Geometric axis bending strength of double angle beams

ELSEVIER PII: S0143-974X(96)00012-0

J. Construct. Steel Res. Vol. 38, No. 1, pp. 23-40, 1996 Copyright © 1996 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 0143-974X/96 $15.00 + 0.00

Geometric Axis Bending Strength of Double Angle Beams

Murty K. S. Madugula, a Toshifumi Kojima, b Yasuyuki Kajita C & Michihiro Ohama d

aprofesso:r, Department of Civil and Environmental Engineering, University of Windsor, Windsor, Ontario, Canada N9B 3P4

bSenior Research Engineer, Heavy Steel Products Laboratory, Keihin Research Department, Material and Processing Research Center, N. K. K. Corporation, Kawasaki, 210 Japan

cStaff of Operation Technology, Plate Department, Fukuyama Works, N. K. K. Corporation, Fukuyama City, 721 Japan

dSenior Manager of Product Design and Quality Control of Rail and Section, Fukuyama Works, N. K. K. Corporation, Fukuyama City, 721 Japan

(Received 15 May 1995; revised version received 30 December 1995; accepted 30 December 1995)

ABSTRACT

Results of tests on 13 double-angle beams bending about the geometric axis are presented. Nine regular size and two ultra-large size angles were included in the investigation. The test failure moments were 2-32% greater than the plastic moments of resistance and 55-95% greater than the nominal flexurcil strengths calculated as per the American Institute of Steel Construc- tion 'Specification for Load and Resistance Factor Design of Single-angle Members' issued in 1993. For the angles tested, the defections at 1.5 times the yield moment were only 1.53-1.74 times the deflections at first yield. Failure strains in compression exceeded the yield strain even for a specimen with a width-to-thickness ratio of 19.0. It is concluded that the nominal resist- ances .for angle members bending about the geometric axis computed using the current AISC-LRFD Specification for Single Angles are highly conservative and there is need to revise the pertinent clauses in the specification in the interest of design economy. Copyright © 1996 Elsevier Science Ltd.

b E Fy

NOTATION

Full width of angle leg with tip (i.e., toe) in compression Modulus of elasticity Yield stress

23

24 M. K. S. Madugula, T. Kojima, Y. Kajita, M. Ohama

L

Mtest

My Pt~st O &

st

Span of the test specimen Nominal flexural strength as per AISC-LRFD (1993) Plastic moment of resistance Failure moment including the moment due to self weight of the test specimen Yield moment Maximum load applied to the specimen before failure Stress reduction factor to account for local buckling Elastic section modulus to the tip in compression relative to the axis of bending Elastic section modulus to the tip in tension relative to the axis of bending Thickness of angle leg

INTRODUCTION

In the nuclear power industry, angles are extensively used as beams to support pipes. They are also often used as beams in walkways, racks, etc. In latticed towers, steel angles are subjected to axial forces and bending moments. Thus, it is necessary to be able to accurately determine the bending strength of angle members as beams and beam-columns.

Most design specifications for angles in flexure are based on the research carried out in Australia. ~ The Australian research consisted of 15 tests (including five tests to failure) of laterally unsupported angle beams subjected to uniform moment along an axis parallel to the leg of the angle. The sizes of the five specimens tested to failure are as follows:

76 x 76 x 4.8 mm (3 × 3 x 3/16 in.): L/t = 400 89 x 64 x 4.8 mm (3½ x 2½ x 3/16 in.): L/t = 400 and 1600 64 x 51 x 6.4 mm (2½ x 2 x ¼ in.): L/t = 400 and 1200.

Bez and Hirt 2 in Europe carried out a total of seven tests on built-up sections consisting of two 150 x 100 x 10 mm angles, 380 mm apart, with the long legs vertical, and toes of horizontal legs facing each other. The specimens were subjected to axial compression (varying from 0 to 60% of squash load) and transverse bending by the application of axial and transverse loads.

