CEE $598$ Advanced Structural Steel Design

HW #$1-2019$

Elastic$-$Plastic Properties of Structural Sections$-$ the Generation of Moment$-$Curvature Relationship

Problem #$1$

Write a Maple$/$matlab symbolic program to calculate the centroid of a standard W and Angle section using geometrical input parameters. Verify the answer with typical sections. Discuss the results.

Problem #$2$

Derive the equations for the moment capacity of material with different elastic moduli in tension and compression. A material has its Young's Modulus Ec in compression and Et in tension. Derive an expression that relates the applied bending moment to the stress. Consider a rectangular cross section, $b$ units wide, and $h$ units deep.

a$)$ Derive the general formula as a function of the variable where: $Ec=Et$

b$)$ Special case, show that the expression reduces to $=+-M\frac{y}{\text{I}}$ for the special case where, $=1$

Problem #$3$

Compute the elastic moment capacity and plastic moment capacity as well as the moment$-$curvature relationship for a steel section of dimension:

a$)$ an equilateral triangle, of dimension, a

b$)$ a round bar, radius, $r$

c$)$ Compute the shape factors defined as the ratio of plastic modulus to elastic modulus

d$)$ generate a comparative plot of the results of moment curvature relationship using a parametric study $($changing variables and discussing the effect of variations$),$ discuss the results using numerical results.