Starred angles supporting secondary trusses

J. Construct. Steel Research 17 (1990) 317-327

Starred Angles Supporting Secondary Trusses*

Murray C. Temple &

Kenneth Hon-Wa Mok*

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

A B S T R A C T

In some large industrial buildings, it is common to span large areas by using primary trusses in one direction and secondary trusses in the other. The secondary trusses frame into the vertical web members in the primary truss. Because of their symmetrical cross-section and the ease with which the connections can be made, starred angles are frequently used as the vertical web members in primary trusses. These starred angles are usually designed as axially loaded members, but the open nature of the cross-section and the fact that the secondary truss frames into one of the angles have raised some doubts about the loading assumption.

As a result of this concern, an experimental research program was undertaken to investigate the behavior and strength of starred angles supporting secondary trusses. The results obtained indicate that these starred-angle compression members are not concentrically loaded as the stress distribution across the angles varies greatly. It was found that, if the slenderness ratio is modified, the load-carrying capacity can be calculated in accordance with the requirements of the Canadian steel standard.

*Presented at the International Colloquium on Stability of Steel Structures held in Budapest, Hungary, 1990. This paper is a summary of a paper first published in the Canadian Journal of Civil Engineering.

*Present address: Plan Examiner, City of Windsor, Windsor, Ontario, Canada.

317 J. Construct. Steel Research 0143-974X/91/$03.50 ~) 1991 Elsevier Science Publishers Ltd, England. Printed in Great Britain

318 Murray C. Temple, Kenneth Hon-Wa Mok

INTRODUCTION

The use of trusses is an economical way to support roofs that cover large areas. These trusses are often arranged in two mutually perpendicular directions but at different elevations. The secondary trusses support roof beams that run in the same direction as the primary trusses. Thus the secondary trusses must frame into the primary trusses at a lower elevation so that the top of the roof beams are at the same elevation as the top of the primary trusses. A convenient way of framing the secondary truss into the primary truss is to use starred angles as the vertical web members in the primary truss.

The worst situation for this truss-to-truss connection occurs at the exterior of the building, with the primary truss parallel to the exterior of the building and a secondary truss framing into the primary truss from one side only. This unsymmetrical connection will be used in this research.

Because of the ease with which the connections can be made, starred angles (see Fig. 1) are often used as vertical web members in primary trusses to support the end reactions from the secondary trusses. A typical connection is illustrated in Fig. 2. It will be noted that the work point of the

U ~ - Gusset p la te V

" [ // >eg , "

\ - - - - - /~- , / /

/ /

V

\ \

\

\ \ \

Leg 4 \

Ang le B, / / /

Z

/ / Leg 3 ~ P / /

- /

~// Angle A. / . / . / Leg 1

.ILL_ | I Ill .. / /x /x

I I I Secondary t russ I I

\ \

U

Fig. I. Starred angle.

Starred angles supporting secondary trusses 319

connection coincides with the longitudinal centroidal axis of the starred angle. Thus, in design, the starred angle is designed as if the member is axially loaded. The open nature of the cross-section and the fact that the secondary truss frames into one angle only have resulted in some concern about this axial-loading assumption. This concern was the reason this research was undertaken.

REQUIREMENTS IN VARIOUS STANDARDS AND SPECIFICATIONS

An examination of the standards and specifications reveals nothing directly related to the design of starred angles supporting secondary trusses. ASCE Manual '52' Guide for Design of Steel Transmission Towers (American Society of Civil Engineers 1988) specifies that the effective length factor, K, depends upon the type of connection used. 1 For

Work point

Starred angle

/ I

I

Main truss

÷ I "

Secondary truss

Fig. 2. Connection detail.


example, with single angles with normal framing eccentricities at both ends of the unsupported panel and with an L/r <- 120, we have:

+) KLr = 60+0.50 ( (1)

where L = length of the compression member, and r = the least radius of gyration. For members unrestrained against rotation at both ends of the unsupported panel, and 120-< L/r <-200, we have:

KL L + r r

{2}

EXPERIMENTAL PROGRAM

Test program

The experimental program involved the testing of eleven starred-angle compression members. Five specimens were tested as concentrically loaded compression members, and the other seven were tested with the main load being applied through a truss. In order to reduce the number of variables, the same-size angles, 1] x 1~ x ,'~ in, (45 x 45 x 5 mm), were used in all tests. Two different lengths of specimen were used, and these were 2100 and 1270 mm, These lengths were measured from the knife edge at the top to the corresponding knife edge at the bottom of the specimen. The two lengths resulted in slenderness ratios, L/rv, of 124 and 75, respectively, where rv = the minimum radius of gyration of the cross-section. Thus the specimens can be classed as 'slender' or of ' intermediate length'.

