Question

A prestressed hollow core slab with typical section is given the following properties:

Area =1.4×10
∧
5 mm2
St=Sb=6.8×10
∧
6 mm3
Overall width =1.2 m
Overall depth =200 mm
​
The section is prestressed with 820kN force at an eccentricity of 63 mm below the neutral axis of the section. Consider slab weight as 2.7kPa, superimposed dead load as 2.0kPa, and live load as 2.9kPa. Assume that the eight-meter span slab is simply supported. Allowable stresses at service loads are +2.0MPa in tension and −15.5MPa in compression. (Consider 15% prestress loss) a) Determine the stress at the top fibers of the slab at the ends due to the initial prestress force. b) Calculate the resulting stress at the top fibers of the slab at midspan due to the loads and prestress force. c) Calculate the maximum total load (kN/m) including its own weight, that the slab can be subjected to if the allowable stress at service loads is not to be exceeded.

Answer 1

To solve for the stresses in a prestressed hollow core slab, we employ structural engineering principles to calculate the stress at the top fibers due to initial prestress, stress at midspan due to combined effects of loads and the prestress, and determine the maximum load capacity based on allowable stress limits.

Step-by-step explanation:

Calculating Prestressed Slab Stresses and Load Capacity

To answer the student's question, we need to perform calculations in structural engineering. Specifically, we calculate stresses in a prestressed concrete element under different loading conditions and determine the maximum allowable load.

Part a: Stress at Top Fibers Due to Initial Prestress

The initial prestress force (after considering a 15% loss) is 0.85 × 820 kN = 697 kN. Using the formula σ = P/A ± (P×e)/St, where σ is the stress at the top fiber, P is the prestress force, A is the area, e is the eccentricity, and St is the section modulus for the top fiber, the stress at the top fiber can be calculated. Note that the second term is subtractive because the prestress force is below the neutral axis.

Part b: Stress at Top Fibers at Midspan Due to Loads and Prestress

At midspan, the top fiber stress is affected by the superimposed dead load, live load, and slab weight, in addition to the prestress force. We calculate the stresses individually and sum them to find the total stress at midspan.

Part c: Maximum Total Load Calculation

The maximum total load capacity of the slab can be computed using the formula σ = P/A ± M/S, against the given allowable tensile stress and compressive stress limitations, where M is the moment caused by the loads and S is the section modulus at the relevant fiber. This takes into account the self-weight of the slab and any superimposed loads.