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QUIZ vedrørende pæleværker

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Beklageligvis findes denne quiz kun i denne engelske version.
This quiz originates from an example of a test quiz created by Gunnar Mohr.
Viewing the complete quiz reqires access to a Portable Document Format reader.
The result of the quiz will count 10 % in the evaluation of the course Advanced Theoretical Soil Mechanics.
Generally the notation from the book Advanced Theoretical Soil Mechanics by Bent Hansen is used.
If nothing else is written explicitely the piles only can support axial loads. The foundation of the structure is assumed to move as a rigid body.

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Please indicate whether the following statements are true or false

F_e can be higher than F_s	[a]true [b]false
F_e can be equal to F_p	[c]true [d]false
F_e can be equal to F_s	[e]true [f]false
In some cases it can be accepted to have F_e < 1	[g]true [h]false
Q_t can be higher than Q_c for the same pile	[i]true [j]false
The calculated bearing capacity of a pile group is higher than (or equal to) the true bearing capacity, when the calculated pile forces fulfil the equations of the equilibrium and no piles exceed the resistance to compression nor tension	[k]true [l]false
A pile driving formula is used to design the cross sectional area of the pile	[m]true [n]false
A pile driving formula is used to choose the right pile driver system	[o]true [p]false
Pore pressures generated during driving of a pile have an influence on the estimated bearing capacity of that pile	[q]true [r]false
Q₀ in the driving formulas is dimensionless	[s]true [t]false
A pile has been driven to a certain estimated bearing capacity according to the Danish driving Formula. If the Weissbach's formula had been applied instead during driving, the driving would then have continued longer	[u]true [v]false
A fixed pile with no lateral support in the topmost part of the soil profile can independently of the moment at the pile top support a transversal force equal to the yield moment of the pile divided by the depth to the fixed level	[w]true [x]false
In the general case (3D) of fixed piles there are exactly three components of pile forces	[y]true [z]false

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[b] [c] [e] [g] [j] [l] [n] [o] [q] [t] [v] [x] [z]

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( -1 2 ) ( 2 -1 ) ( 2 -1 ) ( 2 -1 ) ( -1 2 ) ( -1 4 ) ( -1 2 ) ( 2 -1 ) ( 2 -1 ) ( -1 2 ) ( -1 4 ) ( -1 2 ) ( -1 2 )

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Which of the following three pile groups would have the most economical support of a moment M_Z about the z-axis. Choose a, b or c (or nothing).
pil.jpg
[a] a
[b] b
[c] c

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[b]

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Find the safety against Shake-down for a doubly symmetrical pile with 8 inclined piles. All piles have the same inclination with vertical and the same resistance capacities against compression and tension (Q_c = 200 and Q_t = 65).
The pile group is doubly symmetrically loaded. The results of the elastic calculation are listed in the Table below for all relevant load cases. Piles no. 1, 2, 3 and 4 are placed symmetrically and piles no. 5, 6, 7 and 8 are also placed symmetrically in the coordinate system.

Piles	P_max	P_min
1, 2, 3 and 4	168.65	-52.71
5, 6, 7 and 8	172.87	-72.73

The safety against shake-down is:

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1.028 < ? < 1.05

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In the following 10 special plane pile groups are shown. Mark the correct answers below to wether or not the pile group can support the indicated loads with the indicated line of action. It is assumed that the resistance against compression and tension failure for the individual piles are sufficient.

Pile group	yes	no
a	[a]	[b]
b	[c]	[d]
c	[e]	[f]
d	[g]	[h]
e	[i]	[j]
f	[k]	[l]
g	[m]	[n]
h	[o]	[p]
i	[q]	[r]
j	[s]	[t]

pil41.jpg

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[a] [c] [f] [g] [i] [k] [n] [o] [r] [t]

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( 2 -1 ) ( 2 -1 ) ( -1 2 ) ( 2 -1 ) ( 2 -1 ) ( 2 -1 ) ( -1 2 ) ( 2 -1 ) ( -1 2 ) ( -1 2 )

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How many of the load components V, H_x, H_y, M_x, M_y and M_z can be supported by the following four 3-dimensional pile groups ? (Write the 4 numbers (separated by blanks) corresponding to the 4 cases):

pil51.jpg

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[3; 5; 4; 6]

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3 3 3 3

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For the pile group shown Click here indicate the right values of the elements to the a_ri - matrix for (all the piles have the angle v with vertical):

Pile number 3, horizontal load in y-direction	[a]cos v	[b]-cos v	[c]sin v	[d]-sin v	[e]0.5 cos v	[f]0
Pile number 9, moment about y-axis (M_x)	[g]0.5 a cos v	[h]-0.5 a cos v	[i]1.5 a cos v	[j]-1.5 a cos v	[k]0.5 a sin v	[l]0
Pile number 19, moment about z-axis (M_z)	[m]0.5 a sin v	[n]- 0.5 a sin v	[o] 1.5 a sin v	[p] - 1.5 a sin v	[q] 1.5 a cos v	[r] -1.5 a cos v

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[c] [j] [m]

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( -1 -1 4 -1 -1 -1 ) ( -1 -1 -1 4 -1 -1 ) ( 4 -1 -1 -1 -1 -1 )

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In design of a pile group the task is to arrange a pile group so that the required loads can be supported in an economical way. What is meant by "economical" and how can that be obtained? (Danish or English)

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