For simplicity, the specimens will be referred to as a Type C, B, or W in order to differentiate between loading conditions and connection details. The different types of column may be described as follows:

(a) Type C Specimens. The letter C indicates that the specimen is a starred angle that is loaded concentrically. These test results were run to provide 'base data' that can be used as a basis for comparison with the load-carrying capacities of starred angles loaded through secondary trusses. Five type C specimens were tested, three 2100 mm in length and two 1270 mm long.

(b) Type B Specimens. The letter B is used to denote a specimen in which a bolted connection is used to connect a truss to a starred angle. The starred angle was loaded to failure by applying a load to the truss. This is the most common type of arrangement and is


(c)

illustrated in Fig. 2. Four type B specimens, two 2100 mm long and two 1270 mm in length, representing the vertical web-members of a primary truss, were loaded to failure by applying a load to the secondary truss. Type W Specimens. The letter W indicates that the gusset plate is welded to the angles. In all other respects, the specimens were the same as the Type B specimens.

Specimen designation

Each specimen, for simplicity, was designated by a test-series number. For example, B2100.1 indicates that the specimen was a Type B specimen, 2100 mm in length, and the first specimen of its type tested.

Test set-up

All specimens were tested with double knife edges top and bottom. The Type C specimens were tested under an axial load in a loading

frame in the Structural Engineering Laboratory. The complete test set-up for Type B and Type W specimens is shown in

Fig. 3. A simple steel truss was fabricated and bolted at one end to the specimen and at the other end to an existing column of the structural testing frame in the Structural Laboratory.

Strain gages

Strain gages were attached to the legs of the angles in the Type B and Type W specimens in order to determine the stress distribution across each leg of each angle of the specimen. As many as twenty-four 90 ° rosette strain gages were installed across the legs of the angles.

Test procedure

During the testing of the Type C specimens, the load was applied slowly in increments of 8.9 kN. At about 80% of the predicted failure load, the load increment was reduced to 2.2 kN. The load increment was applied until failure occurred, which was taken as the load at which a large increase in lateral deflection resulted from a very small increase in load.

At the start of each test for a Type B or Type W specimen, a load of 4-45 kN was first applied by using the jack at the top of the specimen. This load was kept constant throughout the test. This axial load was used to represent the load in the vertical web member of the truss that resulted


Fig. 3. Test set-up.

from the loads applied directly to the primary truss but not including the end reactions from the secondary trusses. The total load applied to the specimen was measured by the loadcell at the bottom of the specimen. The load was applied to the truss so that 4.45-kN increments resulted in the specimen. This load increment was used until the specimen failed.

RESULTS

General

The mechanical properties of the steel were determined from tensile tests. The average value of the yield stress and modulus of elasticity were


determined to be 390 and 205 400 MPa, respectively. These values were used in all computations.

Failure loads

Theoretical results The compressive resistance for the Type C specimens, as listed in column 3 of Table 1, were calculated by using the equations in the Canadian Steel Standard. A resistance factor of 1.0 was used.

Experimental failure loads The experimental failure loads are tabulated in Table 1.

The experimental failure loads for the Type C specimens agree quite well with those predicted by using the requirements of the Canadian Steel Standard. Hence, it can be concluded that these values can be used as 'base data' for comparison with the failure loads obtained for the Type B and Type W specimens.

The slender Type B and Type W specimens, with the starred angles loaded primarily through the secondary truss, had failure loads that are very close to those obtained for the same-length Type C specimens, i.e. C2100. The reason for this will become evident when the stress distribution in the legs of the angles is examined. The W2100 specimens had failure loads that are 6--8% higher than the failure loads obtained for the B2100 specimens.

TABLE 1 Experimental Failure Loads

Specimen Experimental Compressive Pex/ Cr number failure load resistance (%)

Pex (kN) Cr (kN)

C2100.1 89.0 88-0 101 C2100.2 93.9 88-0 107 C2100.3 93-4 88-0 106 C1270.1 197-3 177-5 111 C1270.2 216.9 177.5 122 B2100.1 91"9 88.0 104 B2100.2 91.9 88-0 104 B1270.1 133-8 124.3" 108 B1270.2 123-8 124.3" 100 W2100.1 97.9 88-0 111 W2100.2 99-9 88-0 113

*Values are based on the modified slenderness ratios suggested by ASCE Manual 52.1


For the B1270 specimens, the failure loads are 133.8 and 123.8 kN. These failure loads are some 30-40% lower than the failure loads obtained for the C1270 specimens. The drop in load-carrying capacity can be explained when the stress distribution in the legs is examined. Thus, it can be concluded that starred angles of intermediate length supporting secondary trusses cannot be designed as axially loaded columns.

