Statically Indeterminate Beams Essay

1003 words - 5 pages

STATICALLY INDETERMINATE BEAMS

1. INTRODUCTION

Most of the structures encountered in real-life are Statically Indeterminate.

Statically Indeterminate Beams: No. of Reactions > No. of Eqns. of Equilibrium

Degree of Static Indeterminacy = No. of Reactions in excess of the No. of Eqns of Equilibrium.

Static Redundants = excess reactions; must be selected for each particular case.

Assumption throughout this chapter is that the beams are made of Linearly Elastic Materials.

2. TYPES OF STATICALLY INDETERMINATE BEAMS

- Propped Cantilever Beam

- Fixed – End Beam

- Continuous Beam
(more than one span)

There are 4 ways of solving ...view middle of the document...

apply moment – area theorems to find redundant reactions
8. solve for remaining reactions using equations of equilibrium

Once reactions are determined, stresses and deflections can be calculated.

EXAMPLE No. 2

GIVEN:
The beam shown.

FIND:
Reactions at supports using the Moment – Area Method.

SOLn:

10.4 METHOD OF SUPERPOSITION

1. pick redundant reaction(s)
2. remove redundant reaction(s) to leave a statically determinate released structure
3. determine deflections due to loads on released structure
4. apply redundant reaction(s) as loads
5. determine deflections due to redundant reaction(s)
6. sum the deflections for the total deflection – this is the superposition principle
7. solve for the redundant reaction(s)
8. solve for the remaining reaction(s) using the eqns. Of equilibrium

continuous beams:

This beam has 4 supports and 2 eqns of equilibrium. Thus there are 2 redundant forces.

If all loads are vertical and there are no axial deformations,
then all reactions will be vertical.

The number of redundant forces is:

No. of Redundant Forces = No. of Supports – 2

We can analyze continuous beams by any of the previous methods but only superposition is practical.

HINT: when there are more than 2 supports, select the bending moments in the beam at the intermediate supports as the redundants.

Let’s see how this is done.

FBD

Because the beam is continuous across B: [pic]____________ ( 1 )

SUPERPOSITION ( deflection due to LOADS + deflection due to REDUNDANTS

(BL = ( due to MA + ( due to MB + ( due to loads in AB ____________ ( 2a )

(BR = ( due to MB + ( due to MC + ( due to loads in BC ____________ ( 2b )

(BL due to MA: (BL1 = ( due to MB: (BL2 =

(BR due to MB: (BR1 = (BR due to MC: (BR2 =

SUBSTITUTING (the above terms for (BL1 , (BL2 , (BR1 , (BR2 into EQNs ( 2a ) & ( 2b ):

(BL = + + (BL3 due to LOADS in AB _______ ( 3a )

(BR = + + (BR3 due to LOADS in BC _______ ( 3b )

We can use 2nd Moment – Area Theorem ( pg 628 )

Arclength : ∆ = ( L

From 2nd M-A Th: EI∆ = Ax

Substituting in arclength:

GENERIC Moment Diagrams for EXTERNAL LOADS:

Substituting the above terms for...

Other Papers Like Statically Indeterminate Beams

Rational Emotional Behavior Therapy Case Study Conceptualization And Treatment Plan

2140 words - 9 pages Rational Emotional Behavior Therapy Case Study of Sarah: A Conceptualization and Treatment Plan Rational emotive behavior therapy, REBT, was developed by Albert Ellis and holds the central belief that the events in our lives do not cause our disturbances but that they are instead caused by our view of the events (Murdock, 2009). Murdock (2009) states that “people are seen as responsible for their behavior” (p. 279) but, because they are

Holidays In Albania Essay

1636 words - 7 pages Have you ever thought about having exciting and incredibly cheap vacations? Albania might be the right choice. According to My Travel Guide, Albania is ranked the fourth among ten places worth visiting in Eastern Europe (“Top 10 Eastern European Destinations”). One can encounter three kinds of vacations in this Mediterranean country: winter, summer, and cultural. The ideal places to spend your winter vacations are the Albanian Alps. They are

A Heart Of Darkness

1748 words - 7 pages In this short story, there are frequent significant subject and ideas that make the story, "A Heart of Darkness," by Joseph Conrad, and haunting novel. The main theme is absolute white power over the natives. The theme validates the corruption, and the dependence caused by the white people as they took over the Congo. White men were giving all the power; they had no self-control, and in the end they did not use wisely. The white men became

The Aspects Of Vulnerability Among The Exploited In Medical Research

2287 words - 10 pages Essentially, everyone is in some state of vulnerability. However, some of us are more susceptible to harm due to our vulnerabilities. The susceptible are the individuals with the greatest risk. These individuals risk the loss of their autonomy, and maybe even their lives. Vulnerable populations can be found in every subset of society. However, as previously mentioned, there are some vulnerable populations that are at an even greater risk than

