## Phase Diagram of Soil

Soil is composed of solids, liquids, and gases. Liquids and gases are mostly water and air, respectively. These two (water and air) are called voids which occupy between soil particles. The figure shown below is an idealized soil drawn into phases of solids, water, and air.

Weight-Volume Relationship from the Phase Diagram of Soil
total volume = volume of soilds + volume of voids
$V = V_s + V_v$

volume of voids = volume of water + volume of air
$V_v = V_w + V_a$

total weight = weight of solids + weight of water
$W = W_s + W_w$

## Properties of common materials

Material Unit weight
(kN/m3)
Density
(kg/m3)
Specific
Gravity
Aluminum 26.095 2660 2.66
Brass 81.423 8300 8.3
Brick 19.62 2000 2.0
Cast iron 70.632 7200 7.2
Concrete 23.544 2400 2.4

## 14 Review Problem - Weight of concrete surge chamber when full of water

Problem 14
A concrete surge chamber with circular cross section and vertical inner walls has an inside diameter of 100 ft. The outer walls taper uniformly. The outer walls taper uniformly ¼ in. to 1 ft. of rise, and at the base the thickness is 5 ft. The height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 150 lb. per cu. ft. Find the total weight of the chamber when full of water.

## 10 Weight of snow in an igloo with 12 ft inside diameter and 2 ft thick

Example 10
An igloo or Eskimo hut is built in the form of a hemispherical shell with an inside diameter of 12 ft. If the igloo is constructed of snow block having a uniform thickness of 2 ft and weighing 40 lb/ft3, find the weight of the igloo, neglecting the entrance. Also, if fresh air contains 0.04% carbon dioxide, find the amount of this gas in the igloo when freshly ventilated.

## 03 Weight of an 5-cm thick iron shell with 50-cm external diameter

Example 03
An iron ball 10 cm in diameter weighs 4 kg. Find the weight of an iron shell 5 cm thick whose external diameter is 50 cm.

## Volume and area of wire of given density, total mass, and total length

Problem 001
A certain wire that weighs 8.5 g/cc has a total mass of 155 kg.

1. What is the density of the wire in kg/m3?
2. Find the volume of the wire in cubic centimeter.
3. If the total length of the wire is 1500 m, find the cross-sectional area in square millimeters.

Solution to Problem 219 Axial Deformation Jhun Vert Mon, 04/20/2020 - 08:18 pm

Problem 219
A round bar of length L, which tapers uniformly from a diameter D at one end to a smaller diameter d at the other, is suspended vertically from the large end. If w is the weight per unit volume, find the elongation of ω the rod caused by its own weight. Use this result to determine the elongation of a cone suspended from its base.