QNo. 2. For the beam below, calculate the tip deflection for the given loading. In addition to the applied load, the beam weighs 1000 lbs. You should account for this also. Then determine the slope of the deflection at 3 ft from the left end.
The beam is made up of 3 materials, wood, steel, and aluminum. You should be able to find appropriate material properties within your class notes.
Finally, based on your findings, tell me if this is a legitimate exam problem. Does the beam work? (I haven't worked out the solution yet - I'm waiting for all of you to do it for me - then I can alter the problem statement and give it to the class of 2018 as a special problem).
QNo. 3 - Now suppose the beam from No. 2 was rotated 90 deg and subjected to the same loading as in No 2. The beam is held together with a series of 0125 inch diameter aluminum bolts. Recommend a bolt spacing to resist the shear flow between the planks.
QNo 4 - You have been hired by the NFL to design a suspension system for Katie Perry at the Super Bowl. You must design a beam that will support her when she is suspended over the field. Katie weighs 120 pounds.
For deflection, take into account (1) Katie and (2) the beam weight itself. Propose the beam design for a center span deflection less than 2 ft and a bending stress less than the working stress of the materials used. Any end constraints are acceptable. The maximum space envelope for the beam is 12" height and 12" width.
Possible materials are listed in the chart below. You must do the following:
1. Pick a construction type (sandwich face/core, bi-material strip, box beam, singular material, etc)
2. Pick a material or combination of materials.
3. Pick beam dimensions (height, width, circular, square, triangular, rectangular, etc)
4. Pick end constraints (fixed, pinned, roller, free, etc)
|
Material
|
Density lb/in3
|
Max working tens/compr stress Ksi
|
Max working shear stress Ksi
|
E Modulus Msi
|
|
Wood Pine
|
0.04
|
2
|
1
|
0.6
|
|
Wood Balsa
|
0.004
|
0.5
|
0.3
|
0.4
|
|
Steel
|
0.27
|
30
|
20
|
30
|
|
Aluminum
|
0.1
|
20
|
15
|
10
|
|
Uni Glass Composite
|
0.07
|
100
|
50
|
6
|
|
Uni Carbon Composite
|
0.06
|
150
|
75
|
15
|
|
Uni Boron Composite
|
0.08
|
150
|
75
|
35
|
|
Uni HM Carbon Composite
|
0.06
|
100
|
45
|
35
|
|
Uni UHM Carbon Composite
|
0.06
|
50
|
20
|
45
|
|
PVC Foam
|
0.006
|
0.5
|
0.25
|
0.1
|
Katie must not fall due to an engineering error of a Rutgers CE graduate.
Now, instead of a beam, how about building it with a cable (axial loads only, cannot support a moment)
The pinned steel cable(E=30 msi) deflects 2 ft with Katie's weight. Design the steel cable (what is the diameter?)
QNo. 5. A student in an earlier Mechanics of Solids class has designed a bridge using steel bar reinforced concrete box beams. The hollow box beams are made of concrete and imbedded No 9 steel rods (1 square inch). There are 5 box beams, each 24" wide and 40 ft long. The geometry of the beams is shown below.
The external bridge loading is 500lbs per square foot. Assume the asphalt surface is 2 inches thick and weighs 30 lbs per square foot. Also assume that the asphalt surface is free to slide (not attached) over the box beams. Other assumptions you can make:
Concrete compression strength 5000 psi
Concrete density 140 lbs per cubic foot, concrete modulus 2Msi Steel yield strength 30000 psi, steel modulus 30Msi
The weight of the bridge itself must be considered.
A registered Professional Engineer (P.E.) took a look and said that the design is "very marginal". So now you propose two ways to improve the bridge
(1) Bolt and bond a 1/2 inch steel plate to the bottom of the concrete beams
(2) Bolt and bond al/4 inch carbon composite plate to the bottom. (Composite strength 200000 psi, Composite Modulus 15Msi)
Your tasks:
(1) Justify the PE's comment about the design being marginal
(2) Examine the two alternatives and determine what increase in moment capacity is possible with each.
(3) What element governs the capacity of each design?
