Cffi (15 min, max 7pts.)
C#2 (10 min, max 4pts.) . Z0l?
Q# 1 (5 min, max 3pts.)
Q#Z (5 nrin, max 3pts.) ŁA
Q#3 (5 min, max 3pts.) Student's lD number: ą +Óę
TOTAL (40 min, max 20pts.) FINAL SCORE:
Attention: note that completely wrong answer may by evaluated with negative points !
Calculation Job #]: For modelling of a long vertical pile, ahorizontal half-infinite beam on thę winkler subsoil is
considered (rotated axes in the figure). The beam is loaded with a vertical forcę Po ) 0 concentrated at the end Ę: 0.
The general solution for dimensionless Ę- xIL*;,0,
Lw -@ isasfollows:
E)* e-Ę . (Ca . cos Ę+ Co. sinĘ).
1) all boundary conditions (I pt.), 2)find all the constants Ci (3 pts.),
3) present graphically the solutions: y(Ę), M(Ę) and aG)
for 0 < Ę. oo (3 pts.).
(- l,,*lu ^ĄT+Ą e: cn
g-Ę.sinĘ ę-Ę,cosĘ e*Ę.cosĘ ,ł e*Ę,sin
df/dĘ e*Ę,cosĘ - inĘ e*Ę,sinĘ Ę,cosĘ
dzfldŁ2 -\e-Ę.cosĘ v Zę-Ę.sinĘ 14 -2 inĘ ,cosĘ
d3f/dĘ3 Zę-Ę.sinĘ + Zę-Ę.cosĘ _Zę-Ę.sinĘ + 2ę-
,cosĘ 4
-2 Ę - Ze*Ę,cosĘ
Hint: applythe Euler-Bernoulli condition. E %Ą}^^^I"> ,.| N(n-\ ]*) = _El l_. l ą'1L
ł W\+ t,v *"#t{- Trd żo
ł*1='+/"Ł& t:
ltl l0)=O 8<' a-(u\ =
ą,O
Cg.
C9,
M(1)=-H.W,Lł
3,oiltd = --E| , łJ t4rą) ,|
2
'3= M
-A -.ło
U ł
Calculation Job #2: for a cohesionless backfill, derive the expression for the Coulomb active earth pressure eu= Ą,y,z by making use of the Mohr circle and principal stresses oi.
Explain thę relation between e,x: €aas well as o,z:y,z and the principal stresses <rl ) o:: is e" equal to ot or to os?
a chimney - on a mining area; its foundation 1) The object is specially sensitive to one m
2) Present2 different ways to protect the object, i.e. to ręduce values
Jrl|^-
I
q Ł
*{
Ouestion #3|: Preśent in figures 3 situations (/pr. r each) where serious
1) uniform mining subsidęnce w ź cons
2) compressive strains e {0>
ryl
Ouestion #2., Draw a probable plot of the backfill active pressure eu(a cohesionlessmaterial)onthewallA-B-Cif q>0. ,,/)
Assume that the contact of the wall with the soil is very rou8h.4> b - tY
Pay special attention to the angles and the proportion between e" [kPa] values around the point.B,
eu6)>0 |* v7o
e ou (r -) > ęnign) |1łłłl1,1w r<.t''
w*b łWnrł 8N łMavW. ,*ofn
+^"4ó, W BC
->+
miningradiusR> 0 (convex) -.
Whu,1 Wńt,
łA,td,
t^^^Ąń WOrft--
3) 800m
