¶ 冷軋型鋼構造建築物結構設計規範及解說－附錄四 以直接強度法設計冷軋型鋼構材（3／4）
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(d) AISI 2002 冷軋型鋼設計手冊範例I-13 3HU4.5x135
圖 C-D.1.2-1 以有限元素法分析彎矩和軸向載重之彈性挫屈(續)
D.1.3 使用性之決定
由標稱載重所造成之彎矩需考慮撓度因素，撓度過大會降低其斷面之慣性
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矩，斷面之有效慣性矩計算如下：
Leff= Ig(Md/M) ≤ Ig
(D.1.3-1)
其中
Md=依D.2.2 節所訂之Mn值，於D.2.2 節內方程式之My值以M 取代
M=標稱載重所形成之彎矩大小 (M≤My)
解說：本附錄假設斷面強度與慣性矩成線性關係，以簡單化之方式計算撓度，此方法可避免
有效斷面之冗長計算。
D.2 鋼構件
D.2.1 柱設計
柱之標稱軸向強度(Pn)應為Pne, Pnl與 Pnd之最小值，而柱之幾何性質和材料符
合D.1.1.1 之規定者，Ωc及φc之值可由下列公式計算之：
Ωc=1.80 (ASD)
φc=0.85 (LRFD)
若柱斷面未符合D.1.1.1 之規定者，其安全因子(Ω)及強度折減因子(φ)應以
第1.3.1 節或第1.3.2 節的應用方法取得，或以合理之工程分析方法獲得。
解說：傳統規範[A.1]有關柱之強度是考慮挫之標稱柱屈應力和有效斷面積，這說明局部挫屈
會降低實際柱之強度(例如局部與整體之交互作用)。在直接強度法中考慮兩部分：一為
長柱未因局部挫屈(Pne)而降低強度，二為長柱應考慮局部與整體之交互作用(Pnl)。
針對充分支撐柱其局部挫屈與扭曲挫屈之強度曲線圖詳如圖C-D.2.1-1 所示，此曲線呈
現構件長細影響關係，說明長細影響構件之局部或扭曲行為，非彈性及挫屈後強度會
影響局部挫屈與扭曲挫屈之行為模式。扭曲挫屈後之挫屈強度小於局部挫屈後之挫屈
強度，其關係可由曲線圖之相對位置比較得知。
局部挫屈：公式.D.2.1-6
扭曲挫屈：公式.D.2.1-9
彈性臨界挫屈
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圖 C-D.2.1-1 有支撐之柱，其局部挫屈與扭曲挫屈直接強度曲線(Pne=Py)
D.2.1.1 撓曲、扭轉或撓曲-扭轉挫屈
構件若產生撓曲、扭轉或撓曲-扭轉挫屈，其標稱軸向強度(Pne)可由下列公
式計算之：
(a)當
c
λ ≤1.5
(
) y
λ
ne
P
658
.0
P
2
c
=
(D.2.1-1)
(b)當
c
λ >1.5
y
2
c
ne
P
λ
877
.0
P
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
(D.2.1-2)
其中
cre
y
c
P
/
P
λ =
(D.2.1-3)
y
g
y
F
A
P =
(D.2.1-4)
cre
P
=在撓曲、扭轉或撓曲-扭轉挫屈情形下，依D1.1.2 節計算最小臨界彈
性柱挫屈載重
解說：本節所探討之軸向強度(Pne)是柱之上限值，真正柱之強度應考慮局部挫屈所造成之折
減，若有產生扭曲挫屈之情形，亦應考慮其影響，可參考D.1.2 節有關合理性分析以
計算Pcre。
圖 C-D.2.1-2 直接強度法分析承受集中載重並擁有鉸支承之柱
| ne ⎜⎜ 2 ⎟⎟ y (D.2.1-2) ⎝ λ c ⎠ 其中 λ c = P y / P cre (D.2.1-3) P y = A g F y (D.2.1-4) P cre =在撓曲、扭轉或撓曲-扭轉挫屈情形下，依D1.1.2 節計算最小臨界彈 性柱挫屈載重 |
|---|
| λ c = P y / P cre (D.2.1-3) |
| P y = A g F y (D.2.1-4) |
| P cre =在撓曲、扭轉或撓曲-扭轉挫屈情形下，依D1.1.2 節計算最小臨界彈 |
| 性柱挫屈載重 |
| 解說：本節所探討之軸向強度(Pne)是柱之上限值，真正柱之強度應考慮局部挫屈所造成之折 |
| 減，若有產生扭曲挫屈之情形，亦應考慮其影響，可參考D.1.2 |
| 計算Pcre。 |
| 局部挫屈：公式.D.2.1-6 |
| 扭曲挫屈：公式.D.2.1-9 |
| 局部挫屈：公式.D.2.1-6 |
| 扭曲挫屈：公式.D.2.1-9 |
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D.2.1.2 局部挫屈
構件若產生局部挫屈，其標稱軸向強度(
ne
P )可由下列公式計算之：
(a)當
lλ ≤0.776
ne
nl
P
P
=
(D.2.1-5)
(b)當
lλ >0.776
ne
4.0
ne
crl
4.0
ne
crl
nl
P
)
P
P
(
)
P
P
(
15
.0
1
P
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