In order to achieve a better relationship between the experimental and theoretical results, a combined approach is suggested. In this approach, the starred-angle members supporting secondary trusses are designed as axially loaded members according to the requirements of the Canadian Steel Standard. The effective length factors, however, are modified in accordance with the requirements of ASCE Manual 52. In Table 1, a comparison is made between the compressive resistances calculated by using this approach and the experimental results. It is observed that, by modifying the slenderness ratio, the Canadian Steel Standard gives better results than simply calculating the compressive resistance of the starred angle as an axially loaded member.

Stress distribution

Figure 4 shows the stress distribution across the angles for Specimen B2100.1. In these figures, the angles have been straightened out to lie flat on the sheet of paper. Angles A and B and Legs 1-4 are shown in Fig. 1. Both angles display a similar trend. The stress relationship is essentially uniform at small loads. This probably reflects the influence of the 4.45-kN axial load applied at the top of the specimen. As the load on the truss, and hence the load on the specimen, is increased, the stress across tile cross-section becomes very non-uniform. When the failure load is reached, the tips of Legs 2 and 4 are subjected to tensile stresses, whereas the other edges of the angles are subjected to high compressive stresses, of up to about 300 MPa, but still below the yield stress of 390 MPa. It should be pointed out that the stress-distribution curves for the W2100 specimens are very similar to those shown in Fig. 4.

It will be noted that Angle A carries more of the applied load than Angle B. At about 50% of the failure load, Angle A carries about 60% of the load, but this gradually reduces to 55% at the failure load. It will also be noted that Legs 1 and 3 carry most of the applied load.

In the intermediate length columns B1270, the stress, as shown in Fig. 5 (a) and (b), at failure in Leg 1 is equal to the yield stress of 390 MPa. In Leg 2, although measurements of strain were not made right at the tip, it appears that the stress reached the yield stress in tension. It will be noted that, in Leg 3, the stress at highloads actually started to decrease. This is due to local buckling of the leg.


U~ O9 bJ

I ' - ¢13

"°° 1 ' ° ' ,no, . , .~_ ~ ~ Angle A 91.9 kN ss S = 2 5 0 ~ --~ot ~ Leg , ~ I

~ 7 ° m ~°4~-~

I / , / " o 200 I I i I i '.J

150

I00

50

kN

1.4.5 kN

!2.2 kN

kN

' I / Leg 2 Leg I " f l I I t r I ,

-42.5 -3,0 -15 0 15 50 42.5

DISTANCE ALONG CENTRELINE OF ANGLE A (turn)

A a

0. .

0 3 ¢ n h i 0 : : 1-- O3

300

g "~ 250 ==

E 0 o 200

150

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(b) Angle B

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kN

;.5 kN

kN

;... s ~ ' / Leg 4 Leg 3

-42.5 -30 -15 0 15 30 42.5

DISTANCE ALONG CENTRELINE OF ANGLE B (ram)

Fig . 4. S t r e s s d i s t r i b u t i o n B 2100 .1 .


O.

CO CO bJ n : I-- CO

300

200 E o

I00

0

-I00

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c

(a) Angle A r - - .... / ~ " "" I

/ t11.2 - " "

, . t> .-"1 ~ - - " ~ - 89.o ~N

44.5 kN

4.45 kN

/ , t I

~ Angle Leg I

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,,

Leg I

I i I i

0 15 30 42.5

DISTANCE ALONG CENTRELINE OF ANGLE A (ram)

l I / Leg 2

C "J i - 4 2 . 5 - 3 0 -15

A

0 15 30 42.5

40C~- (b) Angle B J /-'-133.8 kN

O.

O3

W

( n

m m 0) & 2oc E 8

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->

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! I S

I Leg 4

- 4 2 . 5 - 3 0 - 1 5 0

A.W. B ~'11~

Leg 5

-42.5 - 50 -15 0 15 50 42.5

DISTANCE ALONG CENTRELINE OF ANGLE B (ram)

Fig. 5. S t ress d i s t r i bu t ion B1270.1.


CONCLUSIONS

The following conclusions for starred angles supporting secondary trusses are based on the preceding work.

1. Standards and specifications do not cover the design of such members.

2. The experimental results for intermediate-length members indicate that such members cannot be designed as axially loaded members.

3. A simplified design method for such angles as proposed. In this approach, the effective length factors are modified in accordance with the requirements of ASCE Manual 52. The compressive resistance is then calculated according to the requirements of the Canadian Steel Standard.

4. Angle A carries more load than Angle B (see Fig. 1), and Legs I and 3 carry much more load than Legs 2 and 4.

R E F E R E N C E

1. American Society of Civil Engineers. Guide for design of steel transmission towers. ASCE Manuals and Reports on Engineering Practice. No. 52, 1988.

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Starred angles supporting secondary trusses