To the best of the authors' knowledge, these are the only two series of bending tests available in the literature. Since there is a need for more research to determine the flexural capacity of angles, an experimental investigation was carded out in 1994 at the Research and Development Laboratories of N. K. K. Corporation in Kawasaki, Japan. Results of tests carded out by the authors

Geometric axis bending strength of double angle beams 25

on the minor axis bending strength of angle beams were recently reported. 3 This paper describes the experimental investigation on double-angle beams (whose behavior is similar to two laterally supported single-angle beams bent about a geometric axis). The test results are compared with the values calculated according to the American Institute of Steel Construction 'Specification for Load and Resistance Factor Design of Single-angle Members', which is the only specification in the world devoted exclusively for angle members. 4

According to clause 5.2.1 of the AISC-LRFD Specification, angle members bending about geometric axis with lateral-torsional restraint along the length shall be ,designed on the basis of geometric axis bending with the nominal flexural strength/14, computed as follows:

(a) For t, he limit state of local buckling, when the tip (i.e. toe) of an angle leg is in compression:

& When bit <-- 0.382 :

Mn = 1.25 FySo. (la)

When 0.2182 <bit <- 0.446 :

Mn = FyS~ [1.25 - 3.9 {(bit) . ~ -0.382}1. (lb) y 1.:,

When b/t >0.446 :

Mn = QFySc. (lc)

Where b = full width of angle leg with tip (i.e. toe) in compression; Q = stress reduction factor as per eqns 2(a-c); Sc = elastic section modulus to the tip in compression relative to the axis of bending; E = modulus of elasticity. The reduction factor Q is given by the following:

m & When b/t <-- 0.446 :


Q = 1.0. (2a)

m m

When 0.446 <b/t < 0.910 :

m

Q = 1 . 3 4 - 0.761 (b/t) ~ . (2b)

m

When b/t -->0.910 :

Q = 0.534 E/[Fy (b/t)2]. (2c)

(b) For the limit state of yielding, when the tip (i.e. toe) of the angle leg is in tension:

mn = 1.25 My (3)

where My = yield moment about the axis of bending = Fy St, i.e. yield stress times the elastic section modulus to the tip in tension relative to the axis of bending.

In the commentary to the AISC-LRFD Specification (1993), it is stated that 'the strength at full yielding is limited to a shape factor of 1.25, which is less than that corresponding to the plastic moment of the angle. The factor of 1.25 corresponds to an allowable stress of 0.75 Fy, which has traditionally been used for rectangular shapes and for weak axis bending. It is used for angles due to uncertainties in developing the full plastic moment and to limit the large distortion required for sections with large shape factors.' Since deflections are a serviceability limit state and are generally not a consideration in the strength limit state, it can be assumed that the factor of 1.25 was used because of limited test data.

EXPERIMENTAL INVESTIGATION

Details of test specimens

A total of 13 double-angle specimens were tested under geometric axis bending. They ranged from the smallest size of 75 x 75 x 9 m m to the largest size


of 350 x 350 x 35 mm. The identification numbers and the cross-sectional dimensions of the test specimens are given in Table 1.

To ensure bending about the geometric axis, each test specimen consisted of two angles, widely separated, with spacer plates welded at load and support points. Tile four different orientations of the specimens are shown in Fig. 1. The 11 regular size specimens (specimens A-1 to M-1) were tested as simply supported beams with a central concentrated load, while the two ultra-large size specimens (specimens N-2 and P-2) were tested as simply supported beams with a constant moment region as shown in Fig. 2. The details of the test specimens are presented in Fig. 3(a) and (b).

Two unequal-leg angles of sizes 125 x 75 x 7 mm and 125 x 90 x 13 mm were tested with two different orientations--long leg vertical and long leg horizontal. Specimen N-2 was fabricated by full penetration groove welding of 3 m lo:ag pieces of 300 x 300 x 35 mm angles available in the laboratory. Thus, there was a weld at the mid-span section of the test specimen (in the constant moment region). To prevent bearing failure, ultra-large size angle specimen,; N-2 and P-2 were welded with 35 mm thick stiffeners at the support points as shown in Fig. 3(b).

