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PRVA ZADAA iz OTPORNOSTI MATERIJALA II 1

OBLAST:Uvijanje napredni kursProstorno naponsko stanje ravno stanje napona i deformacijaSavijanje: neravnomjeran popreni presjek, koso savijanje

Zadaci su preuzeti iz

RC Hibbeler, Mechanics of Materials, Prentice Hall, Eight Edition, 2011.JM Gere, BJ Goodno, Mechanics of Materials, Cengage Learning, Seventh Edition, 2009.

FP Beer, ER Johnson Jr., JT DeWolf, DF Mazurek, Mechanics of Materials, Mc Graw-Hill, Higher Ed-

ucation, Fifth Edition, 2009.

3.129 Each of the three steel bars shown is subjected to a torque of mag-

nitude T 275 N m. Knowing that the allowable shearing stress is 50 MPa,

determine the required dimension b for each bar.

3.130 Each of the three aluminum bars shown is to be twisted through

an angle of 2. Knowing that b 30 mm, all 50 MPa, and G 27 GPa,

determine the shortest allowable length of each bar.

Fig. P3.129, P3.130

(a)

b b

b

1.2b

(b)

(c)

T

T

T

3.136 A 3-m-long steel angle has an L203 152 12.7 cross section.From Appendix C we find that the thickness of the section is 12.7 mm and that

its area is 4350 mm2. Knowing that all 50 MPa and that G 77.2 GPa, and

ignoring the effect of stress concentration, determine (a) the largest torque T

that can be applied, (b) the corresponding angle of twist.

Fig. P3.136

3 m

T

L203 152 12.7

MF-UNZE, 2014-Mar-10


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Fig. P3.143

3.143 A hollow brass shaft has the cross section shown. Knowing thatthe shearing stress must not exceed 12 ksi and neglecting the effect of stress

concentrations, determine the largest torque that can be applied to the shaft.

0.5 in.

5 in.

0.2 in.

0.2 in.

0.2 in.

0.2 in.0.5 in.

6 in.

1.5 in.

1.5 in.

7.6-3 A cube of cast iron with sides of length a 4.0 in.

(see figure) is tested in a laboratory under triaxial stress.

Gages mounted on the testing machine show that the com-

pressive strains in the material are ex 225 106 and

ey ez 37.5 106.

Determine the following quantities: (a) the normal

stresses sx, sy, and sz acting on thex,y, andzfaces of the

cube; (b) the maximum shear stress tmax in the material;

(c) the change V in the volume of the cube; and (d) the

strain energy Ustored in the cube. (AssumeE 14,000 ksi

and n 0.25.)y

x

z

a

a

a

O

7.116 Square plates, each of 16-mm thickness, can be bent and weldedtogether in either of the two ways shown to form the cylindrical portion of a

compressed air tank. Knowing that the allowable normal stress perpendicular

to the weld is 65 MPa, determine the largest allowable gage pressure in each

case.

Fig. P7.116

8 m

5 m 5 m

45

(a) (b)



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*88. The gasstorage tank isfabricated by bolting together

two half cylindrical thin shellsand two hemispherical shells

as shown. If the tank is designed to withstand a pressure

of 3 MPa, determine the required minimum thickness of

the cylindrical and hemispherical shells and the minimum

required number of longitudinal boltsper meter length at

each side of the cylindrical shell. The tank and the 25mm

diameter boltsare made frommaterial having an allowable

normal stress of 150 MPa and 250 MPa, respectively. The

tank hasan inner diameter of 4m.

89. The gasstorage tank isfabricated by bolting together

two half cylindrical thin shellsand two hemispherical shells

asshown. If the tank isdesigned to withstand a pressure of

3 MPa, determine the required minimum thickness of the

cylindrical and hemispherical shells and the minimum

required number of bolts for each hemispherical cap. The

tank and the 25mmdiameter boltsare made frommaterial

having an allowable normal stressof 150 MPa and 250 MPa,

respectively.The tank hasan inner diameter of 4m.

Probs. 88/9

7.7-15 During a test of an airplane wing, the strain gage

readings from a 45 rosette (see figure) are as follows:

gage A, 520 106; gage B, 360 106; and gage C,

80 106.Determine the principal strains and maximum shear

strains, and show them on sketches of properly oriented

elements.

PROBS.7.7-15 and7.7-16

7.7-16 A 45 strain rosette (see figure) mounted on the

surface of an automobile frame gives the following

readings: gage A, 310 106; gage B, 180 106; and

gage C, 160 106.

Determine the principal strains and maximum shear

strains, and show them on sketches of properly oriented

elements.

y

CB

AxO

45

45



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Fig. P4.150

4.150 A beam having the cross section shown is subjected to a coupleM0 acting in a vertical plane. Determine the largest permissible value of the

moment M0 of the couple if the maximum stress is not to exceed 100 MPa.

Given: Iy Iz b436 and Iyz b

472.

20 mm

20 mm

b60 mm

b60 mm

C

M0

y

z

5.7-2 A tall signboard is supported by two vertical beams

consisting of thin-walled, tapered circular tubes (see figure).

For purposes of this analysis, each beam may be represented

as a cantileverAB of lengthL 8.0 m subjected to a lateral

load P 2.4 kN at the free end. The tubes have constant

thickness t 10.0 mm and average diameters dA 90 mm

and dB 270 mm at endsA andB, respectively.

Because the thickness is small compared to the diame-

ters, the moment of inertia at any cross section may be

obtained from the formula I pd3t/8 (see Case 22,

Appendix D), and therefore the section modulus may be

obtained from the formula S pd2t/4.

At what distancex from the free end does the maximum

bending stress occur? What is the magnitude smax of themaximum bending stress? What is the ratio of the maximum

stress to the largest stress sB at the support?

Wind

load

P= 2.4 kN

AB

x

t= 10.0 mm

dA= 90 mm dB= 270 mm

L= 8.0 m

Rok za predaju radova je 25.04.2014. godine (petak)


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