Management: Nature and Purpose

Management

- is an act of handling, directing or exercising control and supervision on the functions of the organization. It's the process of designing and maintaining an environment wherein people work together as a team to reach a specific goal and objective. Basically the purpose of management as a field of study is to achieve certain specific objectives that ultimately will improve the ability of an organization in its effectiveness and efficiency. According to management scholars and practitioners it is

• a distinct process consisting of planning, organizing, actuating and controlling performed to determine and accomplish the objectives by the use of people and resources. (Terry 1982)
• a process of designing and maintaining an environment where in individuals working together as a group effectively and efficiently accomplish the team's goals. (Weihrich 1993)
• a unifying and coordinating activity which combines the actions of individuals into meaningful and purposeful group endeavor. (Mahony 1961)
• a process in which a cooperative group directs action toward common goals (Massie 1964)
• a discipline and a field of study that denotes a social position and authority involving people and their functions (Drucker)
• to accomplish desired objectives by establishing an environment favorable to performance by people operating in organized groups (Koontz)

Management as a field of study it observe the society and the people that comprise it but as a body of knowledge it is pool of realities of human relationships, interactions and transactions.

Strength of Materials: Simple Stress

Simple Stress - is the intensity of force inside a solid material. The object is influenced that may lead to breakage or change on it's physical form. 

It is force per unit area, which is basically Pascal (Pa) Newton per square meter or Megapascal (MPa) which is Newton per square millimeter.

The stress is spread out in the entire cross-section of the item that reacts to the external force or load applied.

Different Kinds of Internal Forces:

• Axial Force - pull and or push action that is perpendicular to the cross section. Pull represents tensile force that tends to elongate the subjected member while Push represents compressive force that tends to shorten the subjected member, load usually denoted as P.
• Shear Force - total resistance to sliding the portion to one side of the exploratory section past the other in vertical or horizontal manner, usually denoted as Vx for horizontal shear force and Vy for vertical shear force.
• Torque - twisting the member either clockwise, counterclockwise or both, usually denoted as T.
• Bending Moments - resistance to bending the member about any axes, and are often denoted as M or Mx for moment about x-axis or My for moment about y-axis.

Studying material's strength is relevant to guarantee that the structure to be used will be safe against maximum internal forces that is produce by combining different kinds of loads. 

Surveying: Stadia Method

Stadia - came from Greek word for a unit of length applied in measuring distances for athletic contests. It denoted 600 Greek units, or 184 meters 93 centimeters or 606 feet and 9 inches as calculated by present-day international standards.

Stadia is the plural of stadium. It is applied to the cross hairs and rod used in making measurements and method. Readings can be taken with almost all surveying instruments such as engineer's level, alidade, theodolite and engineer's transit.

Stadia consists of telescope with two horizontal hairs called stadia hairs and a graduated/stadia rod. Distances can be measured rapidly by stadia method. By observing through  the telescope the apparent locations of the two stadia hairs on a vertically held rod. From the observed interval, the distance from the instrument to the rod is readily computed.

This method can also adapted in mapping requirements and is widely used for locating details and contour points in topographic surveys. More rapid than taping, and under certain conditions could be made as precise. It requires the employment of fewer survey personnel.

Surveying: Tacheometry

Tacheometry - a procedure to obtain horizontal distances and differences in elevations based on the optical geometry of the instrument employed.

It uses subtended intervals and angles observed with an instrument like transit or theodolite, on a graduated scale or rod as a rapid and indirect way of measurement.

A relative accuracy of 1/300 up to 1/500 can be obtained for most horizontal measurements, and differences in elevation to within plus or minus 3 centimeters. This type of measurement also have a lower order of accuracy as compared to taping and differential leveling.

Usage of subtense bar for tacheometric measurements consists of a 2meter long bar mounted horizontally on a tripod aligned perpendicular to the line by means of a sighting device on top of the bar. The horizontal angle subtended by the two sighting marks on the bar is hence read by a transit or theodolite and by trigonometry the distance is computed.

This method may also employs the sighting of a telescope of an instrument in reading a small angle along a vertical plane and in determining the length which the angle subtends on a graduated rod held vertical on the distant point.