Table 2 gives the orientation, total length, simply supported span length, type of loading (a single concentrated load or two point loads), width-to- thickness ratio, and yield stress of the test specimens. The width-to-thickness ratios of the specimens varied from 6.39 to 19.0. For regular size specimens

TABLE 1 Cross-sec t ional D i m e n s i o n s o f Test Spec imens

Specimen Nominal Measured Fillet Toe Heel ID dimensions dimensions radius radius radius

(ram) (ram) (ram) (mm) (ram)

A-1 2 L - - 7 5 × 7 5 × 9

B-1 2 L - - 7 5 × 7 5 x 1 2 C-1 2 L - - 1 0 0 x 7 5 × 7

F-1 2 L - - 1 2 5 x 7 5 x 7

F-2 2 L - - 1 2 5 x 7 5 x 7

G-1 2 L - - 1 2 5 x 7 5 x 1 0

H-1 2 L - - 1 2 5 x 9 0 x 1 0

K-1 2 L - - 1 2 5 x 9 0 x 1 3

K-2 2 L - - 1 2 5 x 9 0 x 1 3

L-1 2 L - - 1 5 0 x 9 0 x 9

M-1 2 L - - 1 5 0 x 9 0 × 1 2

N-2 2L - - 300 x 300 x 35

P-2 2L - - 350 x 350 x 35

2 L - - 7 4 . 1 x 7 4 . 1 x 8.45 8.5 6 - -

2 L - - 74.1 x 74.1 x 11.6 8.5 6 - -

2 L - - 9 8 . 9 x 7 4 . 1 x 6.72 10 5 - -

2 L - - 1 2 5 . 8 x 7 5 . 5 x 6.62 10 5 - -

2 L - - 125.8 x 75.5 x 6.62 10 5 - -

2L - - 125.4 x 75.3 x 9.39 10 7 - -

2 L - - 1 2 6 . 5 x 9 1 . 1 × 9.46 10 7 - -

2L - - 124.4 x 89.6 x 12.7 10 7 - -

2L - - 124.4 x 89.6 x 12.7 10 7 - -

2 L - - 149.3 x 8 9 . 6 x 8.51 12 6 - -

2L - - 1 4 8 . 4 x 8 9 . 0 x 11.3 12 8.5 - -

2L - - 298.5 x 298.5 x 34.38 24 18 10

2L - - 347.8 x 347.8 x 35.35 24 18 10


GAP - 50 mm (approx.)

/

(1)

GAP - 200 mm for N-2 GAP - 100 mm for P-2

=t (2)

Equal - leg angles Toes facing each other with a gap of 50 mm Flanges in compression

Equal - leg angles Back to back with a gap Flanges in tension

~ G A P - 50 mm (approx. )~

(3) (4)

Unequal-leg angles Long leg vertical Toes facing each other with a gap of 50 mm Flanges in compression

Unequal-leg angles Long leg horizontal Toes facing each other with a gap of 50 mm Flanges in compression

Fig. 1. Orientation of specimens.

(A-1 to M-l), one standard tensile test piece was taken from each leg of the angle and the yield stress was the average of the two values thus obtained. Tensile tests were carried out on full-size 3 0 0 x 3 0 0 x 3 5 m m and 350 x 350 x 35 mm angle specimens in a 5000 tonne-force (49.0 MN) tensile test machine, and the yield stresses obtained from these tests on full-size specimens were used for the ultra-large size angle specimens N-2 and P-2. For all tensile test specimens, tensile stress-strain curves obtained were typical of structural quality steels with an elongation at failure of approximately 30% and a yield ratio (ratio of yield strength to tensile strength) of 0.7.

For geometric axis bending, the elastic section moduli with respect to the extreme fibres in compression and tension, plastic section modulus and shape factors of the specimens are given in Table 3. The section moduli are given to the nearest 100 mm 3 to reduce the rounding off error, even though it is customary to present the values to only three signficant figures. These values


P

o.,P o.,P 1 125 mm 1 125 mm

1 . 4 '~,~ I ~ ¢ ~..~1

(a)

(For specimens A-l , B-l, C-1, F-l, F-2, G-l, H-l, K-l, K-2, L-l, and M-l)

0.5 P/~"

0.5 P 0.5 P

2 000 mm for N-2

I qC1 500 mm for P-2 I ~

1 500 mm 2 000 mm for N-2

" - I " 1 500 mm for P-2

(b)

Fig. 2. Type of loading.

~0.5 P

are based on the measured dimensions (and not the nominal dimensions) and take into ~tccount the effect of fillet radius, toe radii and heel radius.

Deflections and strain measurements

For regular size angle specimens (A-1 to M-l), vertical and horizontal deflections were measured at the centre of span. For the ultra-large size angle specimens N-2 and P-2, vertical and horizontal deflections were measured at the two load points. Deflections were measured using strain-type displacement transducer~. Strain gages were attached to two of the regular size angle specimens F-1 and M-1. Strain gages were located at mid-span at 20 mm from the heel and toes, as shown in Fig. 3(a). The strain gages were of the type capable of measuring strains even after the yielding of the specimen.