(D.2.1-6)
其中
crl
ne
l
P
/
P
λ =
(D.2.1-7)
ne
P =由D.2.1.1 節計算之
crl
P =依D.1.2 節計算臨界彈性柱局部挫屈載重
解說：圖C-D.2.1-1 及 C-D.2.1-2 為柱之局部挫屈行為模式，柱受力產生局部與整體挫屈之交
互作用已納入考慮因素，因此局部挫屈模式為長柱之最大強度(Pce)，請參考D.1.2 節有
關合理性分析以計算Pcrl。
D.2.1.3 扭曲挫屈
構件若產生扭曲挫屈，其標稱軸向強度(
nd
P )可由下列公式計算之：
(a)當
d
λ ≤0.561
ny
nd
P
P
=
(D.2.1-8)
(b)當
d
λ >0.561
y
6.0
y
crd
6.0
y
crd
nd
P
)
P
P
(
)
P
P
(
25
.0
1
P
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
(D.2.1-9)
其中
crd
y
d
P
/
P
λ
=
(D.2.1-10)
y
P = 由公式(D.2.1-4)計算之
crd
P
= 依D.1.2 節計算臨界彈性柱扭曲挫屈載重
解說：圖C-D.2.1-1 及 C-D.2.1-2 為柱之局部挫屈行為模式，柱受力產生局部與整體挫屈之交
互作用已納入考慮因素，因此局部挫屈模式為長柱之最大強度(Pce)，請參考D.1.2 節有
關合理性分析以計算Pcrl。
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D.2.2 梁設計
梁之標稱彎矩強度(Mn)依D.2.2.1 至D.2.2.3 節規定計算Mne, Mnl與 Mnd之最小
值，而梁之幾何性質和材料符合D.1.1.2 之規定者，Ωb及Φb之值可由下列公式
計算之：
Ωb=1.67 (ASD)
φb=0.90 (LRFD)
若梁斷面未符合D.1.1.2 之規定者，其安全因子(Ω)及強度折減因子(φ)應以
第1.3.1 節或第1.3.2 節的應用方法取得，或以合理之工程分析方法獲得。
解說：輕量型冷軋型鋼構材的行為與設計是複雜的，當採用彈性挫屈分析構材於強軸彎曲時，
通常需考慮局部挫屈、扭曲挫屈及側向－扭轉挫屈等三種挫屈行為，此附錄之直接強
度設計法採用更精細之方法評估局部挫屈與扭曲挫屈強度，經由試驗證明此分析方式
可預測構材挫屈後強度和扭曲挫屈之破壞行為。
圖 C-D.2.2-1 梁具側向支撐之局部挫屈與扭曲挫屈之直接強度法曲線
傳統規範[A.1]所考慮之梁屬於非充份側向支撐，因此有局部不穩定現象，梁之彎矩強
度計算是由側向挫屈應力(Pc)與有效斷面模數之相乘積，有效斷面模數是由挫屈應力
(Pc)計算而得，這說明局部挫屈行為會降低構材側向扭轉挫屈強度。直接強度設計法將
上述情形分成兩部份考慮，一為構材側向－扭轉挫屈強度不需考慮局部挫屈所造成之
折減，二為構材為局部挫屈與整體挫屈之交互行為。
對充份側向支撐梁斷面有局部挫屈和扭曲挫屈產生時，其強度曲線與臨界彈性挫屈之
關係圖詳如圖C-D.2.2-1 所示，當構材擁有局部挫屈和扭曲挫屈型式，並兼具非彈性及
挫屈後強度等特性時，局部挫屈後強度比扭曲挫屈後強度為大。
局部挫屈：公式.D.2.1-6
扭曲挫屈：公式.D.2.1-9
彈性臨界挫屈
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圖 C-D.2.2-2 梁具側向支撐之直接強度法
D.2.2.1 側向扭轉挫屈
構材若產生側向扭轉挫屈，其標稱彎矩強度(
ne
M
)可由下列公式計算之：
(a)當
y
cre
M
56
.0
M
≤
cre
ne
M
M
=
(D.2.2-1)
(b)當
y
cre
y
M
56
.0
M
M
78
.2
≥
≥
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
cre
y
y
ne
M
36
M
10
1
M
9
10
M
(D.2.2-2)
(c)當
y
cre
M
78
.2
M
≥
y
ne
M
M
=
(D.2.2-3)
其中
cre
M
=依D.1.2 節計算最小臨界彈性側向扭轉挫屈彎矩
y
f
y
F
S
M
=
(D.2.2-4)
而
fS =斷面降伏時所計算之全斷面模數
解說：本節所探討構材之側向扭轉挫屈強度(
ne
M
)是梁強度之上限值，真正梁之
強度應分別考慮構件因局部挫屈或扭曲挫屈等因素，而造成強度是否折
減，請參考D.1.2 節所述之合理性分析法以計算
cre
M
之大小。
D.2.2.2 局部挫屈
構件若產生局部挫屈，其標稱彎矩強度(
nl
M
)可由下列公式計算之：
(a)當
776
.0
λl ≤
| 局部挫屈：公式.D.2.1-6 扭曲挫屈：公式.D.2.1-9 局部挫屈 × 扭曲挫屈 圖 C-D.2.2-2 梁具側向支撐之直接強度法 |
|---|
| 局部挫屈 |
| × 扭曲挫屈 |
| 圖 C-D.2.2-2 梁具側向支撐之直接強度法 |
| × |
|---|
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ne
