Design a reinforced concrete beam to support a uniformly distributed load $($UDL$)$ of $20$ kN$/$m over a span of $6$ meters. The beam is simply supported at both ends and needs to satisfy the following criteria:

Load and Support Conditions:

UDL $=20$ kN$/$m

Span $($L$)=6$ meters

Simply supported beam

Material Properties:

Concrete strength $($f$\_$c$\text{'})=25$ MPa

Yield strength of steel $($f$\_$y$)=400$ MPa

Design Requirements:

Determine the required dimensions $($width and effective depth$)$ of the beam.

Calculate the steel reinforcement required $($area of steel bars and spacing$)$ assuming a balanced design approach.

Check the design for both bending and shear requirements.

Ensure that the beam satisfies deflection limits$.$

Procedure:

Calculate the maximum bending moment $($M$\_$max$)$ using the formula for a simply supported beam under UDL.

Determine the effective depth $($d$)$ based on the bending moment and allowable stress in concrete.

Choose a suitable depth$-$to$-$width ratio.

Calculate the area of steel reinforcement required using the balanced section approach.

Check for shear stress and provide adequate shear reinforcement if necessary.

Verify deflection limits using the appropriate deflection formula and check against permissible limits$.$

What is dynamic programming?