This is my T-Beam Concrete report for Mechanic Solid subject. Its contain introduction,methodology,analysis,conclusion and etc. Could be a guidance for you guys. Full version can open here: https://www.scribd.com/doc/251405472/T-Beam-Concrete-Solid-Mechanic-Report

1. Introduction (background)
Center of Gravity, the point at which all of the weight of an object appears to be concentrated. If
an object rotates when thrown, the center of gravity is also the center of rotation. When an object
is suspended so that it can move freely, its center of gravity is always directly below the point of
suspension. An object can be balanced on a sharp point placed directly beneath its center of
gravity. It is important for automobiles and trucks to have their centers of gravity located close to
the road, because a low center of gravity gives them stability.
In classical mechanics, moment of inertia, also called mass moment of inertia, rotational
inertia, polar moment of inertia of mass, or the angular mass (SI units kg·m2, US units lbm ft2), is
a property of a distribution of mass in space that measures its resistance to rotational
acceleration about an axis. This scalar moment of inertia becomes an element in the inertia
matrix when a distribution of mass is measured around three axes in space. This inertia matrix
appears in the calculation of the angular momentum, kinetic energy and resultant torque in the
dynamics of a rigid body.
Newton's first law, which describes the inertia of a body in linear motion, can be extended to the
inertia of a body rotating about an axis using the moment of inertia. That is, an object that is
rotating at constant angular velocity will remain rotating unless acted upon by an external torque.
In this way, the moment of inertia plays the same role in rotational dynamics as mass does in
linear dynamics, describing the relationship betweenangular momentum and angular
velocity, torque and angular acceleration. The symbols I and sometimes J are usually used to
refer to the moment of inertia or polar moment of inertia.
OBJECTIVE.
After studing this unit, you will be able to determine :
1) position of centre of gravity of uniform-wires of various shapes,
2) position of centre of gravity of masses of plates of various shapes with or
without openings,
3) the volume as well as surface areas of various simple solids and their location
of centre of gravity by using two theorems given by Pappus and Guldinus, and
4) compute moment of inertia of various areas & masses, about the given axes.

2. LITERATURE REVIEW OF T-BEAM CONCRETE
A T-beam, used in construction, is a load-bearing structure of reinforced
concrete, wood or metal, with a t-shaped cross section. The top of the t-shaped cross section
serves as a flange orcompression member in resisting compressive stresses. The web of
the beam below the compression flange serves to resist shear stress and to provide greater
separation for the coupled forces of bending.
The T-beam has a big disadvantage compared to an I-beam because it has no bottom flange with
which to deal with tensile forces. One way to make a T-beam more efficient structurally is to use
an inverted T-beam with a floor slab or bridge deck joining the tops of the beams. Done
properly, the slab acts as the compression flange.
The perpendicular planes of a T beam resist deforming because it requires considerable force to
bend a horizontal plane of material. The advantage of the I beam over the T beam is that it is
easily attached in all directions.
METHODOLOGY
The formula involve:
1) The first moment of area relative to the x-axis and y-axis, 𝑋̅ = ∑
𝑥̅
𝐴𝑖 Ai, 𝑌̅=∑
𝑦̅
𝐴𝑖 Ai
2) Area of the sub-region, 𝐴 = A1 + A2
3) The first moment of area relative to the x-axis, Qx = y.A and
Qx,T = Qx,1 + Qx,2
4) Centroid of the Y-coordinate, 𝑌̅ =
𝑄
𝐴
5) Total moment of inertia, 𝐼x,T = 𝐼̅ x’,T1+ A1 𝑑1
2
+𝐼̅ x’,2+ A2 𝑑2
2
6) Total amount of inertia about thex-axis, Ix,T = Ix,1 + Ix,2

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