nl
M
M
=
(D.2.2-5)
(b)當
776
.0
λl >
ne
4.0
ne
crl
4.0
ne
crl
nl
M
)
M
M
(
)
M
M
(
15
.0
1
M
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛−
=
(D.2.2-6)
其中
crl
ne
l
M
/
M
λ =
(D.2.2-7)
ne
M
=依D.2.2.1 節計算之
fS =斷面降伏時所計算之全斷面模數
crl
M
=依D.1.2 節計算臨界彈性局部挫屈彎矩
解說：梁之局部挫屈分析模式詳如D.2.2 節所述，其結果可參考圖C-D.2.2-1 及C-D.2.2-2。使
用直接強度法分析構件行為，並由實驗推導計算公式[A.14]，其中局部挫屈與整體挫屈
交互作用之因素已考慮在內，所以梁之強度被限制最大只能達到側向扭轉挫屈強度
(Mne)，而具充份側向支撐之梁，最大側向扭轉挫屈強度(Mne)則為斷面降伏強度(My)，
請參考D.1.2 節所述之合理性分析法以計算Mcrl 之大小。
D.2.2.3 扭曲挫屈
構件若產生扭曲挫屈，其標稱彎矩強度(
nd
M
)可由下列公式計算之：
(a)當
673
.0
λd ≤
y
nd
M
M
=
(D.2.2-8)
(b)當
673
.0
λd >
y
5.0
y
crd
5.0
y
crd
nd
M
)
M
M
(
)
M
M
(
22
.0
1
M
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
(D.2.2-9)
其中
crd
y
d
M
/
M
λ
=
(D.2.2-10)
y
M = 依D.2.2.4 節計算之
crd
M
=依D.1.2 節計算臨界彈性扭曲挫屈彎矩
解說：梁之扭曲挫屈分析模式詳如D.2.2 節所述，其結果可參考圖C-D.2.2-1 及C-D.2.2-2。根
據實驗結果[A.15]，梁之扭曲挫屈強度為My，而非Mne，其中扭曲挫屈之產生與側向扭
轉挫屈之形成是無關聯性的，也就是說扭曲挫屈與整體挫屈之交互作用是不存在的，
請參考D.1.2 節所述之合理性分析法以計算Mcrd之大小。
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參考文獻
1.1
內政部，“建築技術規則”。
1.2
內政部，“鋼構造建築物鋼結構設計技術規範”。
1.3
American Iron and Steel Institute, North American Specification for the Design of Cold-Formed
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1.4
Yu, W. W., V. A. Liu, and W. M. Mckinney, “Structural Behavior and Design of Thick,
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Yu, W. W., V. A. Liu, and W. M. Mckinney, “Structural Behavior of thick Cold–Formed steel
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Pekoz, T. B, “Development of a Unified Approach to the Design of Cold–Formed Steel
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Yu, W. W., Cold–Formed Steel Design, 2
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AISI Formulas for Cold Work and Effective Design Width,” First Progress Report, Civil
Engineering Study 79-1, University of Missouri-Rolla, Rolla, MO, January 1979.
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1.14 Rang, T. N., T. V. Galambos, and W. W. Yu, “Load and Resistance Factor Design of
Cold–Formed Steel: Statistical Analysis of Mechanical Properties and Thickness of Material
Combined with Calibration of the AISI Design Provisions on Unstiffened Compression Elements