Testing

For the relgular size specimens, testing was carried out in a 30 tonne-force (294 kN) test frame. The test setup is shown in Fig. 4. For the two ultra-large


Strain gages at 20 mm from toes (a) and heel for F-1 and M-1 only

~f Gage # 2 ~ ,/Gage #1

IN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I\, rl .u. o

250 1 125 mm 1 125 mm 250 / I J , , = l ~ ,,.J .~ ~.=I~.=I 19 mm thick I ~ r l ~" P ] ~ I ~ " - I space r p la tes

2 750 mm Side View I'~ ,,,.i P' - I

Front View

l ...... iJ ......................... !.i .................................. L

Lo~L2Le~ Fig. 3. Details of specimens (a) A-1 to M-1. (b) N-2 and P-2.

specimens, testing was carried out in a 300 tonne-force (2.94 MN) testing machine, using a 1900 kgf (18.6 kN) loading beam, as shown in Fig. 5.

Load was applied in small increments (approximately 40 steps for regular- size specimens and 100 steps for the ultra-large size specimens) and deflections (and strains for specimens F-1 and M-1) were obtained at each load step using a data acquisition system. Close-up of failed specimens F-2, N-2 and P-2 are shown in Fig. 6(a), (b) and (c), respectively. The full-penetration groove weld at the mid-span section of specimen N-2 can be clearly seen in Fig. 6(b).

DISCUSSION OF TEST RESULTS

As expected, for all the specimens, the horizontal deflections were negligibly small till failure, and thus the specimens behaved as laterally supported angle beams under geometric axis bending. The test failure loads are presented in Table 4. Typical load versus mid-span vertical deflection curves for regular


(b) 0.5P 0.5P

Ei ii _LL (~

25~0i ~ 000 mm for N-2~_ 1~_~~1_.2 000 mmfor N-2 ~__ ~0~

~[..1500mmforP-2 ~ 1 5 0 0 m m f 0 r P-2 i ~

Front ViQw

II II II

\ J 35 mm thick 35 mm thick stiffener (typ.) spacer plate (typ.)

Too View

Z f l .

EE EE O O O O

Side View

Fig. 3. Continued.


TABLE 2 Details of Test Specimens

Specimen Orientation Length Simply Type of Width-to- Yield stress ID (refer to (mm) supported loading thickness Fy (MPa)

Fig. 1) span (mm) (refer to ratio Fig. 2)

A-1 (1) 2750 2250 (a) 8.77 296 B- 1 (1) 2750 2250 (a) 6.39 295 C-I (4) 2750 2250 (a) 14.7 352 F- 1 (4) 2750 2250 (a) 19.0 319 F-2 (3) 2750 2250 (a) 11.4 319 G- 1 (4) 2750 2250 (a) 13.4 290 H-1 (3) 2750 2250 (a) 9.63 290 K- 1 (4) 2750 2250 (a) 9.80 310 K-2 (3) 2750 2250 (a) 7.06 310 L- 1 (4) 2750 2250 (a) 17.5 305 M- 1 (4) 2750 2250 (a) 13.1 305 N-2 (2) 6000 5500 (b) 8.68 448 P-2 (2) 5000 4500 (b) 9.84 433

size angle specimens F-1 and M-1 are shown in Fig. 7(a) and (b), and for the two ultra-large size angle specimens N-2 and P-2 in Fig. 7(c) and (d), respectively. The load-strain graphs for the two specimens F-1 and M-1 for which the strain gages were attached are shown in Fig. 8(a) and (b). As mentioned earlier, location of the three strain gages are shown in Fig. 3(a). Strain in compression exceeding the yield strain were recorded even for specimen F-1 with a width-to-thickness ratio of 19.0. Strains in tension reached the strain hardening range. All specimens failed by buckling after excessive deforma- tion.

The test failure moments (including the moment due to self weight), nominal flexural strengths as per AISC-LRFD (1993) and the plastic moments of resistance are given in Table 4 to two decimal place accuracy (which is more than the usual design practice of rounding of the numbers to three significant figures). As can be readily seen from the table, the test failure moments for all specimens greatly exceeded the nominal flexural strengths and they exceeded even the plastic moments of resistance.

