Group Members

• Waqar Talib 11-EE-177• M.Shoaib 11-EE-138• Ijaz Ahmed 11-EE-42• Aetizaz Hassan 11-EE-84• Qudratullah Qamar 11-EE-108

Beams

What is a Beam? Horizontal

structural member used to support horizontal loads such as floors, roofs, and decks.

Types Of Beams

Beams are basically categorized on two basis

• On support configuration

• On their Profile (the shape of their cross-section)

ClassificationOn support configuration

Classification on their profile

I Beam

Hollow Box

SolidBox

H Beam

T Beam

Loading

What is Loading? Loading is the process in which loads are

applied on Beam which causes Bending Moment and shear Force in Beams.

Different Loads Acting On Beams

• Dead LoadStationary loadsOr permanent loads

• Live LoadMoving loads

• Wind LoadLoads due towind

• Snow LoadLoad due to snowfall

• Seismic LoadEffect due to earthquakes

Types Of Loads w.r.t their Action

• Point Load it is also called asConcentrated load. The load which is applied on any point of beam.

Concentrated Load

• Distributed Load such type of load which is equally or unequally distributed over the whole beam or on the some part of beam.

Types of Supports

Supports are basically used to support the weight of load acting on beam. These supports show the reaction which are equal and opposite to the applied load.

There are different types of supports givenAs;

Supports of Beams

• Roller Support

(1 reaction

force)

• Simple Support

(1 reaction

force)

• Pinned Support

(2 reaction

forces)

• Fixed Support

(3 reaction

forces)

Internal Reactions in Beams

• In a beam there are 3 possible internal reactions

required for equilibrium. – normal force.– shear force.– bending moment.

Internal forces in beams Normal Force Any force coming from the surface and acting

at a right angle to the surface is called the Normal Force. Shear Force is the algebraic sum of the vertical forces

acting on a particular section of the beam. Bending Moment: is the algebraic sum of the moment of

the forces to the left or to the right of the section taken about the section

Finding Unknown Reactions•When a beam is loaded Total load = External Load + Self Load•Load is shifted at the supports.•Load is inclined than it is resolved into its components.• In Cantilever beam unknown is equal to total load.• In Simply supported and over hang beam unknown reactions are at both ends.

• Symmetrical beams. In symmetrical beam both reactions are

equal and is equal to half of the total load.

• Unsymmetrical beams. In this unknown reactions can be find out

by finding the moment by all the forces about a point and equating there sum equal to zero

CONTENTS:

Shear Force

Bending Moment

Shear Force Diagram(S.F.D)

Bending Moment Diagram(B.M.D)

Bending Moment: It is the algebraic sum of the

moment of the forces to the left or to the right of the section taken about the section .

• The bending moment is zero on the free ends of cantilever and over hanging beam.

• Bending moment is also zero on the ends of simply supported beam.

• The bending moment is maximum on the fixed end of the cantilever beam.

• Bending force is maximum at the point where shear force changes its sign.

NUMERICAL PROBLEM :

Draw shear force and bending moment diagram of the given beam

SOLUTION

• Calculating reaction forces

• The beam is symmetrical so the both reactions will be • R1=R2=Total load/2• Total load/2=1000kg• R1=R2=1000Kg

• Calculating shear forceShear force at point A=S.F(a)= 1000kg• Shear force at point B=S.F(b)=400kg• Shear force at section B-C=F.S(b-c)=-400kg• Shear force at point C=F.S(c)=-1000kg• Shear force at point D=F.S(d)=0

• Calculating bending moment

• Bending moment at point A and D=0• Bending moment at point C=2000kg.m• Bending moment at point B=2000kg.m

S.F.D And B.M.D

S.F.D• In S.F.D the point load is

shown by a straight line while the Uniformly distributed load(UDL) is shown by the inclined line.

B.M.D• In B.M.D the point load is

shown by inclined line while the UDL is shown by upper curve.

Shear force and bending moment diagram

QUDRATULLAH QAMAR11-EE-108

• INERTIA• MOMENT OF INERTIA• TYPES OF MOMENT OF INERTIA• FORMULAS OF MOMENT OF INERTIA OF

DIFFERENT TYPES OF BEAMS• APPLICATIONS OF BEAMS

INERTIA

o Resistance offered by a body or structure against external forces is known as INERTIA.

o If resistance offered by structure is large then it will be safe otherwise body or

structure will lead to failure.

MOMENT OF INERTIA• DEFINITION: The product of area of body or structure and square of distance

between centroid and reference axes is known as MOMENT OF INERTIA. It is also known as second moment of area. REASON: Because distance(between centroid and refernce axes) is double times

multiplied with area of structure. It is denoted by “M.O.I” or “I”. UNIT: It’s unit is m^4 or cm^4 or inch^4 depending upon the system of units used.

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TYPES OF MOMENT OF INERTIA

• Moment of inertia along X-axis. It is denoted by Ixx• Moment of inertia along Y-axis. It is denoted by Iyy.• Polar moment of inertia. It is denoted by Izz. Izz=Ixx+Iyy

FORMULAS OF MOMENT OF INERTIA OF DIFFERENT TYPES OF BEAMS.

• For square beam: I=D^4/12• For hollow square beam: I=D^4-d^4/12• For rectangle: I=BD^3/12• For hollow rectangle: I=BD^3-bd^3/12• For circle: I=3.14D^4/64• For hollow circle: I=3.14(D^4-d^4)/64• For I-Section: I=BD^3-bd^3/12

Parallel Axis Theorem

The moment of inertia of an area about an axis is equal to the moment of inertia of the area about a parallel axis passing through the centroid plus the product of the area and the square of the perpendicular distance between the axes.

EXAMPLEFind the moment of inertia about the x axis. Of the following figure: SOLUTION:

APPLICATIONS OF BEAMS

oBeams are used everywhere where horizontal support is required.oIt takes the load and transfer to the columns or load bearing walls.oUsed for frame structure of building.oUsed in bridges for supporting the slabs beneath it as a frame structure.

•DON’T SUPPOSE WE ARE ENGINEERS