Design of Tension Members

Introduction Applications Tension Members in Buildings Purlin Sag Rod Top chord Roof Purlin System Tie Rafter Roof Truss Suspenders Suspended Building Bracings Braced Frame Tension Members in Buildings

Cross Sections used Introduction… Single & Double Angles Channel I-Section (Joist / Beam) Rod Cable Built-up Sections

Material Introduction… E = 200 GPa σ High Strength Steel Mild Steel ε fy / fu ≈ 0.6 – 0.85 fu High Strength Steel fy Small elongation fu Mild Steel fy = 250 Large elongation ε 0.00125 0.2% 0.012 ≈ 0.015 0.23 – 0.25 Common Steels

Section Design in Tension

Behaviour in Tension Plate σ ε 2 possible Limit States Important: fy fu ε σ 2 possible Limit States Yielding Ultimate (Rupture) Important: Yielding of Gross Area f

Plate with Hole Behaviour in Tension… ε σ 2 possible Limit States fy fu ε σ 2 possible Limit States Yielding Ultimate (Rupture) Important: Rupture of Net Area fy Elasto-Plastic fu Plastic f Elastic

Net Area Plate with Holes Net Area An = (b – d)  t g t

(b – 2d)  t < An < (b – d)  t Net Area… Plate with Holes t d g b Net Area An = (b – 2d)  t Net Area An = (b – d)  t l (b – 2d)  t < An < (b – d)  t An = ?? d b g t p

Plate with Multiple Holes Net Area… Plate with Multiple Holes All possible failure paths to be investigated Minimum net area to be used in design Tensile strength t d g g b g An = [b – nd + (p2/4g)]  t p2/4g for all inclined parts of the section p p p

Three types of Bolt Holes (Table 19, pp 73) Net Area… Three types of Bolt Holes (Table 19, pp 73) Standard clearance hole Over size hole Slotted hole Short Long 18 18 20 22 56 Standard (STD) Oversized (OVS) Short-slotted (SSL) Long-slotted (LSL) Different holes for 16mm (nominal) diameter bolt

Punctured Bolt Holes (Cl 3.6.1, pp 17) Net Area… Punctured Bolt Holes (Cl 3.6.1, pp 17) 2 mm excess of actual diameter All possible failure paths to be investigated Minimum net area to be used in design t d g g b g An = [b – nd + (p2/4g)]  t p2/4g for all inclined parts of the section p p p

Block Shear Plates More than one bolt line Bolt shear strength and plate bearing strength are higher Courtesy:: Georgia Inst Tech 1 2 4 3 Shear Planes Tension Plane

Design Strategy for Block Shear Gross and Net Areas in Tension & Shear Yield in Tension (Atg) Yield in Shear (Avg) Rupture in Tension (Atn) Yield in Shear (Avg) Yield in Tension (Atg) Rupture in Shear (Avn) Rupture in Tension (Atn) Rupture in Shear (Avn)

Non-Uniform Stress More stress near restraint Less stress near un-restrained / free ends T/2 T/2 T / Ag

Shear Lag Channels Both legs connected Part of cross-section NOT effective Less Stressed Gusset Plate

Angles Shear Lag… Single leg connected Eccentrically loaded through gusset plates Free, Un-stiffened, Un-connected end Part of cross-section NOT effective Less Stressed Gusset Plate

Factors affecting / causing Shear Lag Effects of Shear Lag Strength reduction Part of cross-section ineffective (less stressed) Consider in Design Factors affecting / causing Shear Lag Outstand (unconnected part) More outstand – more shear lag Thin / slender outstand – more shear lag Connection stiffness Flexible connection – more shear lag Single leg connection versus both leg connection One bolt versus multiple bolt connection

Angles in Tension Design Strategy Yielding of gross section Rupture of net section Block shear

Welded Tension Members No “Net” Area No reduction of area due to bolt holes Design strength based on Gross Area only

Threaded Rods in Tension Design Strategy Yielding of gross section Ag × fy / gm0 Rupture of net section 0.9 × An × fu / gm1 Courtesy:: AISC f ≤ fy fy fu d root d gross Elastic Elasto-Plastic Plastic

Member Design in Tension

Design Steps Factored Design Force Demand T Calculate Ag req = T / (fy / gm0) An req = T / (fu / gm1) Choose a trial section Analyse for its strength Td Ensure Td > T (Capacity > Demand) Check l/r to be within prescribed limits Efficiency h = T / (Ag × fy / gm0)

Efficiency h = T / (Ag × fy / gm0) Design Steps… Efficiency h = T / (Ag × fy / gm0) 100% Efficiency Gross Area Yielding Welded connection Bolted Connection Efficiency may reduce due to Bolt holes Net area rupture governing Shear lag Block shear

Summary Tension Members Efficient load carrying members Efficiency may reduce due to Bolt holes Shear lag Block shear

IS 800: 2007 Section 6 (page 32 – 33) 6.1 Tension Members 6.2 Design Strength due to Yielding of Gross Section 6.3 Design Strength due to Rupture of Critical Section 6.4 Design Strength due to Block Shear

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