## A ductile material has the properties Syt = 60 kpsi

A ductile material has the properties Syt = 60 kpsi and Syc = 75 kpsi. Using the ductile Coulomb-Mohr theory, determine the factor of safety for the states of plane stress given in Prob. 5–3.

For a bar of AISI 1030 hot-rolled steel and:

(a) σx = 25 kpsi, σy = 15 kpsi

(b) σx = 15 kpsi, σy = -15 kpsi

(c) σx = 20 kpsi, σy = −10 kpsi

(d) σx = -12 kpsi , σy = 15 kpsi , τxy = -9 kpsi

(e) σx = -24 kpsi , σy = -24 kpsi , τxy = -15 kpsi

## Repeat Prob. 5–1 by first plotting the failure loci in

Repeat Prob. 5–1 by first plotting the failure loci in the σA, σB plane to scale; then, for each stress state, plot the load line and by graphical measurement estimate the factors of safety.

A ductile hot-rolled steel bar has a minimum yield strength in tension and compression of 350 MPa. Using the distortion-energy and maximum-shear-stress theories determine the factors of safety for the following plane stress states:

(a) σx = 100 MPa, σy = 100 MPa

(b) σx = 100 MPa, σy = 50 MPa

(c) σx = 100 MPa, τxy = −75 MPa

(d) σx = -50 MPa, σy = -75 MPa, τxy = -50 MPa

(e) σx = 100 MPa, σy = 20 MPa, τxy = -20 MPa

## A round cold-drawn 1045 steel rod has a mean strength S̅y = 95.5

A round cold-drawn 1045 steel rod has a mean strength y 95.5 kpsi with a standard deviation of σ̂ = 6.59 kpsi. The rod is to be subjected to a mean static axial load of P̅ 65 kip with a standard deviation of σ̂P  5.0 kip. Assuming the strength and load have normal distributions, determine the reliabilities corresponding to the design factors of

(a) 1.2

(b) 1.5.

Also, determine the diameter corresponding to each case.

## Repeat Prob. 5–19 by first plotting the failure loci in

Repeat Prob. 5–19 by first plotting the failure loci in the σA, σB plane to scale; then for each stress state, plot the load line and by graphical measurement estimate the factor of safety.

(a) σx = 25 kpsi, σy = 15 kpsi

(b) σx = 15 kpsi, σy = -15 kpsi

(c) σx = 20 kpsi, τxy = −10 kpsi

(d) σx = -15 kpsi , σy = 10 kpsi , τxy = -15 kpsi

(e) σx = -20 kpsi , σy = -20 kpsi , τxy = -15 kpsi

## A brittle material has the properties Sut = 30 kpsi

A brittle material has the properties Sut = 30 kpsi and Suc = 90 kpsi. Using the brittle CoulombMohr and modified-Mohr theories, determine the factor of safety for the following states of plane stress.

(a) σx = 25 kpsi, σy = 15 kpsi

(b) σx = 15 kpsi, σy = -15 kpsi

(c) σx = 20 kpsi, τxy = −10 kpsi

(d) σx = -15 kpsi , σy = 10 kpsi , τxy = -15 kpsi

(e) σx = -20 kpsi , σy = -20 kpsi , τxy = -15 kpsi

## Repeat Prob. 5–12 by first plotting the failure loci in

Repeat Prob. 5–12 by first plotting the failure loci in the σA, σB plane to scale; then for each stress state, plot the load line and by graphical measurement estimate the factor of safety

A ductile material has the properties Syt = 60 kpsi and Syc = 75 kpsi. Using the ductile Coulomb-Mohr theory, determine the factor of safety for the states of plane stress given in Prob. 5–3.

For a bar of AISI 1030 hot-rolled steel and:

(a) σx = 25 kpsi, σy = 15 kpsi

(b) σx = 15 kpsi, σy = -15 kpsi

(c) σx = 20 kpsi, σy = −10 kpsi

(d) σx = -12 kpsi , σy = 15 kpsi , τxy = -9 kpsi

(e) σx = -24 kpsi , σy = -24 kpsi , τxy = -15 kpsi

## Program the shear-lag solution for the shear-stress state into your

Program the shear-lag solution for the shear-stress state into your computer using Eq. (9–7). Determine the maximum shear stress for each of the following scenarios:

Provide plots of the actual stress distributions predicted by this analysis. You may omit thermal stresses from the calculations, assuming that the service temperature is similar to the stress-free temperature. If the allowable shear stress is 800 psi and the load to be carried is 300 lbf, estimate the respective factors of safety for each geometry. Let l = 1.25 in and b = 1 in.

