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.

Applied Electronics - Outcome 1 & 2 Practice Questions

Here are some questions for you to try over the October break. I may put some more up later, but here are some to get you started.  Remember that a lot of the NAB is description, so put extra effort into the describe questions!

 

For the question above, please note that ID should be 10mA, not 20mA, the supply voltage should be 24v, and that the thermistor is a type 4 thermistor.  Sorry for the edit! 

Applied Electronics - Outcome 3 - Boolean Algebra

Boolean Algebra is another way of describing a logic truth table or circuit.  Just like any other Algebra you need to know the operators to be able to write the equations.

They are:

You need to be able to go between an English statement, a truth table, a logic circuit and a Boolean expression.

From a Boolean expression you can work out which logic gates you will need to perform each part:

To derive a Boolean expression from a truth table you must identify when the output is on, writing an expression for these lines and then combining each of these expressions with an OR operator.

You can also derive a Boolean expression from a circuit diagram by following the signal using the original inputs and the Boolean operators:

Applied Electronics - Outcome 3 - Logic

Outcome 3 is logic.  It is not vastly different from Intermediate 2, but they may ask you to design a more complicate circuit and look at NAND or NOR equivalents.

Firstly lets consider this circuit:

The first thing we should be able to do is draw the truth table for it:

A and B are our two inputs, but we could put in points to help us after the AND gate (C) and after the NOT gate (D).

A B   C   D   Z
0 0     0    1   1
0 1     0    0   0
1 0     0    1   1
1 1     1    0   1

We could also draw the NAND and NOR equivalent circuits.  By taking one gate at a time we can draw the equivalent for that gate, and then connect them as the original circuit is.

The benefit of designing a NAND equivalent is that we then only need one type of chip.  This makes it cheaper as we have simplified the circuit to only need one type of IC, and we could get a smaller end product as we need to include less ICs.

Here is the NAND equivalent of the above circuit.  Notice that there are two inverters in a row so they cancel each other out.  Instead of drawing the whole circuit again, you can simply put a line through them.

This has really simplified the circuit!  Instead of needing 3 ICs we now only need one, and we only need to wire in two gates.

This is the NOR equivalent.

This is less effective for this circuit as it has actually given us more logic gates to wire.  But we do only need 1 IC instead of 3.