February 21, 2020

PROBLEM 8.46

Solve Prob. 8.45, assuming that the structure has been redesigned to use

5

16

-in-diameter pins at A and C as well as at B and that no other changes

have been made.

PROBLEM 8.45 Link AC is made of a steel with a 65-ksi ultimate

normal stress and has a

11

42

×

-in. uniform rectangular cross section. It is

connected to a support at A and to member BCD at C by

3

8

-in.-diameter

pins, while member BCD is connected to its support at B by a

5

16

-in.-

diameter pin. All of the pins are made of a steel with a 25-ksi ultimate

shearing stress and are in single shear. Knowing that a factor of safety of

3.25 is desired, determine the largest load P that can be applied at D.

Note that link AC is not reinforced around the pin holes.

PROBLEM 8.47

Each of the two vertical links CF connecting the two horizontal

members AD and EG has a 10 40-mm uniform rectangular cross

section and is made of a steel with an ultimate strength in tension of

400 MPa, while each of the pins at C and F has a 20-mm diameter and

are made of a steel with an ultimate strength in shear of 150 MPa.

Determine the overall factor of safety for the links CF and the pins

connecting them to the horizontal members.

PROBLEM 8.48

Solve Prob. 8.47, assuming that the pins at C and F have been replaced by

pins with a 30-mm diameter.

PROBLEM 8.47 Each of the two vertical links CF connecting the two

horizontal members AD and EG has a 10 40-mm uniform rectangular

cross section and is made of a steel with an ultimate strength in tension of

400 MPa, while each of the pins at C and F has a 20-mm diameter and are

made of a steel with an ultimate strength in shear of 150 MPa. Determine

the overall factor of safety for the links CF and the pins connecting them

to the horizontal members.

PROBLEM 8.49

A 40-kN axial load is applied to a short wooden post that is

supported by a concrete footing resting on undisturbed soil.

Determine (a) the maximum bearing stress on the concrete

footing, (b) the size of the footing for which the average bearing

stress in the soil is 145 kPa.

PROBLEM 8.50

The frame shown consists of four wooden members, ABC,

DEF, BE, and CF. Knowing that each member has a 2 × 4-in.

rectangular cross section and that each pin has a

1

2

-in.

diameter, determine the maximum value of the average

normal stress (a) in member BE, (b) in member CF.

PROBLEM 8.51

Two steel plates are to be held together by means of 16-mm-

diameter high-strength steel bolts fitting snugly inside cylindrical

brass spacers. Knowing that the average normal stress must not

exceed 200 MPa in the bolts and 130 MPa in the spacers,

determine the outer diameter of the spacers that yields the most

economical and safe design.

PROBLEM 8.52

When the force P reached 8 kN, the wooden specimen shown failed in

shear along the surface indicated by the dashed line. Determine the

average shearing stress along that surface at the time of failure.

PROBLEM 8.53

Knowing that the link DE is

1

8

in. thick and 1 in. wide, determine

the normal stress in the central portion of that link when

(a)

0,

θ

= °

(b)

90 .

θ

= °

PROBLEM 8.54

A steel loop ABCD of length 5 ft and of

3

8

-in. diameter is placed as

shown around a 1-in.-diameter aluminum rod AC. Cables BE and DF,

each of

1

2

-in. diameter, are used to apply the load Q. Knowing that the

ultimate strength of the steel used for the loop and the cables is 70 ksi,

and that the ultimate strength of the aluminum used for the rod is 38 ksi,

determine the largest load Q that can be applied if an overall factor of

safety of 3 is desired.

PROBLEM 8.55

The hydraulic cylinder CF, which partially controls the position of rod

DE, has been locked in the position shown. Member BD is 15 mm

thick and is connected at C to the vertical rod by a 9-mm-diameter

bolt. Knowing that P = 2 kN and

75 ,

θ

= °

determine (a) the average

shearing stress in the bolt, (b) the bearing stress at C in member BD.