Influence Lines Quiz 4

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The influence line quizzes serve as a crucial checkpoint to evaluate your grasp of the foundational concepts necessary for our structural analysis course. Should you encounter difficulties with these quizzes, it suggests that enhancing your knowledge in engineering mechanics - statics is essential before you can successfully embark on our structural analysis journey.

Each quiz features 4 questions. Carefully answer each one in the provided input fields. Once you are confident in your responses, click the submit button. ChatGPT will then review your answers and offer insightful feedback to help you improve.

Question 1

Consider the beam shown below.

Suppose we wish to draw the influence line for the support reaction at D by pushing the point up a unit. In response to moving point D up a unit, how do points C and E move?

How does bar AC displace when D is pushed up a unit?

How does bar EF displace when D is pushed up a unit?

Question 2

Consider the beam shown in Question 1.

Suppose we wish to draw the moment influence line for point B. To do so, we place a fictitious hinge at B and apply a positive bending moment to the hinge. This causes a few joints to move vertically, and some beam segments to rotate.

How does bar AB rotate?

How does bar CE rotate?

How does bar EF rotate?

Question 3

A beam and an influence line are shown below. The influence line belongs to the shear force at B. Three heights are labeled on the influence line: h1, h2, and h3. Determine the heights.

Height h1 equals:

Height h2 equals:

Height h3 equals:

Question 4

The following statically determinate beam is fixed at both ends and has two internal hinges, at points C and D. The influence line for the shear force at B is shown below.

Suppose the beam is subjected to a series of moving concentrated loads (see below).

Using the given influence line, determine the shear force at B when the 20 kN concentrated load is located at point C on the beam.

What is the magnitude of the shear force at B when the 30 kN load is located at point C?

Assuming that the direction of travel of the load series can be reversed, what is the absolute maximum shear force at B due to the moving load series?