7/25/2019 mechanics of materials 1.pdf

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TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES

Quezon City

Special TopicsMechanics of Materials

1.

Two solid cylindrical rods AB and BC

are welded together at B and loaded

as shown. Knowing that the average

normal stress must not exceed 155

MPa in rod AB and 150 MPa in rod BC,

determine the smallest allowable

values of d1 and d2.

2.

Determine the deformation of the steel rod as shown under

the given loads (E = 200 GPa).

3. An L-shaped concrete slab 12ft x 12ft (but with a 6ft x 6ft

cutout) and thickness t = 4in is lifted by three cables

attached at O, B and D as shown. The cables are combined

at point Q which is 7.0 ft above the top of the slab and

directly above the center of mass at C. Each cable has an

effective cross-sectional area of 0.16 in2.

a.

Find the tensile force in each cable

b. Find the average stress in each cable

4. A punch for making holes in steel

plates is shown in the figure.

Assume that a punch having a

diameter d = 20mm is used to

punch a hole in an 8-mm plate. If

force P = 110kN is required to

create a hole,

a. What is the average shear stress in the plate?

b.

What is the average compressive stress in the punch?c.

What is the average bearing stress in the plate?

5.

Two plates, upper plate 15mm thick and lower plate 10mm

thick, are joined by four rivets of 20mm diameter as shown.

Assume the load is equally divided among the rivets.

a.

Calculate load P that can be applied if the shearing

stress in the rivets is limited to 80MPa

b. Calculate load P that can be applied if the bearing stress

in the plates is limited to 140MPa

c.

Calculate load P that can be applied if the tensile stress

in the rivets is limited to 100MPa

d. What is the maximum safe load P?

6. The steel block shown is

subjected to a uniform

pressure on all its faces.

Knowing that the change in

length of edge AB is -30x10-3

mm, determine (a) the

change in length of the other

two edges, (b) the pressure p applied to the faces of the

block. Assume E = 200 GPa and v = 0.29.

7. A steel rectangular block 1in. wide in. deep and 4in. long

is subjected to an axial tensile load of 10.5kips.

Measurement show the block to increase in length by

2.8x10-3in. and to decrease in width by 0.21x10-3in.

a.

Determine the modulus of elasticity of the material

b.

Determine Poissons Ratio of the material

8.

Shaft BC is hollow with innerand outer diameters of 90

mm and 120 mm,

respectively. Shafts AB and

CD are solid and of diameter

d. For the loading shown,

determine (a) the maximum

and minimum shearing stress

in the shaft BC, (b) the

required diameter d of shafts

AB and CD if the allowable

shearing stress in these shafts is 65 MPa.

7/25/2019 mechanics of materials 1.pdf

2/2

TECHNOLOGICAL INSTITUTE OF THE PHILIPPINES

Quezon City

Special TopicsMechanics of Materials

9. Two solid steel shafts are

connected by the gearsshown. Knowing that for each

shaft G = 77 GPa and that the

allowable shearing stess is 55

MPa, determine (a) the

largest T0that may be applied

to end of A of shaft AB, (b) the

corresponding angle through

which end A of shaft AB

rotates.

10.

The shaft shown in the figure is made of bronze and steel

and is fixed at both ends. It is subjected to a concentrated

torque at the junction. The steel segment is 1.5 meters long.

a.

Determine the angle of twist at the interface of the two

materials, in degrees

b. Determine the ratio of the length of steel to that of

bronze such that the allowable stress in each material is

reach simultaneously

c. Determine the reaction at the left end if the maximum

torque is applied to the shaft in kN

11.

A load P is supported by two springs arranged in series. The

upper spring has 20 turns of 29-mm diameter wire on a

mean diameter of 150mm. The lower spring consists of 15

turns of 10-mm diameter wire on a mean diameter of

130mm. Determine the value of P that will cause a total

deflection of 80mm. Assume G = 80GPa for both springs.