Tachemetric methods are used

• to check the more accurate taped distances to uncover gross errors and mistakes
• to determine differences of elevation between points
• to carry lines of levels where a relatively low order of accuracy is required
• to measure lengths of traverse lines

Its most general use is found in compilation of planimetric and topographic maps, in field completion surveys for photogrammetric mapping and in hydrographic surveys' location of details.

Foundation Engineering: Functions of Piles

When the soil bearing capacity is too low, then the land is too weak or too compressible to provide adequate support, hence the loads including dead and live loads are to be transferred to a more suitable material at a greater depth by drilling in piles of piers. 

Piles - structural members of small cross-sectional area compared to their length and are usually installed by a vibrator or hammer. Piles are grouped into clusters or rows each containing enough members to support a load delivered by a single column or wall

Piers - usually larger in cross section capable of transferring entire load from a single column to the supporting stratum

Columns with not much load can require just one single pile. However, field conditions should be considered too like the actual position of a pile that may be several inches away from planned location hence eccentricity of load may occur and can hardly be avoided. Consequently, the heads of piles are usually braced in two directions by grade beams. 

If only two piles are needed, heads may be connected by a concrete cap braced by grade beams in only one direction perpendicular to the line joining the two piles.

Three or more piles clustered together shall be provided with reinforced cap and are considered stable even without the support of grade beams.

Aside from its original purpose, vertical piles can also resist lateral loads such as winds and lateral earthquake at certain point. But when larger lateral loads are to be resisted, an inclined or batter piles are more applicable. A batter of four horizontal and twelve vertical represent about the greatest inclination that can be achieved with ordinary driving equipment. Economically, smaller inclinations are more favorable even if it requires more piles to be battered.

Foundation Engineering: Soil and Rock Definition

Engineers always use terms soil and rock in implicating a clear distinction of two different kinds of foundation materials.

ROCK - is a natural aggregate of mineral grains connected by strong and permanent cohesive forces

SOIL -  is a natural aggregate of mineral grains that can either be with or without organic constituents and can be separated by gentle mechanical means such as agitation in water or strong winds

However, on actual site condition, one can never sharply distinguish rocks from soil because they usually come together. Even the strongest and most rigid rocks may be weaken by natural processes such as weathering and some highly saturated soil may exhibit strengths that is comparable to those of weathered rock.

Structural Theory: Introduction

Overall, engineers design bridges, buildings, ships, machine parts, equipment and other structural installations. To design such it is a must to determine first the layout of the structural, its dictated future shape and constituent members. Estimation or determination of loads that the structure will carry will then proceed.

• The theory of structure concerns about direct stress, shear area and bending moment and deflection at any section of the structure's constituents. After acquiring such, it is vital to design each members proportion to the allowable working stresses of the materials while complying to other requirements and limits for the proper function of the engineered structure.

Four Stages of Design:

1. layout of the structure
2. loadings that consists of dead load (own weight) and live load (which may include snow load, wind load, etc.)
3. direct stresses that the members will carry
4. sizes of the members that will bear the loads and stresses most costly efficiently within the bound limit

• Layout and Classification. Structures layout largely depends on its function, loading conditions and the properties of the materials that will be used. The determination of the layout requires field experience and expertise, judgment and vast knowledge. After considering all the necessary elements in the preliminary design it will be test to determine the preferred design that meet even the unanticipated conditions that the structure might encounter during the stages of creation. Basic structure classification are inclusive but not limited to beams, rigid frames, trusses or combination of two or more of these elements. Generally, a beam is a structural member subjected to transverse loads only that bears shear and bending moment, hence, horizontally oriented. Rigid frames on the other hand is a structure composed of several members connected by rigid joints whether welded or bolted that is completely analyzed when all variations in direct stress, shear and bending moment along  the entire lengths of all members is acquired. Finally, a truss is a structure consists of several members connected by frictionless hinges that is completely analyzed with determined direct stresses. Other structures with members or machine parts are also subjected to react on direct stresses, shear and bending and twisting moments.

• Loads. Structures are subjected to dead loads, live loads and dynamic outside force like nature and impact of live loads. Dead Load is the weight of the structure itself, it has to be first assumed since most of its part cannot be determined until the members have actually been design, then checked after the sizes of the members are finalized although changes are at minimum that in routine design it is seldom modified. Live Load also known as the moving loads are maximum loads to be carried by the structure. Since it is moving, the Impact or its Dynamic Effect is also considered because it is usually more critical than stagnant live loads only since there are times when the live load comes on rather suddenly as a moving, passing or rolling load.

