Problem 1 The Z shaped crosssection beam shown in fig 1 is s

Problem 1 The \"Z\" shaped cross-section beam shown in fig. 1 is sub- jected to a bending moment of magnitude Mb, which is acting in the direction indicated in the figure. (1) De- termine the centroid location. (2) Determine the ax- ial and bending stiffnesses in the centroidal axis system = ( ,) indicated on the figure. (3) Using this axis system, compute the orientation of the neutral axis and compute magnitude and location of the maximum axial stress, Ímax. (4) Find the orientation of the principal centroidal axes of bencling, Tc*( , ). (5) Using these axes, determine the magnitude and location of the maxi mum axial stress. Verify that this is the same result as in step 3, Use the following data: h 95 mm, ba-30 mm. bb = 50 min, tw20 nn, ta-15 mm. and tb = 30 min, =-45 degrees, and Mb 10 kN-m. For this problem, you can make the thin-wall approximation. Perform al the computation in Matlab D C b, Figure 1: \"z\" shaped cross-section

Solution

1) centroid location :

area of section A,

A1= 15*30 =450mm²

A2= 1000mm²

A3= 1500mm²

distance of centroid Y

y1= 15+30+(50/2) = 70mm

y2= 80mm

y3= 25mm

centroid of Z-section is , Y= a1y1+a2y2+a3y3/(a1+a2+a3)

Y= 50mm