and Connections,” Second Progress Report, Civil Engineering Study 79-2, University of
Missouri-Rolla, Rolla, MO, January 1979.
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Cold–Formed Steel: Calibration of the Design Provisions on Connections and Axially Loaded
Compression Members,” Third Progress Report, Civil Engineering Study 79-3, University of
Missouri-Rolla, Rolla, MO, January 1979.
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Cold–Formed Steel: Calibration of the Design Provisions on Laterally Unbraced Beams and
Beam-Columns,” Fourth Progress Report, Civil Engineering Study 79-4, University of
Missouri-Rolla, Rolla, MO, January 1979.
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Cold–Formed Steel: Calibration of the Design Provisions on Beam Webs,” Fifth Progress Report,
Civil Engineering Study 79-5, University of Missouri-Rolla, Rolla, MO, September 1979.
1.18 Ellingwood, B., J. G. MacGregor, T. V. Galambos, and C. A. Cornell, “Probability Based Load
Criteria: Load Factors and Load Combinations,” Journal of the Structural Division, ASCE, Vo1.
108, No. ST5, May 1982.
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Steel: Comparative Study of Design Methods for Cold-Formed Steel,” Eleventh Progress Report,
Civil Engineering Study 88-4, University of Missouri-Rolla, Rolla, MO, February 1988.
2.1
American Society of Civil Engineers, Minimum Design Loads for Buildings and Other Structures,
ASCE Standard 7-05, 2005.
2.2
內政部， “鋼構造建築物鋼結構設計技術規範”。
3.1
American Iron and Steel Institute, North American Specification for the Design of Cold-Formed
Steel Structural Members, 2012 Edition.
3.2
內政部，“鋼構造建築物鋼結構設計技術規範”。
3.3
Karren, K. W. and G. Winter, “Effects of Cold-Work on Light Gage Steel Members,” Journal of
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the Structural Division, ASCE, Vo1. 93, No. ST1, February 1967.
3.4
Chajes, A., S. J. Britvec, and G. Winter, “Effects of Cold-Straining on Structural Steels,” Journal
of Structure Division, ASCE, Vol. 89, No. ST2, February 1963.
3.5
American Society for Testing and Materials, “Standard Methods and Definitions for Mechanical
Testing of Steel Products,” ASTM 370, 1994.