From the load-deflection data obtained during the investigation, vertical deflections at different moment levels are compared in Table 5. For the span and loading conditions used in the investigation, it was found that the deflections at 1.25 times the yield moment were only 25-32% more than the deflections at the beginning of the yielding; deflections at 1.5 times the yield moment were 1.53-1.74 times the yield values. However, deflections at 1.75 times the


TABLE 3 Elastic and Plastic Section Moduli for Bending About the Geometric Axis (based on measured dimensions, including the effect of fillet, toe radii and heel

radius)

Specimen ID Elastic section Elastic section Plastic Shape factor modulus with modulus with section

respect to respect to modulus extreme fiber extreme fiber (mm 3)

in compression in tension (mm 3) (mm 3)

A- 1 55,200 22,200 40,700 1.83 B- 1 68,200 29,700 54,200 1.83 C-1 58,700 18,800 34,100 1.81 F- 1 71,700 19,800 35,700 1.80 F-2 103,500 50,200 90,600 1.80 G- 1 89,400 26,700 49,300 1.85 H- 1 158,200 72,400 132,500 1.83 K- 1 144,000 50,300 92,200 1.83 K-2 191,100 92,100 167,800 1.82 L- 1 126,800 35,700 64,500 1.81 M- 1 149,300 44,700 82,800 1.85 N-2 1 , 4 9 0 , 7 0 0 3,652,800 2,713,400 1.82 P-2 2,144,800 5,298,200 3,841,300 1.82

Fig. 4.


Fig. 5.

Fig. 6. (a).


Fig. 6. (b).

Fig. 6. (c).

yield moment ranged from 1.88 to 4.15 times those at yield. These deflections were significantly less than the deflections at maximum load given in the last column of Table 5.


TABLE 4 Comparison Between the Test Failure Moments and M, Calculated as per AISC-LRFD (1993)

Specimen P . . . . Failure M, for local M, for Plastic Ratio of Ratio of ID (Col. (kN) moment buckling of yieMing of moment of M .... to Mtes, to M,

1) (CoL 2) (including leg tip in leg tip in resistance, smaller (Col. 8) the moment comp. tension Mp (kN.m) value of M, due to self (kN.m) (kN.m) (Col. 6) in Cols 4

weight), (Col. 4) (Col. 5) and 5 (Col. M . . . . (kN.m) 7)

(CoL 3)

A-1 25.5 14.45 20.44 8.21 12.05 1.76 1.20 B-1 33.3 18.90 25.15 10.95 16.00 1.73 1.18 C-1 23.5 13.34 17.98 8.29 11.99 1.61 1.11 F-1 21.6 12.26 17.45 7.90 11.37 1.55 1.08 F-2 54.9 31.01 32.81 20.01 28.89 1.55 1.07 G-1 33.3 18.92 24.71 9.68 14.30 1.95 1.32 H- 1 82.4 46.52 57.36 26.23 39.49 1.77 1.18 K-1 62.8 35.54 55.13 19.48 28.57 1.82 1.24 K-2 117 65.88 74.07 35.68 52.02 1.85 1.27 L- 1 43.1 24.45 31.67 13.61 19.66 1.80 1.24 M-1 53.9 30.58 43.25 17.06 25.24 1.79 1.21 N-2 1230 1240 759.7 2046 1216 1.63 1.02 P-2 2310 1740 908.0 2868 1663 1.92 1.05

25

20

z 15

O

"J 10

q~, 0 0 0 0 0 ~ 0

Vertical Deflection at Center (mm)

Fig. 7. Load-deflection curve for specimen (a) F-l; (b) M-I; (c) N-2; (d) P-2.


b 60

50

g 40

N 30

20

lO

o I 0 0 0 0

LO 0 m 0 0

Vedical Deflection at Center(rnm)

Fig.7. Continued.

Z

0 ._1

1500

1000-

500 ""Vertical Def. at

Left Load Point

0 0 0 0 0

0 0 0

Vertical Deflection at Load Point (ram)

Fig. 7. Continued.

