Question

A simply supported slab spanning 7.5 meters is given the following characteristics: Area =1.2×10

∧
5 mm2 St=Sb=4.16×10
∧
6 mm3 Prestressing Force =500kN Eccentricity =38 mm Slab Weight =2.35kPa Superimposed Dead Load =2.0kPa Live Load =2.4kPa Allowable stresses during service loading stage are indicated as 3.2MPa for tension and 18.5MPa for compression. (Consider 20% loss of prestress.) a) Calculate the resulting stress at the bottom fibers of the slab at L/4 from the center of bearings. b) Calculate the resulting stress at the bottom fibers of the slab at midspan. c) Calculate the maximum total load (kPa) that the slab can carry if the allowable stresses at service loads are not to be exceeded.

Answer 1

To calculate the resulting stress at different locations of the slab and determine the maximum load it can carry, we need to consider the prestressing force, area, eccentricity, slab weight, superimposed dead load, live load, and the allowable stresses. By calculating the stress using the provided formulas and values, we can find the stress at L/4 and midspan. Additionally, by using the area and allowable stresses, we can determine the maximum load the slab can carry.

Step-by-step explanation:

In order to calculate the resulting stress at the bottom fibers of the slab at L/4 from the center of bearings, we need to consider the prestressing force and the losses in prestress. The formula to calculate the stress is given by:

Stress = (Prestressing Force - Losses in Prestress) / Area

Substituting the given values, we get:

Stress = (500kN - 20% of 500kN) / 1.2×105 mm2

Solving this equation will give us the resulting stress at L/4.

To calculate the resulting stress at the bottom fibers of the slab at midspan, we use the same formula but with the eccentricity factored in:

Stress = (Prestressing Force - Losses in Prestress + Eccentricity * Slab Weight) / Area

Finally, to calculate the maximum total load that the slab can carry without exceeding the allowable stresses, we need to consider the different load types. The formula for this is:

Total Load = Area * (Allowable Tension Stress + Allowable Compression Stress) - Prestressing Force - Slab Weight - Superimposed Dead Load - Live Load