Week 6 Challenge

Structural Systems of Industrial structures

Question 1: -

Chequered Plate design

Design a chequered plate to carry a uniformly distributed Factored live load of 15 kN/m2. Consider the plate is spanned with dimension of 1200 mm x 5000 mm with all edges fixed. (Refer Roark’s chart table 11.4)

Given data:-

Factored Live load = 15 kN/m²

Plate dimension = 1200 mm x 5000 mm

All edges are fixed

Answer:-

Procedure:-

Step 1:-

Assume the thickness of plate = 10 mm

F_y = 250 N/mm²

E = 2 x 10⁵ N/mm²

Density of Steel = 78.5 kN/m³

Therefore Self weight of Plate = 0.01 x 78.5 = 0.785 kN/m²

Step 2:-

Stress at centre:

As per Roark’s formula Table 11.4 Case No 8a

σ = β₂qb² / t²

a / b = 5000 / 1200 = 4.167

Therefore, β₁ = 0.5000, β₂ = 0.2500, α = 0.0284

σ = 0.2500 x 15 x 1.2² / 0.01²

= 54000 kN/m²

σ = 54 N/mm²

Step 3:-

Stress at centre of Long edge:

σ_max = -β₁qb² / t²

a / b = 5000 / 1200 = 4.167

Therefore, β₁ = 0.5000, β₂ = 0.2500, α = 0.0284

σ_max = -0.5000 x 15 x 1.2² / 0.01²

= -108000 kN/m²

σ_max = -108 N/mm²

Hence safe.

Step 4:-

Deflection at centre:

y_max = αqb⁴ / Et³

= 0.0284 x 15 x 1.2⁴ / (2 x 10⁵ x 0.01³)

y_max = 4.42 mm

Allowable deflection is half of Thicness of Plate = 10 / 2 = 5 mm.

Hence Maximum deflection of plate is lesser than the allowable deflection.

So the plate is safe to carry the load.

Question 3: -

Lateral Load resisting system & Gravity Load resisting system

Draw the load path and identify the Axial force type in different type of bracing system below to resist horizontal shear & gravity load. Also state the type of bracing system

Answer: -

• The type of given bracing is Single diagonal bracing. And having Lateral load. Load path of the given bracing shows in above figure (i). It shows the diagonal bracings are in compression and all horizontal members are in axial tension.
• The type of given bracing is Single diagonal bracing. And having Lateral load. Load path of the given bracing shows in above figure (ii). It shows the diagonal bracings are alternatively carrying compression & tension force and all horizontal members will not carry any force because no restraint is provided by the beams to develop force.
• The type of given bracing is Double diagonal bracing. And having Lateral load. Load path of the given bracing shows in above figure (iii). It shows the one diagonal bracings are in compression, another one in tension and all horizontal members will not carry any force because no restraint is provided by the beams to develop force.
• The type of given bracing is one type of K-bracing or Eccentric bracing and also knowns as Knee bracing. And having Lateral load. Load path of the given bracing shows in above figure (iv). It shows the half of the web members and both horizontal and inclined will be subjected to tension and compression simultaneously. Forces and deformations in each member of braced bent will be reversed as the building is subjected to lateral loading in opposite direction.

• The type of given bracing is Single diagonal bracing. And having gravity load. Load path of the given bracing shows in above figure (v). It shows the Vertical columns are in compression and all horizontal and diagonal members will not carry any force.
• The type of given bracing is Single diagonal bracing. And having gravity load. Load path of the given bracing shows in above figure (vi). It shows the diagonal bracings and vertical columns are in compression and all horizontal members are in axial tension.
• The type of given bracing is Double diagonal bracing. And having gravity load. Load path of the given bracing shows in above figure (vii). It shows the diagonal bracings and vertical columns are in compression and all horizontal members will not carry any force.
• The type of given bracing is one type of K-bracing or Eccentric bracing and also knowns as Knee bracing. And having gravity load. Load path of the given bracing shows in above figure (viii). It shows the vertical column members are in compression and all other members will not carry any force.