• Methods. Theory of Structures deals with the principles and methods wherein direct stress, shear and bending moment at any section of the member may be found under the conditions of loading. It is then assumed that the forces acting on each structural elements are on the same plane and in equilibrium.
• General coplanar-force system:
• Summation of Forces on X-axis = 0
• Summation of Forces on Y-axis = 0
• Summation of Moment at a certain joint or point = 0

Economics: Interest

Interest: amount of money earned by given principal money.
Borrower's Viewpoint - interest is the amount of money to be paid for the use of a borrowed capital.
Lender's Viewpoint - interest is the income generated by the capital that was lent.

• Simple Interest - varies directly with time since it is computed after or at the end of the invested period
• Ordinary Simple Interest - base on one banker's year
• Exact Simple Interest - based on exact number of days of a year, which considers ordinary year of 365 days and leap years that have 366 days

Formula: Future Worth = Present Worth + Interest Earned 

(F = P + i)

• Compound Interest - computed every end of each interest period which is called compounding interest and the interest is added to the principal (which is now interest plus principal) that will produce a bigger interest 

Formula: Future Worth = Present Worth (1 + Interest Earned) ^total number of compounding period 

(F = P [1 + i]^n) 

Engineering Mechanics: Introduction

Engineering Mechanics - is a field of science that deals with forces and its effect on rigid bodies. Engineering Mechanics are subdivided into two parts:

•  Statics - rigid bodies remains at rest while absorbing the effects and distributions of forces
• Force System - any arrangement where in two or more forces act on a body or on group of related bodies. 
• Three Major Divisions of Force System
• Concurrent - all forces pass through a common point
• Non-Concurrent - all of the lines of action of the forces in this system do not meet at one point
• Parallel - forces whose line of action are parallel, in same or opposite direction
• Applications - trusses, centroids, friction

• Dynamics - rigid bodies motion caused by the force applied to it, it deals with bodies in motion
• Kinematics - is the geometry of motion, the motion of a particle without considering the forces causing the motion
• Motion of Particles
• Translation - motion of rigid bodies where in a straight line pass through any two of its particles always remain to be parallel on its original position
• Rotation - motion of rigid bodies where in the particles move in circular paths with centers or axis of rotation on a fixed straight line
• Plane Motion - motion of rigid bodies where in all particles in the body remain at a constant distance form a fixed reference plane
• Kinetics - relates the force action on the body to its mass and acceleration
• Newton's Law of Motion
• a body at rest will remain to be at rest or in motion will remain in motion along a straight path unless acted upon by unbalanced force
• a particle acted upon by an unbalanced force system has an acceleration in line with and directly proportional to the resultant of the force system and inversely proportional to its mass
• in every action there is always an equal and opposite reaction
• D'Alembert's Principle
• the resultant of the external forces applied to a body rigid or non-rigid composed of a system of particles is equivalent to the vector summation of the effective forces acting on all particles

Solid Geometry: Polyhedrons

Polyhedrons - solids whose faces are plane polygons.

Regular Polyhedrons - are polyhedrons that have identical faces. There are only five known kinds of polyhedrons.

Let:
a = length of the edge
n = number of vertices
f = number of faces
m = number of polygons meeting at a vertex

• Tetrahedron - four faces - a pyramid
• faces: 4
• edges: 6
• vertices: 4
• number of polygons meeting at a vertex: 3
• surface area: a square * square root of 3
• volume: a cube / 6 * square root of 2 

• Hexahedron - six faces - a cube
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 3
• surface area: 6 * a square
• volume: a cube

• Octahedron - eight faces
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 4
• surface area: 6 * a square
• volume: a cube

• Dodecahedron - twelve faces
  • faces: 12
  • edges: 30
  • vertices: 20
  • number of polygons meeting at a vertex: 3

• Icosahedron - twenty faces
• faces: 6
• edges: 12
• vertices: 8
• number of polygons meeting at a vertex: 5

For any Polyhedron:

Number of Edges: nf/2

Number of Vertices: nf/m

Tips and Tricks: Multiplication

The multiplication table of 1 is a no-brainer, BUT, let's face it! even adults sometimes are having a hard time doing numbers in their heads!