The Hitchhiker’S Guide To The Galaxy

1171 words - 5 pages The Hitchhiker’s Guide to the Galaxy As the human race makes life-changing discoveries, it is made apparent that there is always more to learn as the universe, instead of becoming familiar, is becoming absurd. The Hitchhiker’s Guide to the Galaxy, written by Douglas Adams, as well as the 2005 film adaption, portrays absurdity to be an all-encompassing system in the universe. Through the introduction and attempt to understand lack of reason, the

The Ford Motor Company Wage Increase Of 1914 And The Theory Of Incentives And Efficiency Wages

1252 words - 6 pages ‘It’s not the employer who pays the wages. Employers only handle the money. It is the customer who pays the wages’ (Henry Ford, cited in Johnson and Weinstein 2004, p. 2). When the Ford Motor Company announced that it would more than double the wages of its workers in January 1914 to a ‘five-dollar day’ minimum, was this a contradiction to Henry Ford’s statement? If customers are actually the ultimate payers of wages, then more than

Historical Analysis Of The Economical Breakthroughs Of The Industrial Revolution

1396 words - 6 pages A Historical Analysis of the Economical Breakthroughs of the Industrial Revolution During the Industrial Revolution, many elements of society experienced huge breakthroughs that would change the way they functioned forever. Economics were definitely one of them. With many new inventions and many factories appearing, many, many, more resources were being created than ever before. Also, all of the revenue from these resources was being given to

Leadership Portrayed in Monologue from Shakespeare’s Henry V

1214 words - 5 pages Leadership is defined as a socially constructed process and which also affect organizational future outcomes. Leader is someone at high position who have overall duty for an organization, she or he decide what to do and the way how to achieve it. (Carter and Greer, 2013)The role of leader is extremely important for an organization, leader use their own power to influence the followers though many different ways such as motivation in order to

Cuba Civil Rights

1906 words - 8 pages Picture a country that has limits on how much you can make random government imprisonments and more what do you do. That is the situation for the eleven million seventy-five thousand two hundred forty-four people of Cuba since the takeover of Fidel Castro. The US is opposed to Castro taking control of Cuba. Castro managed to ease the United States nerves when he said that Cuba was against all forms of communism. According to Lana Wylie the Union

US Freight System

1273 words - 6 pages General Environment Each American requires the movement of approximately 40 tons of freight per year across the freight network. This includes everything from shirts to lawn mower to orange juice. • As the U.S. population expands, the U.S. freight system will be called upon to meet the demands of a larger population • Between 2010 and 2035, the system will experience a 22 percent increase in the total amount of tonnage it moves • By 2050, with

Democratic Peace Theory

1852 words - 8 pages Intro: US Presidents have made it a goal during their term(s) in office to establish a good relationship with foreign countries and even try to improve upon existing connections with our allies. Some believe it is to prevent conflicts between the countries while others dispute that it is a threat assessment by the United States to pick and choose their friends and enemies. Preventing conflict between two democracies or countries that practice

Related Essays

Buet Wre Syllabus Essay

5652 words - 23 pages testing of bricks for absorption, unit weight, efflorescence and compressive strength. CE 321 : Structural Analysis and Design I 4.00 Credit, 4 hrs/week Stability and determinacy of structures; analysis of statically determinate trusses and arches; influence lines; moving loads on beams, frames and trusses; analysis of suspension bridge. Wind and earthquake loads; approximate analysis of statically indeterminate structures: braced trusses, portal

Spaghetti Bridge Essay

2948 words - 12 pages and stability of a bridge. The structure can be analysed using equations of equilibrium alone and is statically determinate using the following formula. (Parra M., 2013) Truss analysis Structural stability formula K=2J-R Where: K= The unknown to be solved J= Number of Joints M= Number of members R= 3(numbers of sides of a triangle) K Results Analysis If M=K : Stable Design If MK : Indeterminate Design Structural

Freedom And Responsibility Essay

2141 words - 9 pages Built within the Constitution of the United States are specifically defined freedoms that are guaranteed to all citizens. Conversely, with every constitutional freedom there comes a corresponding responsibility. On September 25, 1789, the state legislature’s twelve proposed amendments were transmitted by congress, the first two dealing with congressional representation and congressional pay. The following numbers three through twelve were

Hate Crime Laws Essay

2348 words - 10 pages On June 7, 1998, 49-year-old James Byrd Jr. of Texas accepted a ride from three white men, who then beat him severely, urinated on him, chained him by his ankles to the back of their pick-up truck, dragged him for three miles into the countryside, and dumped his corpse in front of an African-American cemetery (Graczyk). A little over a year later, a jury sentenced ring leader John King to death by lethal injection (“Man Executed for Dragging