Week 2 Challenge

Aim: To design tension members from the concept and procedure learnt from Week 2 videos.

Introduction: Tension members are structural elements that are subjected to axial tensile forces. Examples of tension members are bracing for buildings and bridges, truss members, and cables in suspended roof systems.

Design of Tension Member

1. Net Area for tension member calculation problem

Calculate the net section area for the tension member as shown in Figure below. The plate size is 260 x 20 thick and Bolt size is 20 mm.

Tip Steps:

• Refer Slide 26 for Net area calculation formula
• For angle section Flatten the member and calculate the gauge distance

Plate – Drilled Hole

Diameter of bolt, d = 20mm

Diameter of bolt hole, d₀ = 20mm + 2mm clearance = 22mm

Thickness of plate = 20mm

Width of plate (b) = 260mm

There is no staggering p_si = 0

No. of bolt holes in the weakest section = 4

Net area at weakest section

A_n = [260 - 4x22] x 20 = 3440mm²

Plate – Zigzag bolting

Diameter of bolt, d = 20mm

Diameter of bolt hole, d₀ = 20mm + 2mm clearance = 22mm

Thickness of plate = 20mm

Width of plate (b) = 260mm

Staggering p_si = 60mm & 50mm ; g = 60mm

No. of bolt holes in the weakest section = 3

Assuming critical section as A-C-F,

Net area at weakest section

A_n = [260 - 3x22 + (60² /4x60) + (50² /4x60)] x 20 = 4388 mm²

Angle (200 x 100 x 12 with M20 bolt)

Diameter of bolt, d = 20mm

Diameter of bolt hole, d₀ = 20mm + 2mm clearance = 22mm

Thickness of plate = 20mm

Width of plate (b) = 260mm

Staggering psi = 100mm & 50mm ; g = 90mm

No. of bolt holes in the weakest section = 2

Net area at weakest section

A_n = [200 - 2x22 + (50² /4x90)] x 12 = 1955 mm²

2. Sag rod design problem

Design a sag rod as shown in Figure below. Purlins are supported at 1/3^rd points by sag rods.

Assume centre to centre distance of Rafter spaced at 8 m , spacing of purlin = 1.2 m, Self weight of roofing (including thermal insulation)= 60 kg/m² , Wind pressure intensity = 150 kg/m²,Slope of rafter = 15 degrees, Live Load =75 kg/m². Assume self weight of purlin as 100 kg/m.

Tip Steps :

• Calculate total gravity load (DL & LL) on the purlin
• Calculate Wind load acting on the purlin. Note that wind load acts perpendicular to the member.
• Resolve and calculate the load acting parallel to the roof
• Force contribution to each sag rod is calculated
• Calculate required net area and chose a desired sag rod size.

Total gravity load = 100kg/m + (75kg/m² x 8m) + (60kg/m²x1.2) = 772kg/m²

F =5/8 *w *sin0 *s*4

F = 5/8 * 772*9.81*sin15*8*4

F= 39202.38 N

Area = F /0.6fy

Pi*d² = 39202.38 / 0.6x250

d = 9.12mm

3. Determine section size for given tensile load

Design a single angle member of length 5m to carry axial tensile force of 500 kN. Yield strength fy of the material to be considered is 350 N/mm².

Tip Steps :

• Calculate required area of cross section from factored load
• Choose an angle section from required area calculated
• Calculate design strength of the member due to yielding
• Calculate design strength of member by tearing of net section
• For a given member assume bolts placed with appropriate edge/end/pitch/gauge distance and calculate block shear capacity
• Check slenderness is within limit

Gross area required = (500x1000)/(350/1.1) = 1299mm²

Try ISA 150x75x8, Ag = 1742 mm²

Use gusset plate of thickness 10mm

Strength of M20 bolt in Single shear = 45272N

Adopting edge distance = 40mm and pitch distance = 60mm

K_b is smaller of 40/3*22, 60/3*22 -0.25, 400/410, 1

i.e., K_b = 0.606

No of bolts required = 500*1000/45272 = 11.044, say 12

Checking for Design:

• Strength against yielding = Agfy/Y_mo = 1742*350/1.1 = 554273 N > 500000
• Strength of plate in rupture:

Area of connected leg Anc = (150-22-8/2)*8 = 992 mm²

Area of outstanding leg Ago = (75-8/2)*8 = 568 mm²

Beta = 1.206

Tdn = 0.9*410*992/1.25 + 1.206 *568*350/1.1 =510795 N > 500000N

• Strength against block shear failure

Avg = (40+60x10)8=5120mm2

Avn = (40+60x10-10.5x22)x8 = 3272mm2

Atg = (150-40)x8 = 880mm2

Atn = (150-40-0.5x22)8 = 792mm2

Strength against block shear failure is smaller of

= 5120x350/sqrt(3)x1.1 + 0.9x792x410/1.25 = 1174354 N > 500000N

= 0.9x3272x410/sqrt(3)x1.25 + 880x350/1.1 = 837659 N > 500000N

Hence safe.

Check for maximum l/r

r- least radius of gyration = 16mm

l/r = 5000/16 = 312.5 > 300 , Not OK

Revise the section.