Question

For the same singly-reinforced (reinforcement in tension only) concrete section used in Homework 3, we want to investigate the impact of using a parabolic semi-segment for the shape of the concrete stress-strain curve in the determination of the ultimate capacity of the beam. Note that steel stress-strain behavior will be modeled using elasto-plastic model. The properties of the materials are s"-4500 psi for the concrete and Jy -60 ksi for the reinforcement. Using this type of behavior leads to the stress block shown below at ultimate (with peak of the semi-parabola at the very top of the cross-section, where the limiting strairn value of 0.003 is reached) fe -4500psi N.A 24" 26" 4-#8 Bars Note: stress block has perfectly vertical slope at maximum stress value (not at NA location) a) Draw the complete diagrams showing strain, stress, and equivalent forces acting along the depth of the cross-section assuming the section is under-reinforced. In the equivalent force diagram, clearly indicate both the magnitude of the force and its point of application using symbols b) Determine the symbolic equation used to solve for the neutral axis location. Only one unknown variable should be present in the equation.(Note we are assuming the section is under-reinforced)

Answer 1