Question

Many worldwide cities are in locations where extreme weather conditions can damage critical urban infrastructures. Select a representative at-risk city and design a structural system to shield the city. Develop a set of requirements and at least two different design concepts. Estimate the worst-case loading conditions for two of your design concepts, and draw a free body diagram for them. Which concept do you think is better in the worst-case conditions?

Answer 1

In New Delhi temperature variations is in between -5°C to 50°C and mean temperature is around 29°C. If shield is designed for 29°C, then max temperature difference is 34°C.

 

Schematic of concept 1 is given below.

Weight of the shield, W = 77100 KN

Length of the shield, l = 1000 m

Height of the shield support, h = 10 m

Cross-sectional area of the shield, A = 1 m2

 

At low temperature i.e. -5°C the temperature difference is 34°C. Due to decrease in temperature the shield tries to contract, tries to pull the support at points A and B.

 

Considering shield is made of steel, linear thermal coefficient α = 13.6 × 10-6 m/m°C and modulus of elasticity E = 2 × 1011 N/m2. The pull is equal at both ends and it is given by,

FH = ΔT × α × E × A

= 34 × 13.6 × 10-6 × 2 × 1011 × 1

= 924.8 × 105 N

= 92480 KN

 

The free body diagram of Shield (concept 1)

 

Reaction force in horizontal direction at both the reactions will be same and equal to force due to thermal expansion.

RAx = RBx = FH = 92480 KN

 

Weight of shield is uniformly distributed and total vertical reactions at supports will be same at both ends. It is given by

RAy = RBy = W/2 38550 KN

 

Reaction force at A

RA = √(RAx)2 + (RAy)2

= √(92480)2 + (38550)2

= 100194 KN

 

Reaction force at A and B is 100194 KN

 

Moment at point C is given by,

ΣMC = RAx × h

= 92480 × 10

= 924800 KN ∙ m

 

Moment at point C is 924800 KN ∙ m

 

Due to very large moment about C, it may lead to failure of support.

 

Free body diagram of Shield (concept 2)

 

Strings are added to give more support at columns and to avoid horizontal force on supports. Horizontal reaction force on supports at point A and B will be zero and moment at point C also zero.

RAx = RBx = 0

 

For static equilibrium, horizontal forces at A should be zero.

ΣFAH = 0

-Tsin 30° + FH = 0

T = 92480/sin 30°

= 184960 KN

 

Tension in string, T is 184960 KN.

 

For static equilibrium, vertical forces at A should be zero.

ΣFAV = 0

-Tcos 30° + FAy – W/2 = 0

 

FAy = 184960 cos 30° + 38550

= 198730 KN

 

Since reaction force from support is only vertical component, resultant reaction forces at point A and B are in vertical direction and it is given by,

FA = FB = FAy = 198730 KN

 

Reaction force at support in concept 2 is almost two times that of in concept 1, but moment about C is zero. It reduces the chances of failure of support.

In New Delhi temperature variations is in between -5°C to 50°C and mean temperature is around 29°C. If shield is designed for 29°C, then max temperature difference is 34°C.