NAME:________________________
Midterm Exam #2
CEE 003: Engineering Statics
Fall 2017
This exam is closed book, and only the following are permitted:
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Pencil
Calculator (conventional, graphing, or scientific)
Ruler (if needed)
Programmed material of any kind on a scientific or graphing calculator is prohibited. Cell phone
or internet use of any kind during this exam is forbidden. Sharing information with others or
copying the work of others during an exam is strictly prohibited.
For each solution, please do the following:
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Box or circle your answers.
Provide units with your final answers.
Write legibly.
Show your work. Partial credit will be given for solutions that show the correct
methodology but produce an incorrect numerical answer.
Other notes:
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Gravitational acceleration, g = 9.81 m/s2 or 32.2 ft/s2
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𝑐𝑜𝑠 2 𝜃𝑥 + 𝑐𝑜𝑠 2 𝜃𝑦 + 𝑐𝑜𝑠 2 𝜃𝑧 = 1
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Law of Sines:
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Law of Cosines: 𝐴2 = 𝐵2 + 𝐶 2 − 2𝐵𝐶𝑐𝑜𝑠(𝑎)
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Moment about a point O: MO = rB/O x FB
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Moment about an axis OA: MOA = λOA · (rB/O x FB)
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Parabolic Cable Equation: 𝑦 =
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Parabolic Cable Length: 𝑠 = 𝑥 [1 + 3 (𝑥 ) − 5 (𝑥 ) + ⋯ ]
sin(𝑎)
𝐴
=
sin(𝑏)
𝐵
=
A
c
sin(𝑐)
𝐶
2 𝑦 2
a
b
C
𝑤𝑥 2
2𝑇𝑜
2 𝑦 4
B
CEE 003 Midterm Exam #2
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CEE 003 Midterm Exam #2
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CEE 003 Midterm Exam #2
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PROBLEM #1 (15 points)
The 2 suspension cables on the main span (between points A and B as shown) of the Golden Gate
Bridge each support a uniformly distributed load w0 = 11.1 kips/ft along its horizontal deck. The
cables have a parabolic shape in the main span, and their self-weight can be neglected. If the span
L = 4150 ft and sag h = 464 ft, calculate the following:
a) The maximum tension in each cable in the main span
b) The total length of each cable in the main span
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CEE 003 Midterm Exam #2
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CEE 003 Midterm Exam #2
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PROBLEM #2 (30 points)
The gravity dam shown below has two sections: the left side is made of gravel (density = 1600
kg/m3, and the right side is made of concrete (density = 2400 kg/m3). The concrete section is in
contact with the water (density = 1000 kg/m3). The concrete section also has a rectangular cutout
as shown, which serves as an access duct. Assume a unit width of 1 meter (into the page) when
making your calculations for the following:
a) Calculate the horizontal (i.e. x-direction) distance from the toe of the dam (at the axis origin as
shown) to the dam’s center of gravity.
b) Calculate the resultant force (H and V) that the water exerts on the dam when its depth d = 4m.
d
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CEE 003 Midterm Exam #2
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PROBLEM #3 (30 points)
The frame shown below consists of 4 members and is supported by pins at A and E. The selfweight of the members can be neglected for all calculations.
a) Prove that this frame is statically determinate by filling in the following:
List all frame members: _____________________________________________________
List all truss (or 2-force) members: ____________________________________________
List all unknown forces & reactions: ___________________________________________
Total # of equilibrium equations = ________
Total # of unknowns = ________
b) Solve for all unknown forces that are
applied to member CDE.
Hint: Member AD is connected to the pin at A
but NOT to member AB.
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CEE 003 Midterm Exam #2
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PROBLEM #4 (25 points)
The truss shown below is supported by a pin at I and a vertical cable link at B.
a) List all zero-force elements: __________________________________________________
b) Solve for the force in the following 5 elements: AB, BC, BH, CH, and GH. Clearly note
whether they are in compression or tension.
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