ANALYSIS OF TENSION MEMBERS

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1 CHATER Structural Steel Design LRFD Metod Tird Edition ANALYSIS OF TENSION MEMBERS A. J. Clark Scool of Engineering Department of Civil and Environmental Engineering art II Structural Steel Design and Analysis 3a FALL 2002 By Dr. Ibraim. Assakkaf ENCE to Structural Design Department of Civil and Environmental Engineering University of Maryland, College ark CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 1 Tension members are found in Bridges and roof trusses Towers Bracing systems Cases were tey are used as tie rods Te design of tension members is very simple and straigtforward. No buckling problems are encountered as in te case of compression members. 1

2 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 2 RHINE BRIDGE, COLOGNE-RODENKIRCHEN, ( ), 47), SAN m CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 3 Transmission Towers 2

3 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 4 Tension Members Trusses CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 5 Tension Members Tension Structures 3

4 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 6 Rods One of te simplest forms of tension members is te circular rod. Te rod as been used frequently in te past, but as only occasional uses nowadays in bracing systems, ligt trusses, and in timber construction. Te problems associated wit rods tat tere is some difficulty connecting tem to many structures. CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 7 Rolled Sapes (Standard Sections) Today, tension members include Single angles Double angles Tees Cannels W sections, and Built-up sections Tese members look better, are stiffer, and are easier to connect to oter structures. 4

5 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 8 Steel Sections CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 9 Tie lates (bars) Members consisting of more tan one section need to be tied togeter. Tie plates (also called tie bars) located at various intervals or perforated cover plates serve to old te various pieces in teir correct positions. Tese plates elp correct any an equal distribution of loads between te various parts. 5

6 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 10 Steel Cables Tey are made wit special steel alloy wire ropes tat are cold-drawn to a desired diameter. Te resulting wire strengts of about 200,000 to 250,000 psi can be economically used for suspension bridges, cable supported roofs, ski lifts, and oter similar applications. CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 11 Nominal Strengt Te strengt of a tension member may be described in terms of te limit states tat govern. Te controlling strengt limit state for a tension member can eiter Yielding of te gross cross-section of te member away from te connection, or Fracture of te effective net area (i.e., troug te oles) at te connection 6

7 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 12 LRFD Specification Wen te limit state is general yielding of te gross section over te member lengt, as for a tension member witout oles (i.e., wit welded connection), te nominal strengt n is expressed as = F A n u t y y g φ F A F y = yield stress A g = gross cross-sectional area g wit φ = 0.90 t (1) CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 13 LRFD Specification For tension members aving oles, suc as for rivet or bolts, te reduced cross section is referred to as te net area. Holes in member cause stress concentration (nonuniform stresses). For example, a ole in a plate wit a tensile service force produces a stress distribution at service load as sown in Fig. 1 7

8 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 14 Figure 1. Elastic Stress Distribution wit Holes resent f avg on net section f max = 3 f avg CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 15 LRFD Specification Teory of elasticity sows tat tensile stress adjacent to te ole will about tree times te average stress on te net area. However, as eac fiber reaces yield strain, tat is ε y = F y /E s, its stress ten becomes a constant F y wit deformation continuing wit increasing load until finally all fibers ave acieved or exceeded te strain ε y (see Fig. 2) 8

9 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 16 Figure 2. Ultimate Condition - Stress Distribution wit Holes resent F y CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 17 LRFD Specification Wen te limit state is a localized yielding resulting in a fracture troug te effective net area of a tension member aving oles, te nominal strengt n is expressed as = F A n u t u u e φ F A e wit φ = 0.75 t (2) F u = tensile strengt A e = effective net area = UA n A n = net area U = efficiency factor 9

10 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 18 Table 1 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 19 Net Areas, A n Wenever a tension member is to be fastened by means of bolts or rivets, oles must be provided at te connection. Terefore, te member cross sectional area is reduced and te strengt of te member may also be reduced depending on te size and location of te oles. Te term net cross-sectional area or net area refers to te gross sectional area of te member minus te oles, notces, or oter indentations. 10

11 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 20 Net Areas, A n (cont d) Metods for Cutting Holes 1. Te most common and least expensive metod is to punc standard oles 1/16 in. (1.6 mm) larger tan te diameter of te rivet or bolt. In general te plate tickness is less tan te punc diameter. Tis is accounted in design by assuming tat te extend of te damage is limited to a radial distance of 1/32 in. (0.8 mm) around te ole. CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 21 Net Areas, A n (cont d) Metods for Cutting Holes 2. A second metod of cutting oles consists of subpuncing tem 3/16 in. (4.8 mm) diameter undersize and tem reaming te oles to te finised size after te pieces being joined are assembled. Tis metod is more expensive, but offers te advantage of accurate alignment. Tis metod produces better strengt. 11

12 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 22 Net Areas, A n (cont d) Metods for Cutting Holes 3. A tird metod consists of drilling oles to a diameter of te rivet or bolt plus 1/32 in. (0.8 mm). Tis metod is used to join tick pieces, and is te most expensive of te all common metods. CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 23 Net Areas, A n (cont d) How to find te area of te ole? Te area f te ole is considered a rectangular area, and is computed as follows: A d t = (3) p For fastener in standard oles, d = diameter of fastener + 1/8 in. (3.2 mm) t p = tickness of plate or metal used 12

13 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 24 s A = d t p CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 25 Example 1 Wat is te net area A n for te tension member sown? 1 late Standard ole for a 3 - in - diam. bolt 4 13

14 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 26 Example 1 (cont d) 4 in. A g 2 ( 0.25) 1.0 in = 4 = widt to be deducted for ole = + = in. = A n 7 1 = 1.0 = 8 4 d = Ag A = Ag dt p in 1 4 in. Area (A ) of ole CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 27 Example 2 Determine te net area of te 3/8 8-in plate sown. Te plate is connected at its ends wit two lines of ¾-in bolts. u u u 2 u 2 1 late - 8 in 4 3 late - 8 in 8 u 1 late - 8 in 4 14

15 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 28 Example 2 (cont d) 3 2 A g = () 8 = 3in widt to be deducted for one ole = + = in. = A n = Ag 2A = Ag 2dt p 7 3 = = in d CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 29 Example 3 Compute te net area for te member sown in te figure. WT in 4 bolts 15

16 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 30 Example 3 (cont d) Using a WT12 31, te following properties can be obtained from te AISC Steel Manual (age 1-44): A = 9.16 in 2 Terefore, t w = in t f =0.59 in A g = A = 9.16 in 2 CHATER 3a. ANALYSIS OF TENSION MEMBERS Slide No. 31 Example 3 (cont d) widt to be deducted for one ole = + = in. = An = Ag = Ag = A g = ( A ) ( A ) Flange ( d t ) ( d t ) 2d t f p Falnge d t w 7 8 Web p Web 2 ( 0.59) ( 0.430) = 7.75 in d 16

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