CE133 Sheet 1

8/18/2019 CE133 Sheet 1

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Tutorial (1)

1) A circular aluminum tube of length L = 400 mm is loaded in compression by forces P .

The outside and inside diameters are 60 mm and 50 mm, respectively. A strain gage is

placed on the outside of the bar to measure normal strains in the longitudinal direction.

(a) If the measured strain is , what is the shortening of the bar?

(b) If the compressive stress in the bar is intended to be 40 Mpa, what should be the load P ?

1- اطmm044L=غ ة Pخااو جرا ا ,40 mm , 60 mmاا

: جو .

ن اذإايو4.444. لا ف صا را جو

يو غا دجإ ن اذإ40 Mpaا را ن P

2) A bar made of structural steel having the stress-strain diagram shown in the figure has a

length of 22 cm. The yield stress of the steel is 250 Mpa and the slope of the initial linear

part of the stress-strain curve (modulus of elasticity) is 200Gpa. The bar is loaded axiallyuntil it elongates 6.20 mm., and then the load is removed. How does the final length of

the bar compare with its original length?

2-جا

– اا

ع

ط

22وي

اع

وإجد

,

250 Mpaا

و

ئااE=200Gpa ير ا ,را لا6.2mmا ازإ كاذ ,.

. ئا لا

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3) A wire of length L =15cm and diameter d= 1.2cm. is stretched by tensile forces P = 600

N. The wire is made of a copper alloy having a stress-strain relationship that may bedescribed mathematically by the following equation:

in which is non-dimensional and has units of Mpa

(a) Construct a stress-strain diagram for the material.

(b) Determine the elongation of the wire due to the forces P .

(c) If the force is removed, what is the permanent set of the bar? 3-سا ط1هو 1.2را ش ة 44دجا . -ا

ر : ا

a)اجد

را

– ا

. b)ةا كا لط ف ةدا44.

c)ن ا ازإ اذاا.

4) A steel bar of length 2.5 m with a square cross section 100 mm on each side is subjected

to an axial tensile force of 1300 kN (see figure). Assume that E = 200 GP and =0.3Determine the increase in volume of the bar.

0-ط ا 2. شهد 144ش ة إ ض, 1344 تو .

واE=200 Gpaا و=4.3ا ... ا ف ةد

5) A steel pipe having yield stress Mpa

is to carry an axial compressive load P= 1200kN .A factor of safety of 1.8 against yielding is

to be used .If the thickness t of the pipe is to be

one-eighth of its outer diameter, what is theminimum required outer diameter d min?

-يو ا ب عا دجإ270Mpaهرا غ ,1244جرا . اذإ ب ن تيو8/1= 1.8ا و ان


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6) A long steel wire hanging from a balloon carries a weight W at its lower end. The 4-mm

diameter wire is 25 m long. What is the maximum weight W max that can safely be

carried if the tensile yield stress for the wire is 350 MPa and a margin of safety

against yielding of 1.5 is desired? (Include the weight of the wire in the calculations.)

-نزو د ق ط كWكا لط.2هو 0= و 34إذا ن إجد اع

= ا1.كا نزو جوWmax.

7) An aluminum tube is required to transmit an axial tensile force P = 30 kN (see figure).

The thickness of the wall of the tube is to be 0.5 mm. What is the minimum required

outer diameter d min if the allowable tensile stress is 90 Mpa?

, ث ن ك ا34ض ة ش ار ام-7 4.. ا ا ن .ذإ جر

حا دجا ن.90 Mpa

CE133 Sheet 1

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