I can mentally calculate tables 2 to 5, and table of 10 is as no-braner as the multiplication of 1. :D
Then comes, 6, 7, 8 and 9.

You might already knew this, and forgotten about is, so this will help you refresh a Math skill!

• The Multiplication by Hands - applicable for 6, 7, 8, 9 and 10 as multiplier and multiplicand
• Step 1 - look at your hands, your thumbs represents number 10, the index finger as 9 and so on, hence, your pinky is number 6.
• Step 2 - let's set an example. So lets say its 7 x 8. (No calculators pls! that's cheating!) What you do is connect the fingers representing 7 and 8.
• From the connecting fingers, count each fingers downwards by ten. So thats 10, 20, 30, 40, 50.
• Step 3 - Count the remaining left fingers and add it to the sum of the remaining right fingers. so that's 3 x 2 = 6
• Step 4 - Add the sum of step 5 and 6, so that will give you 50 + 6 = 56. Awesom I    know! :D

Take a look:

Photo Courtesy of helpingwithmath.com

I first observed that the digits of the answers if added will always be 9.
And aside from tables 1 and 10, 9 is a no-brainer too! you just have to know the trick!

Example: 9x7. Instead of counting 9 + 9 + 9 + 9 + 9 + 9 + 9... All you need to do is add zero to the digit you are multiplying to 9, in this case 7 will become 70. Then we have to minus that digit to the new set of number, 70 - 7 = 63.

In short: 8 x 9 = 80 - 8 = 72.

Get it, got it!

Do you have more math tricks to share? Comment down below, its time to share yours! Click like for more math tricks! :P

Algebra: Laws and Theorems of Equality and Inequality

Equality - two equations or quantities are of equal and the same value.

Inequality - two equations or quantities are lesser or greater than each other.

Basic Laws of Equality

• Reflexive Property: x = x
• Symmetric Property: if x = y, then y = x
• Transitive Property: 
• if x = y, and y = z, then, x = z. (x = y = z)
• if w = x, and y = z, then, w + y = x + z.
• if w = x, and y = z, then, wy = xz.

• First Conclusion: things equal to the same thing are equal to each other.
• Second Conclusion: equals added to equals are equals
• Third Conclusion: equals multiplied to equals are equals

Basic Laws of Inequality

• x > y;        x is greater than y
• x < y;        x is less than y
• x </= y;     x is less than or equal to y
• x>/=y;       x is greater than or equal to y

Basic Theorems on Inequalities

• x > y if and only if -x < -y
• if x > 0, then -x < 0 
• if -x > 0, then x < 0
• if x > y, z < 0, then ac < bc
• if x > y, w > z, then (x + w) > (y + z)
• if x > y, w> z, and w, x, y, z > 0, then xw > yz
• if x > 0, y > 0, x > y, then 1/x < 1/y

Algebra: Law of Natural Numbers

Natural numbers refer to members of the set of positive integers or set of non-negative integers.

In Law of Natural Numbers, let x, y and z be any number, hence,

Law 1 - closure for addition: 
x + y

Law 2 - commutative law for addition: 
x + y = y + x

Law 3 - associative law for addition:
(x + y) + z = x + (y + z) = x + y + z

Law 4 - closure for multiplication:
x * y


Law 5 -  commutative law for multiplication:
x * y = y * x


Law 6 - associative law for multiplication:
x(y*z) = (x*y)z

Law 7 - distributive property of addition and multiplication:
x(y +z) = x*y + x*z

Behind Structural Engineering

Structural Engineering is a field of analytic thinking and designing of structures to oppose the resisting loads it is subjected to carry. It is a specialty of doctorate and mastery in the Civil Engineering field.

Structural Engineers are engage to designing vertical and horizontal structures like buildings, skyscrapers, subways and bridges, etc.

The need to satisfy the design criteria for a certain structure is a must and hence it approves the structural integrity in a certain level. This field of engineering is based and is always evolving in the physical laws of the materials of the structure, landscape and climate. By following criteria, the engineer can calculate the years of serviceability of a structure, its performance against earthquake, natural disasters and wind/snow load and its safety for occupancy. It is the Structural Engineer's responsibility to make effective structures that is equally cost efficient.

Hence, one can say, "I didn't just build it, I engineered it!"