EME 150A, SQ 2024 Homework 2

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EME 150A, SQ 2024

Homework 2

1) A cantilevered beam is loaded as shown. The cross section at the wall is shown, with points of interest A (at the top), B (at the center), and C (midway between A and B).

(a) Plot shear force and bending moment along the beam length.

(b) Sketch the stress elements at points A, B, and C. Calculate the magnitudes of the stresses acting on the stress elements. Do not neglect transverse shear stress.

(c) Find the maximum shear stresses (i.e., from Mohr’s circle) for the stress elements at A, B, and C.

(d) Assuming the critical stress element is the one with the largest maximum shear stress from part (b), which point is critical?

(e) If the length of the beam is varied from longer to shorter, the critical stress element will switch from point A to point B. At what length does this happen?

2) For the beam shown,

(a) Plot shear force and bending moment along the beam length,

(b) Determine critical cross sections along the beam,

(c) Determine the maximum tensile and compressive bending stresses on the critical cross section,

(d) Determine the maximum shear stress due to V, and

(e) Determine the maximum shear stress in the beam.

3) The cantilevered bar in the figure is made from a ductile material and is statically loaded with Fx = 75 lbf, Fy = –

200 lbf, and Fz = 100 lbf. Analyze the stress situation in rod AB by obtaining the following information.

(a) Determine the precise location of the critical stress element (cross section location and the point of the cross section in rod AB).

(b) Sketch the critical stress element and determine magnitudes and directions for all stresses acting on it.

(c) For the critical stress element, determine the principal stresses and the maximum shear stress.