Calculate the magnitude and show the location of the

Question

Problem 1

Select the best single answer for each question below.

1. Internal bending moments (M) cause ______________ stresses on a cross-section.

(A) Normal
(B) Shear
(C) Normal and shear
(D) Deflecting

2. The stresses caused by Bending Moments __________________________.

(A) are uniform over the entire cross section

(B) vary linearly along the direction of the cross-section perpendicular to the bending moment vector

(C) vary parabolically along the direction of the cross-section perpendicular to the bending moment vector

(D) None of the above

3. Considered alone, a bending moment always creates a combination of _________________ on the cross-section.

(A) compression and tension

(B) positive and negative shear

(C) moments of inertia

(D) differential elements

4. Does increasing the depth of a beam always increase the max/min stresses due to bending? Why?

(A) Yes σ = -My/I (if "y" gets bigger, then the magnitude of the stress must increase as well).

(B) Yes. An increase in depth will always result in the same or lower moment of inertia.

(C) No. An increase in depth may result in a higher moment of inertia "I", which may counteract the increase in "y" and reduce the stress.

(D) None of the above

Problem 2

The simply-supported beam above is subject to the loadings shown. The cross-section is uniform and is shown to the right.

Complete the following:

(A) Calculate the maximum magnitude of the internal bending moment about the z-axis (M₂) due to the 12 kN point loads

(B) Determine the:

a. Location of the neutral axis for bending about the z-axis (Y_???? )

b. Moment of inertia about the z-axis (??₂)

c. Location of the neutral axis for bending about the y-axis (Z_????)

d. Moment of inertia about the y-axis (??_Y)

(C) Calculate the magnitude and show the location of the maximum compressive and tensile normal stresses on the cross-section due to the following:

a. The maximum moment calculated in part (A), M₂

b. A bending moment about the y-axis equal to M_y = +6 ??N · ??

c. M₂ and M_y acting concurrently