Answer:
Part a: The yield moment is 400 k.in.
Part b: The strain is 
Part c: The plastic moment is 600 ksi.
Explanation:
Part a:
As per bending equation

Here
- M is the moment which is to be calculated
- I is the moment of inertia given as

Here
- b is the breath given as 0.75"
- d is the depth which is given as 8"



The yield moment is 400 k.in.
Part b:
The strain is given as

The stress at the station 2" down from the top is estimated by ratio of triangles as

Now the steel has the elastic modulus of E=29000 ksi

So the strain is 
Part c:
For a rectangular shape the shape factor is given as 1.5.
Now the plastic moment is given as

The plastic moment is 600 ksi.
Answer:
Explanation:
a) the steady-state, 1-D incompressible and no energy generation equation can be expressed as follows:

b) For a transient, 1-D, constant with energy generation
suppose T = f(x)
Then; the equation can be expressed as:

where;
= heat generated per unit volume
= Thermal diffusivity
c) The heat equation for a cylinder steady-state with 2-D constant and no compressible energy generation is:

where;
The radial directional term =
and the axial directional term is 
d) The heat equation for a wire going through a furnace is:
![\dfrac{\partial ^2 T}{\partial z^2} = \dfrac{1}{\alpha}\Big [\dfrac{\partial ^2 T}{\partial ^2 t}+ V_z \dfrac{\partial ^2T}{\partial ^2z} \Big ]](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Cpartial%20%5E2%20T%7D%7B%5Cpartial%20z%5E2%7D%20%3D%20%5Cdfrac%7B1%7D%7B%5Calpha%7D%5CBig%20%5B%5Cdfrac%7B%5Cpartial%20%5E2%20T%7D%7B%5Cpartial%20%5E2%20t%7D%2B%20V_z%20%5Cdfrac%7B%5Cpartial%20%5E2T%7D%7B%5Cpartial%20%5E2z%7D%20%5CBig%20%5D)
since;
the steady-state is zero, Then:
'
e) The heat equation for a sphere that is transient, 1-D, and incompressible with energy generation is:

Answer:
The voltages of all nodes are, IE = 4.65 mA, IB =46.039μA, IC=4.6039 mA, VB = 10v, VE =10.7, Vc =4.6039 v
Explanation:
Solution
Given that:
V+ = 20v
Re = 2kΩ
Rc = 1kΩ
Now we will amke use of the method KVL in the loop.
= - Ve + IE . Re + VEB + VB = 0
Thus
IE = V+ -VEB -VB/Re
Which gives us the following:
IE = 20-0.7 - 10/2k
= 9.3/2k
so, IE = 4.65 mA
IB = IE/β +1 = 4.65 m /101
Thus,
IB = 0.046039 mA
IB = 46.039μA
IC =βIB
Now,
IC = 100 * 0.046039
IC is 4.6039 mA
Now,
VB = 10v
VE = VB + VEB
= 10 +0.7 = 10.7 v
So,
Vc =Ic . Rc = 4.6039 * 1k
=4.6039 v
Finally, this is the table summary from calculations carried out.
Summary Table
Parameters IE IC IB VE VB Vc
Unit mA mA μA V V V
Value 4.65 4.6039 46.039 10.7 10 4.6039
Answer:
2.77mpa
Explanation:
compressive strength = 20 MPa. We are to find the estimated flexure strength
We calculate the estimated flexural strength R as
R = 0.62√fc
Where fc is the compressive strength and it is in Mpa
When we substitute 20 for gc
Flexure strength is
0.62x√20
= 0.62x4.472
= 2.77Mpa
The estimated flexure strength is therefore 2.77Mpa