CONCLUSIONS

For the span and loading conditions of the experimental investigation reported herein, the following conclusions about the strength of double angle beams, whose behavior is similar to laterally supported angle beams bent about the geometric axis, can be drawn:

(1) The 13 double-angle beam specimens included in the investigation developed moments which are 2-32% greater than the plastic moment


Z

"o a~ o

2500

2000-

1500"

1000-

500

0 0 0 143 0

OJ U3 D~, 0 C~ T- ~'-

-Vertical Def. at Right Load Point

Vert ical Deflect ion

at Load Point (mm)

Fig. 7. Continued.

25 z2O' 15-

Gage #2 - -

5-

0 0 0 0 0 0 0 0 0

Microstrain

Fig. 8. Load-strain graph for specimen (a) F-l; (b) M-1.


b 60

50

Z 40-

~ 3o o _J

20

10-

, ~ 1 & 2 ~ ~ 3

o I I I

~ " ' , " C~I C~ "@ U'J

Microstrain

Fig. 8. Continued.

T A B L E 5 Comparison Between Deflections at Different Moment Levels

Specimen Def. at Def. at 1.25 ID My (mm) My (mm)

(Col. 1) (Co,1. 2) (Col. 3)

(CoL Def. at (Col. Def. at 1.75 (Col. Def. at 3/(Col. 1.50 My 5)~Col. My (ram) 7)/(Col. max. load

2) (ram) 2) (Col. 7) 2) (mm) (Col. 4) (Col. 5) (Col. 6) (Col. 8) (CoL 9)

A-1 11.26 14.09 1.25 17.64 1.57 23.72 2 .11 141.62 B-1 11.57 14.64 1.27 18.34 1.59 27.02 2.34 143.91 C- 1 12.76 16.26 1.27 20.97 1.64 30.69 2 .41 139.82 F-1 11.2 14.61 1.30 19.47 1.74 46.50 4.15 148.75 F-2 8.01 10.14 1.27 12.86 1.61 17.51 2.19 80.56 G-1 10.19 12.81 1.26 15.56 1.53 19.12 1.88 155.98 H-1 7.42 9.40 1.27 11.90 1.60 16.12 2.17 183.18 K-1 9'.97 12.72 1.28 15.86 1.59 21.13 2.12 165.80 K-2 7.79 9.89 1.27 12.62 1.62 17.19 2 .21 175.22 L-1 9..11 11.68 1.28 15.16 1.66 21.68 2.38 164.85 M- 1 9..44 11.94 1.26 15.51 1.64 23.02 2.44 166.72 N-2 28.2 37.2 1.32 50.0 1.71 105 3.72 188.9 P-2 16,.38 20.66 1.26 26.70 1.63 43.49 2.66 101.18

of resistance. Even the specimen with a width-to-thickness ratio o f 19.0, when subjected to a single concentrated load at mid-span, developed failure momen t which is 8% greater than the plastic moment o f resist-

ance.


(2) The test failure moments were 55-95% greater than the nominal flexural strengths calculated as per AISC-LRFD (1993).

(3) The deflections even at 1.5 times the yield moment were only 1.53- 1.74 times the deflections at yield.

(4) Strains in compression exceeding the yield strains were observed even for the double-angle specimen with a width-to-thickness ratio of 19.0. The tensile strains reached the strain hardening range.

(5) The current AISC-LRFD specification is highly conservative as regards the geometric axis bending strength. The maximum nominal flexural strength can be increased to 1.5 My without excessive deflections.

ACKNOWLEDGEMENT

The first author gratefully acknowledges the financial support provided by N. K. K. Corporation, Japan, for carrying out this investigation.

REFERENCES

1. Thomas, B. F., Leigh, J, M. & Lay, M. G., The behaviour of laterally unsupported angles. Civil Engineering Transactions. The Institution of Engineers, Australia, pp. 103-110, 1973.

2. Bez, R. & Hirt, M. A. Dimensionnen plastique et phenomenes d'istabilite de cornieres metalliques. Construction Metallique, 1 (1982) 33-39 (in French).

3. Madugula, M. K. S., Kojima, T., Kajita, Y. & Ohama, M., Minor axis bending strength of angle beams. Proc. Int. Conf. Structural Stability and Design. Sydney, Australia, 30 October - 1 November 1995. A. A. Balkema, Rotterdam, Nether- lands, 1995.

4. AISC, Specification for Load and Resistance Factor Design of Single-angle Mem- bers. American Institute of Steel Construction, Chicago, IL, U.S.A., 1993.

Geometric axis bending strength of double angle beams

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