STRUCTURAL ENGINEERING

George Baltzopoulos PhD MSc

Academic Year $2023/2024$

Final $($fourth$)$ homework assignment

Design of a continuous reinforced concrete beam against flexure and shear

Consider the three$-$span prismatic beam from the third homework assignment. The beam is to be constructed out of reinforced concrete with a $T$ cross section as shown in the figure below. Concrete grade is $C\frac{30}{37}$ and reinforcing steel of grade B$500$C will be used. Using the bending moments and shear forces calculated for the third homework assignment, you are to design the beam at ultimate limit state against flexure $($bending$)$ and shear.

Specific assignments:

Design for flexure and shear the critical cross$-$sections at the supports $B$ and $C$ and design for flexure the critical cross$-$sections along the spans $AB,BC,CD,$ selecting the critical design combination for each case $($out of four given in the $3^{rd}$ assignment.

Make sure that sections subjected to both positive and negative moment are designed against both, assuming that, in either case, the concrete compression zone will remain within a constant$-$width portion of the cross$-$section.

Draw a summary diagram showing all shear and longitudinal reinforcement calculated, as in the figure above $($NOTE: bar diameters and detailing in the figure are purely for illustrative purposes, each student is expected to provide what emerges from one's own calculations$).$

Make sure that all intermediate calculations are clearly presented and in agreement with the reinforcement drawing.

Due date: Monday, January ${15}^{th}2024$