Sand Cone Method to Determine Density - A solved Example

Hi,
This is an example of a problem that deals with the application of the Sand Cone Test to determine the density of the compacted soil. The solution is given in details. 

Problem: 
A sand cone density test was conducted on soil compaction at a land development project. It has the following data:
the volume of the standard Proctor mould = 1/30 cubic feet
Mass of the sand drained to fill the mould = 3.30 lbs
Mass of the sand to fill the cone = 0.53 lbs
Mass of the soil dug from the hole = 8.11 lbs (and have water content w = 11.11%)
Mass of jug + Sand + Cone before used to fill the hole = 10.20 lbs
Mass of jug+ Sand cone after used = 3.20 lbs

Determine: (A) The density of the Ottawa Sand(pcf)
                    (B) The volume of the cone (cubic feet)
                    (C) The volume of the hole dug  + Cone (Cubic ft)
                    (D)  The volume of the hole dug
                    (E)  The dry density of the compacted soil

Solution (see image): 




Thanks!

Treating the Dredged Marine Sediment with Bentonite and OPC

Hi
Sediments that are dredged from the water bodies such as reservoir, lakes or oceans are weak in strength and highly compressible, in general. This is nothing more than a waste material. However, it can be treated with certain chemicals such as the Bentonite and OPC(Ordinary Portland Cement) to give it the desired properties of a fill material in back-fills. 





It is found that the OPC acts as the binder and provides the strength, while the Bentonite provides the volume and also the strength to the clay. Therefore this treated soil can then be used as the fill, or also it can be used to form the dikes or trenches above the water surface. 

Thanks!

Solved Example of Pinned Truss - the average normal and shear stresses in members and pins respectively and Pin Diamater

Hi,
A simple truss has pin-connected members. The members carry only axial forces, but the pins have to bear the shear stresses. Given example shows the calculation for the minimum required diameter of pin connected in double shear.

Problem: Two structural members AB and BC (shown below) are connected by a pin at B that is subjected to two 5-kip horizontal forces. The pins used at A and C are identical to the pin at B. The allowable shear stress for pins is 15 ksi, and the allowable bearing stress for members AB and BC is 20 ksi. Determine:
(a) the maximum average normal stress in members AB and BC.
(b) the minimum required diameters of the pins.


Solution:

Area of traverse by Average End Area Method - Solved Example

Hi,

For the trapezoidal sections, when the end heights are given, the area can be found by averaging the end heights and multiplying it with the distance between those heights.

Given examples show the closed traverses with the straight baselines.


Solution:

How to Balance a Closed Traverse - Use of Compass(Bowditch) Rule - Solved Example

Hi,

Problem:
Following is the Field Data for a 4 sided, closed traverse, and you have to find the azimuth, bearings and corrected distances using Compass Rule or Bowditch Method.



Solution: 
Download the image, solution is written for the angular closure, correction, azimuth, bearings, latitude and departure and corrected distance calculations. 

Derivation of Mass moment of Inertia for a Solid Cone

Hi,

Problem:
Derive the Mass Moment of Inertia of a solid cone with given mass density and angle half at vertex equal to 35 degrees. If the length of the cone is 5 m and mass density is 2.5 kg/m3, what is the mass moment of inertia. 

Solution:

Complete Derivation of Mass Moment of Inertia of Hemisphere(Half Sphere) about the symmetric axis of Rotation.

Hi,

Problem: 
The top half of the sphere is created by rotating the circle of x2+y2=r2 around the y-axis. If the rigid body has mass m and density (rho), find the mass moment of inertia about y-axis in terms of m and rho. 





Solution: