198 | 1092 | 0.911 | 5.51 | 1201 | 1098 | 0.914 | 5.86 | 1252 | 1065 | 0.850 | 6.18 |
315 | 1506 | 1369 | 0.909 | 3.54 | 1506 | 1379 | 0.915 | 3.55 | 1525 | 1305 | 0.855 | 3.86 | |
355 | 1650 | 1493 | 0.904 | 2.93 | 1651 | 1507 | 0.912 | 2.93 | 1657 | 1419 | 0.856 | 3.15 | |
450 | 1960 | 1743 | 0.889 | 2.04 | 1964 | 1763 | 0.897 | 2.04 | 1938 | 1640 | 0.846 | 2.20 | |
650 | 2402 | 2032 | 0.846 | 1.00(2)
| 2434 | 2107 | 0.865 | 1.00(2)
| 2341 | 1953 | 0.834 | 1.00(2)
|