Instituto Tecnológico de Celaya

Departamento de ingeniería mecánica

Catedrático: José Alberto Zavala Bustos

1

DISEÑO MECÁNICO 1, programa ingeniería mecánica, Grupo FJ21/A

Problemario correspondiente a la primera competencia.

Instrucciones: Resuelve, presenta, expresa o determina, según el caso, lo que se pide.

Rúbrica:

En hojas blancas tamaño carta

A mano

Utilizar tinta no lápiz

Presentar diagrama de cuerpo libre o diagrama en su caso

Planteamiento: ecuaciones y/o principios a emplear

Hasta Aquí valor del 90%

Operaciones y resultado

Integrar a su carpeta de evidencias, entregar el día del examen, hora de clase, salón de clase.

Resto valor del 10%

Entregar un juego por equipo de 5 integrantes …

1. Electrical strain gauges were applied to a notched specimen to determine the stresses in the

notch. The results were 0021.0x and 00067.00y . Find x and y if the material

is carbon steel.

2. The state of stress at a point is 2x , 6y , 4z , 3xy , 2yz , and 5zx

kpsi. Determine the principal stresses, draw a complete Mohr’s three-circle diagram, labeling

all points of interest, and report the maximum shear stress for this case.

3. In the figure, shaft AB is rotating at 1000 rev/min and transmits 10 hp to shaft CD through a

set of bevel gears contacting at point E. The contact force at E on the gear of shaft CD

is determined to be kjiF CDE 0.8088.3628.92 lbf. For shaft CD:

(a) draw a free-body diagram and determine the reactions at C and D assuming simple

supports (assume also that bearing C is a thrust bearing),

(b) draw the shear-force and bending-moment diagrams, and

(c) assuming that the shaft diameter is 1.25 in, determine the maximum tensile and

shear stresses in the beam.

Instituto Tecnológico de Celaya

Departamento de ingeniería mecánica

Catedrático: José Alberto Zavala Bustos

2

4. Illustrated in the figure 4 is a 1 1/2 in-diameter steel countershaft that supports two pulleys.

Pulley A delivers power to a machine causing a tension of 600 lbf in the tight side of the belt

and 80 lbf in the loose side, as indicated. Pulley B receives power from a motor. The belt

tensions on pulley B have the relation T1 = 0.125T2 . Find the deflection of the shaft in the z

direction at pulleys A and B. Determine the maximum tensile and shear stresses in the beam.

Assume that the bearings constitute simple supports.

5. The figure shows a steel countershaft that supports two pulleys. Pulley C receives power from a

motor producing the belt tensions shown. Pulley A transmits this power to another

machine through the belt tensions T1 and T2 such that T1 = 8T2.

(a) Find the deflection of the overhanging end of the shaft, assuming simple supports at

the bearings.

(b) Determine the maximum tensile and shear stresses in the beam.

Instituto Tecnológico de Celaya

Departamento de ingeniería mecánica

Catedrático: José Alberto Zavala Bustos

3

6. Among the decisions a designer must make is selection of the failure criteria that is applicable

to the material and its static loading. A 1020 hot-rolled steel has the following properties: Sy

= 42 kpsi, Su t = 66.2 kpsi, and true strain at fracture εf = 0.90. Plot the failure locus and, for

the static stress states at the critical locations listed below, plot the load line and estimate the

fac-tor of safety analytically and graphically.

(a) σx = 9 kpsi, σy = −5 kpsi.

(b) σx = 12 kpsi, τx y = 3 kpsi ccw.

(c) σx = −4 kpsi, σy = −9 kpsi, τx y = 5 kpsi cw.

(d) σx = 11 kpsi, σy = 4 kpsi, τx y = 1 kpsi cw.

7. An ASTM cast iron, grade 30 (see Table A–24), carries static loading resulting in the stress

state listed below at the critical locations. Choose the appropriate failure locus, plot it

and the load lines, and estimate the factors of safety analytically and graphically.

(a) σA = 20 kpsi, σB = 20 kpsi.

(b) τx y = 15 kpsi.

(c) σA = σB = −80 kpsi.

(d) σA = 15 kpsi, σB = −25 kpsi.

8. The figure is a schematic drawing of a countershaft that supports two V-belt pulleys.

For each pulley, the belt tensions are parallel. For pulley A consider the loose belt tension is 15

percent of the tension on the tight side. A cold-drawn UNS G10180 steel shaft of uniform

diameter is to be selected for this application. For a static analysis with a factor of safety

of 3.0, determine the minimum preferred size diameter. Use the distortion-energy theory.

Instituto Tecnológico de Celaya

Departamento de ingeniería mecánica

Catedrático: José Alberto Zavala Bustos

4

9. The figure shows a shaft mounted in bearings at A and D and having pulleys at B and C. The

forces shown acting on the pulley surfaces represent the belt tensions. The shaft is to be made

of ASTM grade 25 cast iron using a design factor nd = 2.8. What diameter should be used for

the shaft?

10. A 2-in-diameter solid steel shaft has a gear with ASTM grade 20 cast-iron hub (E = 14.5 Mpsi)

shrink-fitted to it. The specifications for the shaft are

The hole in the hub is sized at 1.999 ± 0.0004 in with an OD of 4.00 ± 1/ 32 in. Using the

midrange values and the modified Mohr theory, estimate the factor of safety guarding against

fracture in the gear hub due to the shrink fit.