The cross section given in Figure a) of Problem 5.4 is subjected to an additional moment, its value is M = 36 kNm. Determine the stresses in the steel and in the extreme compressed concrete fibre. Final value of the shrinkage is εcs = 5×10-4. Elastic modulus of concrete is Ec = 31 GPa, elastic modulus of steel is Es = 200 GPa. Assume uncracked concrete. Diameter of steel bars is Φ = 12 mm.
Solve Problem
Maximum stress in the concrete, σc [N/mm2]= Maximum stress in the steel, σs [N/mm2]=Solve
Do you need help?
Steps
Step 1. Calculate the section properties. Cross sectional properties of the replacement homogeneous cross section are the following Step 2. Determine the kinematic load and deformations of the beam. The kinematic load is The cross section is symmetric, thus the curvature from the axial load is zero, the elongation of the beam is Step 3. Determine deformation from the bending moment. From the moment the curvature of the beam’s axis is: Step 4. Summarize stresses in the concrete and in the steel from the bending and from the shrinkage.Step by step
Check section properties
Check deformations
Check bending deformation
Check stresses
Results
Cross sectional properties of the replacement homogeneous cross section are the following The kinematic load is The cross section is symmetric, thus the curvature from the axial load is zero, the elongation of the beam is The beam’s axis curves also from the bending moment. Stresses in the concrete and in the steel from the bending and from the shrinkage are summarized as followsWorked out solution