EAS211 Homework 6 201804

This homework assignment is due at the beginning of class (2:05pm) on Wednesday, November 28th (11/28).

Late assignments will be accepted (20% deduction) until the end of class (3:50pm). Make sure to follow the

homework formatting guidelines and examples posted on D2L.

This assignment is worth double the points of a regular assignment and cannot be dropped.

Shear/Moment Diagrams & Functions

This assignment is intended to help you understand the relationship between external loads/reactions,

internal shear, and internal bending moment in a beam. For each problem, you will provide 3 diagrams

(loading, shear, and moment) similar to Figure 1 below.

Figure 1: Example loading, internal shear, and internal bending moment diagram (Hibbeler Text)

The only task to complete is the attached worksheet. Print out and complete the worksheet (do not include

this first page).

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Last Name: _______________________________

First Name: _______________________________

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Problem 1 (25%)

Complete the following for this problem:

(A) (5 pts) Calculate the support reactions; show them on the beam (top diagram)

(B) (10 pts) Draw the shear diagram; identify critical values (at A/B/C, max/min, transitions)

(C) (10 pts) Draw the moment diagram; identify critical values (at A/B/C, max/min, transitions)

Do not show your work – only provide the final results required above.

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–

+

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M

V

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Problem 2 (25%)

Complete the following for this problem:

(A) (5 pts) Calculate the support reactions; show them on the beam (top diagram)

(B) (10 pts) Draw the shear diagram; identify critical values (at A/B/C, max/min, transitions)

(C) (10 pts) Draw the moment diagram; identify critical values (at A/B/C, max/min, transitions)

Do not show your work – only provide the final results required above.

+

–

+

–

M

V

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Problem 3 (25%)

Complete the following for this problem:

(A) (5 pts) Calculate the support reactions; show them on the beam (top diagram)

(B) (10 pts) Draw the shear diagram; identify critical values (at A/B/C, max/min, transitions)

(C) (10 pts) Draw the moment diagram; identify critical values (at A/B/C, max/min, transitions)

Do not show your work – only provide the final results required above.

+

–

+

–

M

V

EAS211 Homework 6 201804

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Problem 4 (25%)

Complete the following for this problem:

(A) (5 pts) Calculate the support reactions; show them on the beam (top diagram)

(B) (10 pts) Draw the shear diagram; identify critical values (at A/B/C, max/min, transitions)

(C) (10 pts) Draw the moment diagram; identify critical values (at A/B/C, max/min, transitions)

Do not show your work – only provide the final results required above.

+

–

+

–

M

V

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Problem 5 (100%)

The compound beam above is fixed at point A and supported by a roller at point D. There is a hinge (internal

pin) at point C.

For this problem, you are required to determine the equations for internal shear and moment as functions of

x, and then plot the graphs. Provide all of your work on the provided pages – if you run out of room, print

additional copies of the “Additional Work Space” page.

(A) (20%) SUPPORT REACTIONS: Determine the support reactions at points A and C. This will require two

FBDs (one for section CD, the one for section ABC).

𝑥1 𝑥2

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[Additional Work Space]

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(B) (20%) SECTION CUT 1: Make a section cut at 𝑥1, which is valid between points A and B, i.e. {0 𝑓𝑡 ≤ 𝑥1 ≤ 4 𝑓𝑡}. Create a complete FBD using the portion of the beam to the left of the section cut.

Use equilibrium to solve for the internal shear (𝑉1) and bending moment (𝑀1).

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(C) (20%) SECTION CUT 2: Make a section cut at 𝑥2, which is valid between points B and D, i.e. {4 𝑓𝑡 ≤ 𝑥2 ≤ 9 𝑓𝑡}. Create a complete using the portion of the beam to the left of the section cut. Use

equilibrium to solve for the internal shear (𝑉2) and bending moment (𝑀2).

NOTE: even though there is a hinge at point C, it does not produce a “discontinuity” in the moment diagram, so

there is no need for an additional section cut to the right of C.

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(D) (20%) SHEAR AND MOMENT DIAGRAM

– Show the support reactions (at points A and C) on the beam below (top diagram)

– Provide V & M diagrams; show values (at points A/B/C, max/min, and at transitions) with units

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M

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(E) (20%) CHECKS: Complete the following to verify/check the V/M diagrams:

a. (4%) The change in shear between two points is equal to the area under the distributed load

between the same two points. Use this to verify the change in shear from point A to B. Provide the

calculation below.

b. (4%) The change in moment between two points is equal to the area under the shear diagram

between the same two points. Use this to verify the change in moment from point A to B. Provide

the calculation below.

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c. (4%) The internal moment at a hinge has to be zero. Confirm that your internal moment at point C

is zero. If not, explain what the issue might be (for partial credit).

d. (4%) An externally applied force applied to a beam will cause an abrupt change in the internal shear

at the same point. An upwards-facing force will cause an increase in internal shear, when moving

from left-to-right across the beam. Verify that the support reaction (i.e. vertical force) at point D

causes the shear to jump up at point D. If not, explain what the issue might be (for partial credit).

e. (4%) An externally-applied couple moment applied to a beam will cause an abrupt change in

internal moment at the same point. A clock-wise external couple moment will cause an increase in

internal moment, when moving from left-to-right across the beam. Verify that the couple moment

at point D causes a drop at point D. If not, explain what the issue might be (for partial credit).