Question

Analytically develop the following:

1. Vertical stress caused by a loaded rectangular area.

2. Stress caused by a point load.

3. Vertical stress caused by a linear load.

4. Vertical stress under a uniformly loaded circular
area.

Course: soil mechanics

Answer #1

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A rectangular flower garden with an area of 110m^2 is surrounded
by a grass border 1 m wide on two sides and a 2 m wide on the other
two sides as shown in the figure. What dimensions of the garden
minimize the combined area of the garden and borders?
1) A=
2) The interval of interest of the objective function is
3)The vertical height of the garden that will minimize the total
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4) The horizontal width of...

Determine the effective stress increase in the soil at a depth
of 4 m below the footing of area 3 x 5 m2 under an axial load of
4500 kN. Also determine the increase in the stress due to a drop of
the water table from originally 1 m below the footing to 5 m below
the footing bottom.
Please help me with this question with graph and calculation
details, thanks.

A wide loaded area carries a net uniformly distributed
pressure q = 150 kPa on a soil profile that consists of 3 layers [4
m sand (20 kN/m³) over 2 m clay (18 kN/m³) over 3. m sand]. The
water table is at the top of clay layer. The permeability of sand
is very large. Cv = 0.50 m2/year; Calpha= 0.05; eo = 1.00. Compute
the settlement due to secondary compression after 60 years.

#1-6 A 1.6 inches by 5.8 inches rectangular beam of wood
is 11.4 feet long and has a modulus of elasticity of 1,500,000 psi.
It is loaded in the JOIST (vertical) position at the center with
355 lbs.
1. What is the length of the beam in inches? (in)
2. What is the base of the beam? (in)
3. What is the height of the beam? (in)
4. What is the moment of inertia of the beam? (in 4 )...

2: Two meters of fill (=2.04 Mg/m3)
are compacted over a large area of soil (thus 100% of its influence
is felt throughout the depth). Above the compacted fill, a 3*3m
spread footing loaded with 3000 kN is placed. Assume that the
average density of the soil is 1.68 Mg/m3, and the water table is
very deep. Then it is required to (a) compute and plot the profile
of effective vertical stresses at the middles of ten 2m intervals
or...

Two parallel, coaxial circular disks 1 and 2, each of area 21.8
cm^2, are separated by a small distance 0.8 mm. The disks 1 and 2
are charged uniformly with charge -4 nC and 1 nC, respectively. How
much work is required for an external force to move a proton
located between and far from the edges of the disks very slowly
from a point very close to disk 1 to one very close to disk 2?

A steel wire has the following properties: Length = 5.00 m
Cross-sectional area = 4.60×10−2 cm2 Young's modulus = 2.0×1011Pa
Shear modulus = 0.84×1011Pa Proportional limit = 3.60×108Pa
Breaking stress = 11.0×108Pa The proportional limit is the maximum
stress for which the wire still obeys Hooke's law (point B in
(Figure 1)). The wire is fastened at its upper end and hangs
vertically.
A) How great a weight can be hung from the wire without
exceeding the proportional limit?
B)...

(1 point)
Convert the following point from rectangular to cylindrical
coordinates:
(4√2,−4√2,9)
(r,θ,z)=

Suppose that(X,Y)is uniformly distributed over the rectangular
region with corners(0, 0),(2, 0),(2, 1),(0, 1).
Compute the following:
(1)P{X=Y}
(2)P{X < Y}
(3)P{X < Y^2}

(1 point) Convert the following polar coordinates into
rectangular coordinates.
(a) 〈2∠45∘〉
x= _____, y= _____.
(b) 〈4∠120∘〉
x= _____, y= _____.
(c) 〈6∠270∘〉
x= _____, y= _____.
(d) 〈6∠300∘〉
x= _____, y= _____.

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