Week 1 Challenge
1. Truss type reasoning
Out of the two through type truss systems shown below, which is the most efficient in carrying gravity load? Reason it out.
Solution: Truss A is "Pratt truss" & Truss B is "Howe truss".
Pratt truss is one of the most common forms of truss and is made up of vertical and diagonal members that form an 'N' shape or pattern. The diagonal members are arranged so that they only develop tensile forces. As such, they can be designed to resist axial tension only, avoiding the need for a compression buckling analysis. The vertical members in a Pratt truss develop compression forces. This means they will typically be more robust and capable of resisting buckling.
Howe trusses are essentially the opposite of Pratt trusses in terms of geometry. In fact, looking at a Pratt truss upside-down will visualize a Howe truss of sorts. The entire structure is still relatively the same, but the diagonal braces are now occupying the opposite or the unoccupied joints. This switch in position of the diagonal members has a very important effect structurally.
Pratt trusses have their vertical members in compression and diagonal members in tension upon the application of gravity loads at the joints of the top chord. For Howe trusses, the reverse becomes true as diagonal members are now in compression, while the vertical loads are in tension.
Pratt trusses can have more unloaded members than Howe trusses.
Hence Truss A is most efficient in carrying gravity loads.
2. Deflection shape & Bending Moment Drawing (Qualitative approach)
For the beam & Frame below draw deflected shape and bending moment drawing. (Qualitative approach). E & I are constants.
Solution:
3. Determine MOI, Weight, C/S area of sections below
Solution:
a)
- MOI ALONG Iz-18341333.3333 mm4
- MOI ALONG ly-1843244.9123 mm4
- Weight per meter= 23.84kg/m
b)
- MOI ALONG Iz-5442066666.6667 mm4
- MOI ALONG ly-135042666.6667 mm4
- Weight per meter= 204.1 kg/m
c)
- MOI ALONG Iz-18540000 mrn4
- MOI ALONG ly-1420000 mm4
- Weight per meter= 74.34 kg/m
d)
- MOI ALONG Iz-64180000 mm4
- MOI ALONG ly-81630000 mm4
- Weight per meter= 74.34 kg/m
4. Load calculation problem
For the floor framing below, Calculate the load on interior beam, Exterior beam, Interior Girder and exterior girder having Floor Load of 10kN/m2
Solution:
- INTERIOR COLUMN- 49.04 KN
- CORNER COLUMN- 12.26 KN
- INTERIOR BEAM- 20 KN/M
- EXTERIOR BEAM- 1O KN/M
- INTERIOR GIRDER- 22.5 KN/M
- EXTERIOR GIRDER- 20.1 KN/M
5. Expansion joint size determination for temperature stated problem
Assuming a bridge, made of steel, with an initial total length of 2000 m at -20 ºC, calculate the length difference at 40 ºC and its total length. Coefficient of Thermal expansion of steel = 12x10-6/°C
Solution:
GIVEN: An initial total length of 2000 m at -20°C, Coefficient of Thermal expansion of steel = 12x10-6/°C
RESULT:
Length difference = 12x10-6/°C X 2000M X 40°C
TOTAL length difference at 40°C is 0.96M