4.1
Yu, W. W., Cold–Formed Steel Design, 3rd Edition, John Wiley & Sons, New York, NY, 2000.
4.2
American Iron and Steel Institute, Specification for the Design of Cold-Formed Steel Structural
Members, 1996 Edition.
4.3
Winter, G., “Performance of Thin Steel Compression Flanges,” Preliminary Publication, 3
rd
Congress of the International Association of Bridge and Structural Engineering, Liege, Belgium,
1948.
4.4
Winter, G., Commentary on the 1968 Edition of the Specification for the Design of Cold-Formed
Steel Structural Members, American Iron and Steel Institute, New York, NY, 1970.
4.5
LaBoube, R. A. and W. W. Yu, “Structural Behavior of Beam Webs Subjected Primarily to Shear
Stress,” Final Report, Civil Engineering Study 78-2, University of Missouri-Rolla, Rolla, MO, June
1978.
4.6
LaBoube, R. A. and W. W. Yu, “Structural Behavior of Beam Webs Subjected to a Combination of
Bending and Shear,” Final Report, Civil Engineering Study 78-3, University of Missouri-Rolla,
Rolla, MO, June 1978.
4.7
LaBoube, R. A. and W. W. Yu, “Bending Strength of Webs of Cold-Formed Steel Beams,”
Journal of the Structural Division, ASCE, Vol. 108, No. ST7, July 1982.
4.8
Hetrakul, N. and W. W. Yu, “Structural Behavior of Beam Webs Subjected to Web Crippling and a
Combination of Web Crippling and Bending,” Final Report, Civil Engineering Study 78-4,
University of Missouri-Rolla, Rolla, MO, June 1978.
4.9
Hetrakul, N. and W. W. Yu, “Cold-Formed Steel I-Beams Subjected to Combined Bending and
Web Crippling,” Thin-Walled Structures – Recent Technical Advances and Trends in Design,
Research and Construction, Rhodes, J. and A. C. Walker (Eds), Granada Publishing Limited,
London, 1980.
4.10 Nguyen, P. and W. W. Yu, “Structural Behavior of Transversely Reinforced Beams Webs,” Final
Report, Civil Engineering Study 78-5, University of Missouri-Rolla, Rolla, MO, July 1978.
4.11 Nguyen, P. and W. W. Yu, “Structural Behavior of Longitudinally Reinforced Beams Webs,”
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Final Report, Civil Engineering Study 78-6, University of Missouri-Rolla, Rolla, MO, July 1978.
4.12 Yu, W. W., Cold-Formed Steel Design, 2
nd Edition, Wiley-Interscience, New York, NY, 1991.
4.13 Bleich, F., Buckling strength of Metal Structures, McGraw-Hill Book Co., New York, NY, 1952.
4.14 Weng, C. C. and T. B. Pekoz, “Subultimate Behavior of Uniformly Compressed Stiffened Plate
Elements,” Research Report, Cornell University, Ithaca, NY, 1986.
4.15 Ortiz-Colberg, R. and T. B. Pekoz, “Load Carrying Capacity of Perforated Cold-Formed Steel
Columns,” Research Report No. 81-12, Cornell University, Ithaca, NY, 1981.
4.16 Miller, T. H. and T. Pekoz, “Unstiffened Strip Approach for Perforated Wall Studs,” Journal of
Structural Engineering, ASCE, Vol. 120, No. 2, 1994.
4.17 Pan, C. L. and J. L., Peng, “Performance of Cold-Formed Steel Wall Frames under
Compression,” Steel & Composite Structures, Vol. 5, No. 5, 2005.
4.18 Pekoz, T. B., “Development of a Unified Approach to the Design of Cold-Formed Steel
Members,” Report SG-86-4, American Iron and Steel Institute, 1986.
4.19 Cohen, J. M. and T. B. Pekoz, “Local Buckling Behavior of Plate Elements,” Research Report,
Cornell University, Ithaca, NY, 1987.
4.20 Schafer, B. W. and T. Pekoz, “Laterally Braced Cold-formed Steel Flexural Members with Edge
Stiffened Flanges,” Journal of Structural Engineering, ASCE, Vol. 125, No. 2, 1999.
