Structures - Nodal Analysis Practice

Here is the question we did today:

First I took the bottom node to work out the internal forces in B and A.

I then took the middle node.  To build on last time's question this node now has a force acting on it and so C is not redundant.  Simultaneous equations are now required to solve the forces here.

Because we now know the force in D, we know that the reaction X in the wall is equal and opposite to it.

And finally looking at the bottom node we can work out the reaction Y.

Structures - Nodal Analysis Practice

Here is the practice question we did today:

 

First of all we can find the reaction of the roller using moments:

 

Then I took the top node first to do nodal analysis:

Then I moved down.  C is clearly redundant as e and a act in a straight line and if you remove c you still have a triangle. (If there was an external load at this node then that would effect the internal forces in C and it would no longer be redundant.)

I moved down again to work out the force in d.

I could then look at the last node to find the reaction of the hinge.

Structures - Practice after Homework

Today we did a couple more questions together.

First of all we looked just at moments with forces which are not acting perpendicularly onto the beam.  This means that we must resolve these forces into their component parts to find the magnitude of the component which acts perpendicularly to the beam.  To help do this, I would have turned this question so that the beam was horizontal, this is how my working is done.

Then we looked at finding a hinge reaction. First of all we needed to use moments to find an unknown force. 

Two methods are shown below:

A moment is the force x the perpendicular distance.  The 500N force is already acting at right angles to the beam so the anticlockwise moment is simple to calculate.  The unknown force is not acting at right angles to the beam it is acting on. So we need to find the perpendicular distance of this force to the hinge.

The alternative is to resolve F into its components and work out how much of F is acting at right angles to the beam.  This can then be multiplied by 3 to find the clockwise moment and therefore the magnitude of F.

Now that you know all the forces acting on this beam you can work out the hinge reaction.  The very first thing to do is draw an up/down right/left diagram to calculate the components of the reaction, and therefore use pythagoras to work out the hinge, and trig to work out the angle.

Case Study

For the last class period of Case Study we looked at the introduction and conclusion.

Therefore your completed Case Study should be handed in on:

Monday 12th December

Introduction:
You need to briefly introduce your topic.  State what you will study and how you will go about it.  Are you focusing on a specific aspect of technology?
This should be around 250-300 words.

Conclusion:
This must be written in your own words as it is your summary of what you have found.  Sum up your findings and make a final statement about what you found based on your research and analysis.
This should be around 300-400 words.

Bibliography/References:
You must include where every piece of text, diagram or picture was sourced.  This could be done by putting little reference numbers throughout your report and then listed at the back with where these came from, or just a list of references.

Books: Author surname and initials, (Year), Title, Publisher, Place of Publication, Page Numbers

Journals: Author surname and initials, (Year), Title of article, Name of Journal, Volume number (and part), Page numbers

Websites

Structures - Outcome 2 - Nodal Analysis

We need to be able to find the forces in different frame structures.

The first thing we need to look at are how the members react under different applied forces.  We need to therefore look at the internal forces in members:

Knowing this, we can look at analysing structures.  We will need to use our previous knowledge of how to resolve forces into their component parts, and the conditions of equilibrium: vertical forces, horizontal forces and moments.

Stages for Nodal Analysis:

•  Work out any unknown external forces using moments (where possible)
• Mark on your freebody diagram the directions of all the internal forces
• Take the nodes in turn - start with the node you know the most information for.
• Redraw the node.  Redraw and resolve any forces at an angle.
• Draw an up/down, right/left diagram
• Find out your unknowns and state whether the member is a strut or a tie.
• Move on to the next node
• Remember that there may be a hinge reaction at a node, in which case you need to make sure that you work out the horizontal and vertical components of it, and then use Pythagoras to find the magnitude and trig to work out the angle.

Now here is the worked example on page 2.  Take some time to make sure you understand the different stages of the nodal analysis.

Structures - Outcome 1 - Forces and Moments

We need to be able to work out beam reactions with simple (pivots), roller (straight up) and hinge reactions.  We can use moments in the same way as we have been previously for simple supports and rollers, however hinges will have a reaction equal and opposite to all of the horizontal and vertical forces acting on the beam.

Here is an example:

Here is a more challenging example of using moments and forces at an angle. We did this today on the board.

Homework 7 on moments and forces is due on 21/1/11

Structures - Outcome 1 - Forces and Moments Introduction

First of all we needed to revise some concepts from Intermediate 2:

Mass: Is the bulk of an object - the amount of "stuff" which makes up a body.
Weight: Is the force that body has due to the Earth's Gravitational Field strength (9.81m/s/s) because F = m.a
Moment: The turning effect of a force.  It is found using: M=Fd (force x distance)

We then reminded ourselves of the conditions of equilibrium:

And from that did some work on moments:

Using R1 as our pivot we could use moments to find R2:

Then use the vertical forces to find R1:

In Higher, however, we will also have to deal with forces which act at an angle.  To be able to work with these forces we must be able to convert a force into its horizontal and vertical components:

Case Study for Today

Today we are looking at the impact of your project on the wider world under the headingsSocial, Economic and Environmental Effects.  This section should be around 350-450 words.

These questions could be useful to you:

Social Effects:

• Have jobs been created or lost, directly or indirectly through use of this technology?
• Have lifestyles been changed through this technology?
• Have cultures been changed through this technology?
• Have these effects been positive or negative? Explain

Economic Effects:

• Has this technology increased profits/income for people or companies?
• Has it affected economies?
• Does it provide cheaper/more expensive products/technology?
• Is it expensive to own and use/run this technology?
• Have any of these effects been positive or negative? Explain.

Environmental Effects:

• Has this technology had an environmental effect for people. cultures or companies?
• Is the product recyclable/made from recycled components?
• Has it effected the natural/urban environment, directly or indirectly?
• Does the product manufacture use/provide environmentally cleaner/dirtier products?
• Have these effects been positive or negative? Explain.

You also had to submit a first draft of your analysis and description.