AISC sakla2001Q3.pdf
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1、ENGINEERING JOURNAL / THIRD QUARTER / 2001 / 127 ABSTRACT T he design of eccentrically-loaded single angle struts is a tedious and lengthy procedure. A computer program was developed to perform these time consuming calcula- tions and generate design tables for 36 ksi and 50 ksi equal and unequal leg
2、 angles. The program uses the less conser- vative approach permitted by the AISC Specification for Load and Resistance Factor Design of Single-Angle Mem- bers (AISC, 1993). This approach involves applying the interaction equation separately at the corner and the two leg tips of the angle, with the p
3、roper signs for compression and tension. Two step-by-step numerical examples are pre- sented in this paper to outline the procedure implemented to generate load tables for equal and unequal leg angles. INTRODUCTION Single angles are the most basic shape of hot rolled steel sections. They are typical
4、ly attached by one leg at their ends to gusset plates or other structural elements. In spite of the simplicity of their cross-section, single-angle com- pression members are among the most difficult structural elements to analyze and design. The AISC Manual of Steel Construction, Load and Resis- tan
5、ce Factor Design (AISC, 1994) requires that such mem- bers be designed as beam-columns. The design is governed by the AISC Specification for Load and Resistance Factor Design of Single-Angle Members (AISC, 1993), which is reproduced in Part 6 of the AISC Manual of Steel Con- struction. A numerical e
6、xample is given in that Manual to outline this procedure. The load is assumed to act at the mid-plane of the gusset plate and at the center of the attached leg as shown in Figure 1. The example as presented did not illus- trate the less conservative and more correct approach allowed by the AISC Spec
7、ification for Load and Resistance Factor Design of Single-Angle Members. No numerical examples were provided to illustrate the application of the interaction equation to unequal-leg single-angle struts. The evaluation of the axial capacity of equal-leg single angle struts with due consideration of t
8、he sign of the stress was later addressed by Lutz (1996). It was shown that consid- eration of the sign of the stress at a location when evaluat- ing the interaction expression leads to a significant increase in axial capacity. In addition, practicing engineers find the AISC LRFD procedure for the d
9、esign of single angle struts connected by one leg tedious and lengthy for what appears to be a simple structural element. Tables for the allowable axial load of equal-leg single angles in compression were presented by Walker (1991). No design tables, based on the LRFD approach, are available for sin
10、gle angle compression members connected by one leg. The lack of design tables and the amount of effort involved in hand calculations make practicing engineers tend to use very conservative approxi- mate methods for the design of such structural elements. DESIGN TABLES The purpose of this paper is to
11、 provide tables (see Table 1) for the design strength of equal and unequal leg single- angles connected by one leg to gusset plates. Two steel strengths are included in the design tables, 36 ksi and 50 ksi. The basis for the design method is contained in the AISC LRFD Manual (AISC, 1994) and is illu
12、strated in this paper by two step-by-step examples. The following assumptions were made: Tables for the Design Strength of Eccentrically-Loaded Single Angle Struts SHERIEF S. S. SAKLA Sherief S.S. Sakla is assistant professor, civil engineering department, Tanta University, Tanta, Egypt. Fig. 1. Ang
13、le plan view. Sakla 2000-5R.qxd 9/7/2001 3:33 PM Page 127 2003 by American Institute of Steel Construction, Inc. All rights reserved. This publication or any part thereof must not be reproduced in any form without the written permission of the publisher. 128 / ENGINEERING JOURNAL / THIRD QUARTER / 2
14、001 1. The eccentric axial load is applied at the center of the gusset plate and at the center of the connected leg. 2. The maximum slenderness ratio with respect to the minor principal axis, the z-axis, is 200. 3. The effective length factors about the principal axes, Kzand Kw, are equal. 4. The gu
15、sset plate thickness is 1.5 times the angle thick- ness. For common structures, the practical range of the gusset plate thickness may vary from 1.0 to 2.0 times the angle thickness. Increasing the gusset plate thickness increases the eccentricity about the x-axis which, in turn, decreases the load c
16、arrying capacity. For a 441/2angle with a slen- derness ratio of 200 and yield stress of 50 ksi, changing the gusset plate thickness from 1.0 to 2.0 times the angle thick- ness changes the design strength from 16.6 to 15.6 kips (i.e. the design strength decreases by about 6 percent). For the same an
17、gle with a slenderness ratio of 60, changing the gus- set plate thickness from 1.0 to 2.0 times the angle thickness changes the design strength from 70.0 to 60.4 kips (i.e. about 14 percent decrease in the design strength). This jus- tifies the use of a gusset plate thickness of 1.5 times the angle
18、thickness in producing the design tables. The tabu- lated values are conservative if the gusset plate thickness is less than 1.5 times the angle thickness and it is not common to have a gusset plate thickness greater than 1.5 times the angle thickness. The following examples illustrate the procedure
19、 used by the program for the case of unequal-leg single angles. Example I shows the case of an angle attached by the short leg while example II illustrates the case of an angle attached by the long leg. NUMERICAL EXAMPLE I Given: An angle 841/2is attached by the short leg to a gusset plate. The guss
20、et plate thickness is 0.75 in. as shown in Fig- ure 2. The effective length KL is 100.0 in. Calculate the maximum factored compressive load which may be applied through the center of the gusset plate. Angle Properties: A= 5.75 in.2 Ix= 38.5 in.4Iy= 6.74 in.4 rx= 2.59 in.ry= 1.08 in. y = 2.86 in.x =
21、0.859 in. rz= 0.865 in. = 14.95o Fy= 50 ksiE = 29,000 ksi Solution: Determine the angle properties with respect to the princi- pal w and z axis. Iz= Arz2= 5.75 (0.865)2= 4.30 in.4 Iw= Ix+ Iy Iz= 38.50 + 6.74 4.30 = 40.94 in.4 The distances between Points A, B, and C and the angle principal axes are
22、shown in Figure 2. At the angle tip of the connected leg (Point A) Sz= 4.30/2.36 = 1.82 in.3 Sw= 40.94/3.33 = 12.29 in.3 At the angle corner (Point B) Sz= 4.30/1.57 = 2.74 in.3 Sw= 40.94/2.54 = 16.12 in.3 At the angle tip of the outstanding leg (Point C) Sz= 4.30/0.74 = 5.81 in.3 Sw= 40.94/5.12 = 8.
23、00 in.3 The angle concentric design compressive strength Pn= 84.7 kips (from AISC LRFD Manual Single Angle Columns Table for L841/2with KL = 8.33 ft). The interaction of flexure and axial compression shall be evaluated for the principal bending axes at the angle corner and tips using LRFD Single Ang
24、le Spec. Equations 6-1a and 6-1b. The flexural terms are either added to or sub- tracted from the axial load term depending on the sense of flexural stresses at the considered point. For a tiny load applied at Point D, stresses at the angle tips and corner could be calculated as follows: 2.67 in. w
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