A square 4m x 4m is isotropically reinforced at the bottom. If it is ...
Working load W = 14kpa
Ultimate load Wu = Wn x load factor
= 14 x 1.5
= 21 kpa
where l = 4
Moment capacity
= 14 KN.m/m
Hence the correct answer is option D.
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A square 4m x 4m is isotropically reinforced at the bottom. If it is ...
To determine the moment capacity required as per yield line theory, we need to consider the given working load and the dimensions of the reinforced square.
Given:
Working load = 14 kPa
Square dimensions = 4m x 4m
1. Calculating the distributed load:
The working load of 14 kPa can be converted to a distributed load by multiplying it with the area of the square. Since the square has an area of 4m x 4m = 16m², the distributed load can be calculated as:
Distributed load = Working load x Area = 14 kPa x 16m² = 224 kN
2. Calculating the moment due to the distributed load:
The moment due to the distributed load can be determined by considering the distance from the centroid of the square to the point where the load is acting. In a square, the centroid is located at the center. Therefore, the distance from the centroid to any side is half the length of the side.
Distance from centroid to side = 4m / 2 = 2m
The moment due to the distributed load can be calculated using the formula:
Moment = Distributed load x Distance from centroid to side
Moment = 224 kN x 2m = 448 kN.m/m
3. Determining the moment capacity:
According to the yield line theory, the moment capacity required for a reinforced square is equal to the moment due to the distributed load. Therefore, the moment capacity required in this case is 448 kN.m/m.
Thus, the correct answer is option 'D' - 14 kN.m/m.