## The drawing shown is of a mounting fixture to locate

The drawing shown is of a mounting fixture to locate and orient a rod (not shown) through the large bore. The fixture will be bolted to a frame through the four bolt holes that are countersunk to recess the bolt heads. The bolt holes have too much clearance to properly align the rod, so the fixture will be aligned with two locating pins in the frame that will fit in the ∅6 hole and slot.

(a) Determine the minimum diameter allowed for the countersink.

(b) Determine the maximum depth allowed for the countersink.

(c) Determine the diameter of the bolt holes at MMC.

(d) Identify every feature that qualifies as a feature of size.

(e) The width of the base is specified with a basic dimension of 60, with no tolerance. What are the minimum and maximum allowed dimensions for the base width? Explain how they are determined.

(f) Describe the datum features A, B, and C. Describe their corresponding datums. Describe the datum reference frame that is defined by applying A, B, and C in that order. Describe how the part is stabilized by these datums. Explain why this is more appropriate for this application than using the edges of the base for datums B and C.

(g) If datum feature B is produced with a diameter of ∅6.00, what is the diameter of the tolerance zone in which its axis must lie? What if it is produced at ∅6.05?

(h) If the bolt holes are produced at ∅6.0, what is the diameter of the tolerance zones locating the bolt hole pattern with respect to the true position specified by the basic dimensions? What if the bolt holes are produced at ∅6.1?

(i) If the bolt holes are produced at ∅6.0, what is the diameter of the tolerance zones locating the position of the bolt holes with respect to one another? What if the bolt holes are produced at ∅6.1?

(j) Explain why the M modifier is appropriate for the bolt hole position tolerance.

(k) For the large bore, explain what provides control of each of the following: orientation, straightness of its center axis, and cylindricity of its surface.

(l) Assume the part is cast, and the casting operation can provide a surface profile tolerance of less than 0.5. Which surfaces can likely be left in the as-cast condition without compromising any of the requirements of the drawing? How would this change if the drawing were modified to use the edges of the base as datum features B and C, while still maintaining the functional goals for the alignment of the rod?

## Answer the following questions regarding material condition modifiers.(a) What are

Answer the following questions regarding material condition modifiers.

(a) What are the three material condition modifiers?

(b) Which one is the default if nothing is specified?

(c) Which one(s) can provide “bonus” tolerance?

(d) Which of the following is increased by a bonus tolerance? (Select one.)

i. A size dimension.

ii. A ± tolerance of a size dimension.

iii. A basic dimension locating a feature.

iv. A size of a tolerance zone controlling a feature.

(e) To which of the following can a material condition modifier symbol be applied? (Select one.)

i. A size dimension.

ii. A ± tolerance of a size dimension.

iii. A tolerance of a geometric characteristic controlling a feature of size.

iv. A tolerance of a geometric characteristic controlling any feature.

(f) Which material condition modifier should be considered if the goal is to ensure a minimum clearance fit for a bolt in a hole, but to give greater manufacturing flexibility if the hole is produced with a greater clearance?

(g) Which material condition modifier should be considered if the goal is to provide a consistent press fit between interchangeable parts?

(h) Which material condition modifier should be considered if the goal is to ensure a minimum wall thickness for a casting, but to give greater manufacturing flexibility if the wall is produced with a greater thickness?

## For the part shown, answer the following questions with regard

For the part shown, answer the following questions with regard to the cylindrical boss.

(a) What are the maximum and minimum diameters allowed for the boss?

(b) What is the effect of the position tolerance of 0.2 on the diameters specified in part (a)?

(c) The position control defines a tolerance zone. Specifically what must stay within that tolerance zone?

(d) What is the diameter of the tolerance zone if the boss is produced with a diameter of 50.3?

(e) What is the diameter of the tolerance zone if the boss is produced with a diameter of 49.7?

(f) Describe the significance of the datum references to the determination of the position tolerance zone.

(g) What is the perpendicularity tolerance with respect to datum A? (Select one.)

i. Not defined.

ii. Controlled by the position tolerance; 0.2 at MMC to 0.5 at LMC.

iii. Controlled by the size tolerance; 0.3.

iv. Must be perfectly perpendicular; 0.

(h) What controls the cylindricity? (Select one.)

i. There is no control on the cylindricity.

ii. From Rule #1, the envelope of a perfect cylinder with diameter of 50.

iii. From Rule #1, the envelope of a perfect cylinder with diameter of 50.3.

iv. From the position control, the center axis of each cross section must be within the 0.2 cylindrical tolerance zone.