hw_01-civl111-07experimental verification of bernoulli equation (prof. m

7/24/2019 HW_01-civl111-07Experimental verification of Bernoulli equation (Prof. M

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CIVL 111 Construction Mat erials

Assignment #1 Due on 26 Feb. 2007

1. The truss shown in the following figure is made of steel. The cross sectional area of the

bars is 580 mm2

. The yield stress is 260 MPa.(i) calculate the stress in members 1, 2 and 3 when P = 90 kN.

(ii) calculate the vertical displacement when P = 90 kN.

(iii) calculate the load P1 at which the bar 2 is just yield.

(iv) calculate the load P2 at which all the bars would yield.

P = 90 kN

300 mm

Δ

300 mm

321

300 mm

2. Consider a cylindrical pressure vessel with the information given in the following figure.

R= 1.5 m; h = 0.025 m ; σys = 1500 MPa ; K IC = 60 MPa m1/2. Suppose that the vessel is

designed on the basis of the yield stress σys, reduced by a safety factor of 4.

a). Get the expression of the normal stress, σ, in the wall of vessel as a function of internal

pressure of p.

b).Assume that a I

K π σ 12.1= , Calculate the failure pressure for a

minimum detectable flaw size, a = 1.5 mm.

c). Calculate the critical crack depth at the designed operating pressure.

h

R

1



3. Assume the behavior of a creeping material to be represented by the Burger’s body

given below. The material parameters are:

E1 = 20 GPa, η1 = 10,000 GPa. day, E2 = 50 GPa, η2 = 5,000 GPa. Day

E 1 1

2

E 2

(a) Find a mathematical expression for the Creep Compliance J in terms of time in

days (Note: the unit should be /MPa)

(b)

The material is placed under the following stress history:

Stress

20 MPa

10 MPa

Time (day)

0 50 100

Derive expressions for the strain for

(i) 0 < time < 50 days

(ii) 50 < time < 100 days

(iii)

time > 100 days

Specifically, what are the strain values

(i) at time = 0

(ii) at 50 days, before and after loading increase

(iii) at 100 days, before and after unloading

(iv)

at 150 days

2



4. A centre-cracked plate made of 2024-T351 Al has dimensions of b=50 mm, t=4 mm

and an initial crack length of ai =2 mm.

a) How many cycles of loading in tension between Pmin = 6 KN and Pmax = 24 KN are

required to grow the crack to a length of af = 12mm ?

b)

Does either fully plastic yielding or brittle fracture occurs prior to reaching this af ?(C= 1.42 x 10-11 m/cycle; m=3.59; σy =325 MPa; K Ic= 34 MPa m )

2a

2b

b

aaK

2

secπ

π σ =

3

hw_01-civl111-07experimental verification of bernoulli equation (prof. m

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