Week 4 Challenge

Aim:

To find section classifications for given steel sections, deflection values and beam strength for the given data.

 

1. Section classification

ISMB500

b=180mm

t=17.2

b/Tf = 10.46, Which is under class-2 limit of 10.5. This is Compact section.

 

ISMC200

b=75mm

t=11.4mm

b/Tf=6.57, Which is under class-1 limit of 9.4. This is plastic section.

 

PG1300X450X20X12

b=450mm

t=20mm

b/Tf=450/20=22.5, Which is beyond class-3 limit of 13.6. This is slender section.

 

Double Angle (Back to back) 2x75x75x6

b=75mm

T=6mm

b/Tf=12.5, Which is less than class-3 limit of 15.7. This is semi-compact section

 

RHS 150x100x10

d=100mm

t=10mm

d/t=10, Which is less than class-1 limit of 84. This is plastic section.

 

Builtup box 1000x450x20x12

d=1000mm

t=12mm

d/t=83.3, which is less than class-1 limit of 84. This is plastic section.

 

2. Effective length calculation

Major axis(X-X):

L=Unsupported length of Rafter = 2x 20/cos15 = 41.4 m

Both ends rotation restrained (Due to Knee bracing) + translation restrained.Thus adopting condition-6 from Table-11 of IS800

Effective length (Le)=0.65L = 0.65x41.4 = 26.91 m

 

Minor axis (Y-Y):

L=unsupported length of Rafter=1.2 m

Both ends translation restrained + rotation free. Thus adopting condition-3 from Table-11 of IS800

Effective length (Le)=1.0xL = 1.0x1.2 = 1.2 m

 

3. Calculation of deflection

(a) Data

EI = 20x10^6 Nm2

 

Deflection for UDL= 5wL^4/384EI

w = 6 N/m

L = 7 m

Deflection due to UDL = 5x6x(7)^4 / (384x20x10^6) = 72030 / 7680000000 = 0.0094 mm

 

Deflection for Two point loads

= 100x2/24x20x10^6 x ((3x7^2) - (4x2^2))

= 4.1666x10^-7 x 131

= 0.055 mm

 

Total deflection due to both UDL and Point loads = 0.0094 + 0.055 = 0.064 mm

 

(b) Data

EI = 25x10^6 Nm2

 

Deflection for UDL= 5wL^4/384EI

w = 1.5 N/m

L = 5 m

Deflection due to UDL = 5x1.5x(5)^4 / (384x25x10^6) = 4687.5 / 96000000000 = 0.0005 mm

 

Deflection for Two point loads

Taking average load and average distance, P=3.5N, a=2m

= 3.5x2/24x25x10^6 x ((3x5^2) - (4x2^2))

= 1.1666x10^-8 x 59

= 0.0007 mm

 

Total deflection due to both UDL and Point loads = 0.0005 + 0.0007 = 0.0012 mm

 

(c) Data

L=10 m

UDL=10kN/m

Deflection=5 mm

 

Deflection formula for UDL=5wL^4/384EI

EI = 5wL^4/384d, where d=deflection

EI = (5x10x10^4) / (384x0.005)

EI = 260417 Nm2

 

 4. Steel section design for given loadings:

Data:

Span = L = 6m

Baywidth = 3m

Dead load= 5kN/m2

Live load= 6 kN/m2

Point load at midspan= 100KN

Laterally restrained beam

 

All Floor load into UDL= 33kn/m, Resulting BMD=wl^2/8 = 148.5 kNm, Factored BMD M=1.5x148.5 = 223 kNm

BMD due to point load = wl/4 = 100x6/4 = 150 kNm, Factored BMD M=1.5x150 = 225 kNM

Shear force due to ULD=wl/2 = 99kN, Factored Shear force V=150 kN

Shear force due to Point load=w/2=50 kN, factored shear force V=75 KN

 

Total design BMD=448 kNM

Total design Shear = 225 KN

 

As per IS-800, clause 8.2.1.2,

M=BZFy/ym

(448x10^6) = 1xZx250/1.1

Z = 1.63x10^6 mm3

Selecting ISMB-500, with Z=1.81x10^6 mm3

 

Check for shear as per clause 8.4,

Av = Web area = 500x10.2 = 5100 mm2

Vp = 5100x250/sqrt(3) = 736 kN, > Design shear. Hence SAFE

 

Deflection for UDL = 5wl^4/384EI

= 5x33x6000^4/384x2x10^5x4.52x10^8

Deflection due to UDL = 6.16 mm

 

Deflection for Point load = pL^3/48EI

= 100x6000^3/48x2x10^5x4.52x10^8

Deflection due to Point load = 4.98 mm

 

Total deflection = 6.16+4.98 = 11.14 mm

Limit as per IS-800 Table-6, Span/240 = 25mm, Hence SAFE

 

b = 180mm, Tf=17.2mm

b/Tf = 10.41, Section is compact as per Table-2 in IS-800. Hence not a Slender section.

 

5. Purlin design for given loading

Data:

Gravity floor load= 0.75+1.4 = 2.15 kN/m2

UDL acting on the purlin = 2.15x2 = 4.3 kN/m

Resolving to normal to purlin, 4.3xcos20 = 4.04 kN/m

Gravity + Lateral load UDL = 4.04 x (1x2) = 6.04 kN/m

BMD = 6.04x4^2/8 = 12.08 kNm

SFD = wxl/2 = 12.08 kN

 

As per IS-800, clause 8.2.1.2,

M=BZFy/ym

(12.08x10^6) = 1xZx250/1.1

Z = 53152 mm^3

Selecting ISMC125, with 6810 mm^3

 

Check for shear as per clause 8.4,

Av = Web area = 125x5.3 = 662.5 mm2

Vp = 662.5x250/sqrt(3) = 95.6 kN, > Design shear. Hence SAFE

 

Deflection for UDL = 5wl^4/384EI

= 5x6.08x4000^4/384x2x10^5x4250000

Deflection due to UDL = 23.8 mm, Not satisfied since the deflection limit is Span/180 = 22.2 mm

 

b = 65mm, Tf=8.2mm

b/Tf = 7.92, Section is plastic as per Table-2 in IS-800. Hence not a Slender section.