engineering mechanics statics problem

EAS211 Homework 3 201804

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This homework assignment is due at 4:00pm on Friday, October 19th (10/19) to the CEE Office (EB200)

homework dropbox. Make sure to timestamp your submission and to follow the homework formatting

guidelines and examples posted on D2L.

Rigid Body Equilibrium

The following problem requires you to analyze a real-world structure to calculate the support reactions (which

would then be used for foundation design).

Problem 1 (100 Points): “Single Mast Arm Pole”

This problem requires you to complete the tasks below related to a standard “MAP-30 Single Mast Arm Pole”

signal support, as provided in the PBOT Standard Details catalog, Dwg. No. P-601.

Figure 1: PBOT Std. Dwg. No. P-601

The standard design is proposed to be used for a new (much needed) stop light on SW 4th Ave at SW College

St, as shown in Figure 2 below. Although these “standard designs” are engineered and checked by PBOT,

assume that your supervisor has asked you to begin structural calculations because she has learned that new

lighted signs (proposed for 2020 implementation) have increased weight.

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Figure 2: SW 4th Ave. at SW College St. (Looking East)

Use the following parameters and simplifications/assumptions when analyzing the structure:

▪ Analyze the structure in 2D, as diagramed in Dwg. No. P-601

▪ Ignore the radius of the mast arm. Treat it as a straight member, inclined at angle α.

▪ The mast arm and post are fabricated from structural steel, with a unit weight of 490 pcf.

▪ Assume that the cross-sectional area (and therefore self-weight) of the mast arm and post linearly vary

along the length/height of each member. The cross-sectional area at the end of each member is:

- Mast Arm End: 4.00 in2 (at free end)

- Mast Arm Base: 10.0 in2 (at connection to post)

- Post End: 12.0 in2 (at connection to mast arm)

- Post Base: 24.0 in2 (at bottom of post)

▪ To calculate the weight per lineal foot, simply multiply the cross-sectional area by the unit weight. Be

careful with units!

- Example: (8.00 𝑖𝑛2) ∙ ( 1 𝑓𝑡

12 𝑖𝑛 )

2

∙ ( 490 𝑙𝑏

𝑓𝑡3 ) = 27.22

𝑙𝑏

𝑓𝑡

▪ Ignore the weight of bolt, caps, compartments, etc. and the voids in member – only consider the gross

self-weight of the main structural tubing (mast arm and post).

▪ Ignore the 12” portion of the post that extends above the mast arm connection

▪ The bottom of the post is a fixed connection to the foundation

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▪ Assume that the horizontal wind load only acts on the vertical post. Although the post is tapered, you

will treat the wind load as two uniformly distributed loads, as follows:

- Bottom of Post (0’-20’ height above base): 20 lbs/ft

- Top of Post (20’+ height above base): 30 lbs/ft

▪ Use the following geometry and loading parameters:

- Mast Arm Length: 30.0 ft (Horizontal Projection)

- Post Riser Height: 24.0 ft (Vertical)

- Attached Signs/Signals: The following sign/signals are supported by the mast arm

Type Horiz. Distance From Post Centerline (ft) Weight (lbs)

30”x36” Sign 29.5 100

5-Section Head 26.5 300

30”x36” Sign 21.5 100

3-Section Head 18.5 200

3-Section Head 10.5 200

Tasks to complete:

A) “Dead” Load: considering only the self-weight of the mast arm and the post

a. Provide a loading diagram showing the dead loading on the mast arm and post. Note that there

should be linearly varying loads for the weight of both members.

b. Determine the dead load support reactions at the fixed post base

B) “Live” Load: considering only the weight of the signs and signals (“heads”)

a. Provide a loading diagram showing the live loading on the mast arm and post.

b. Determine the live load support reactions at the fixed post base

C) “Wind” Load: considering only the wind load acting on the vertical post

a. Provide a loading diagram showing the wind loading on the post.

b. Determine the live load support reactions at the fixed post base

c. The assumed/prescribed wind loading for this 2d example is very simplified. Provide a 3d

sketch of the mast arm and post structure, then discuss/conclude which of the 6 possible

support reactions (3 forces, 3 moments) could be caused by wind loading. Use complete

sentences to explain your reasoning. Calculations are not required, but some basic equations in

conjunction with your diagram may be helpful to support your conclusion.

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Grading Rubric

Your submission will be graded on the following criteria:

CRITERIA MAX POINTS

Cover page and rubric provided w/o modification (except name) 5

LastName, FirstName added to cover page and rubric 5

Given/Required/Solution format followed - OK to attach folded, annotated copy of P-601 for portion of “given” information

5

Engineering paper used 5

Proper header provided 5

Proper engineering figures (straightedge, to scale, etc.) 5

Subheaders provided in “Solution” section to organize work 5

Final answers clearly identified 5

Final answer units of feet and pounds 5

(B) Dead Load: Loading Diagram 5

(B) Dead Load: Support Reactions 10

(B) Live Load: Loading Diagram 5

(B) Live Load: Support Reactions 10

(C) Wind Load: Loading Diagram 5

(C) Wind Load: Support Reactions 10

(C) Wind Load: 3D Wind Load Reaction Discussion w/ Diagram & Reasoning 5

Overall professional presentation (well organized, easy to follow, proper grammar, clear calcs, etc.)

5

MAX/MIN 100