4.21 Shan, M. Y., R. A. LaBoube, and W. W. Yu, “Behavior of Web Elements with Openings Subjected
to Bending, Shear and Combination of Bending and Shear,” Final Report, Civil Engineering Series
94-2, Cold-Formed Steel Series, Department of Civil Engineering, University if Missouri-Rolla,
1994.
4.22 Bambach, M. R. and K. J. R. Rasmussen, “Tests on Unstiffened Elements under Combined
Bending and Compression,” Research Report R818, Department of Civil Engineering, University
of Sydney, Australia, 2002.
4.23 Bambach, M. R. and K. J. R. Rasmussen, “Elastic and Plastic Effective Width Equations for
Unstiffened Elements,” Research Report R819, Department of Civil Engineering, University of
Sydney, Australia, 2002.
4.24 Bambach, M. R. and K. J. R. Rasmussen, “Design Method for Thin-Walled Sections Containing
Unstiffened Elements,” Research Report R820, Department of Civil Engineering, University of
Sydney, Australia, 2002.
4.25 Bulson, P. S., The Stability of Flat Plates, American Elsevier Publishing Company, New York, NY,
1969.
4.26 Pekoz, T. B., “Development of a Unified Approach to the Design of Cold-Formed Steel
展開本頁可搜尋文字與辨識表格
Members,” Proceedings of the Eighth International Specialty Conference on Cold-Formed Steel
Structures, University of Missouri-Rolla, Rolla, MO, November 1986.
4.27 Desmond, T. P., T. B. Pekoz, and G. Winter, “Edge Stiffeners for Thin-Walled Members,”
Journal of Structural Division, ASCE, Vol. 107, No. ST2, Feb. 1981.
4.28 Schafer, B. W., A. Sarawit, T. Pekoz, “Complex Edge Stiffeners for Thin-Walled Members,”
Journal of Structural Engineering, ASCE, Vol. 132, No. 2, 2006.
4.29 Yang, H. and B. W. Schafer, “Comparison of AISI Specification Methods for Members with
Single Intermediate Longitudinal Stiffeners,” Report to American Iron and Steel Institute,
Washington, DC, 2006.
5.1 American Institute of Steel Construction, Specification for Structural Steel Buildings, ANSI/AISC
360-05, 2005.
6.1 American Iron and Steel Institute, LRFD Cold-Formed Steel Design Manual, Washington, D. C.,
1991.
6.2 Hsiao, L. E., W. W. Yu, and T. V. Galambos, “Load and Resistance Factor Design of Cold-Formed
Steel: Calibration of the AISI Design Provisions,” Ninth Progress Report, Civil Engineering Study
88-2 University of Missouri-Rolla, Rolla, MO, February 1988.
6.3 Reck, H. P., T. Pekoz, and G. Winter, “Inelastic Strength of Cold-Formed Steel Beams,” Journal
of Structural Division, ASCE, Vol. 101, No. ST11, November 1975.
6.4 Yener, M. and T. B. Pekoz, “Partial Stress Redistribution in Cold-Formed Steel,” Journal of
Structural Engineering, ASCE, Vol. 111, No. 6, June 1985.
6.5 Yener, M. and T. B. Pekoz, “Partial Moment Redistribution in Cold-Formed Steel,” Journal of
Structural Engineering, ASCE, Vol. 111, No. 6, June 1985.
6.6 American Iron and Steel Institute, Cold-Formed Steel Design Manual, Washington, D. C., 2008.
6.7 Yu, W. W., Cold-Formed Steel Design, 3rd edition, John Wiley & Sons, NY, 2000.
6.8 Bambach, M. R. and K. J. R. Rasmussen, “Tests on Unstiffened Elements under Combined
Bending and Compression,” Research Report R818, Department of Civil Engineering, University
of Sydney, Australia, 2002.
6.9 Bambach, M. R. and K. J. R. Rasmussen, “Elastic and Plastic Effective Width Equations for
Unstiffened Elements” Research Report R819, Department of Civil Engineering, University of