Question

u Review Part B - Calculate the moment of inertia Learning Goal: To find the centroid and moment of inertia of an I-beam's cross section, and to use the flexure formula to find the stress at a point on the cross section due to an internal bending moment. Once the position of the centroid is known, the moment of inertia can be calculated. What is the moment of inertia of the section for bending around the z-axis? Express your answer to three significant figures and include the appropriate units. View Available Hint(s) When a beam is subjected to an internal bending moment M (Figure 1), the stress distribution acting on a cross section can be related to the moment at that section and the geometric properties of the cross section using the flexure formula. The relationship can be written in terms of the maximum stress, Omax = "", where c is the perpendicular distance from the neutral axis to the farthest point in the section. It can also be written in terms of the vertical distance from the neutral axis, yo = - In each equation, I is the moment of inertia of the cross- sectional area about the same neutral axis. The neutral axis of the section passes through the centroid. I = Value Units Submit Part C. Maximum bending stress Figure < 1 of 3 > Determine the absolute maximum bending stress in the section if it is subjected to an internal moment of 545 ft. lb around the 2- axis. Include the sign of the stress in your answer. Express your answer in psi to three significant figures. View Available Hint(s) A vec mo ? psi Submit

Answer 1

Wi- A2)=) L I O tot W, =10 in n=614 in We = 3.5 in f = 15 in w = 0.5 in L un

Past-A y = Asy,+ A2 Y2 + A3Y3 A+ A2+ A3 5(10x15) (6.4+15+1,5) +(6:4X015) X (1+5+6:4 ) + 3.5x15)(15) 10X15 + 6.4X0.5 +3.5x15 129,757 15804 + 3.9375 23:45 y = 6.3423 7 part- 12 I; = 10x15 3+(10x15) (810 5–6.343)? =82.69468 int I, = 0.55x6:43 +10.5464) (47–6:3493)? = 19.5535 int 73 = 3.5X1,53 + (305215) (6.3493-01772 12

– 165, 1711 9 in+ I = I + I2 + I3 = 82. сочь8+ ) 9. 5535 +165.1719 т= 267,92 in / part-C If x = x bшо – 545х12x6:39 22 a67:42 omax = 1551106 7pse