CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

“You have enemies? Good. That means you’ve stood up for something, sometime in your life” – Winston Churchill LESSON 39: VIRTUAL WORK FOR INDETERMINATE FRAMES

Friday, December 1, 2017 LESSON OBJECTIVES

1. State the Principal of Virtual work and give the formulae for axial and bending.

2. Calculate frame (or beam) deflections using the principle of virtual work.

3. Solve 1-DOI indeterminate frames and beams using deflections calculated using the principle of virtual work

READING Online, from Hibbeler, second example (9.8) covered in class HOMEWORK ASSIGNMENT (DUE MONDAY)

1. Use the principle of virtual work to compute the deflection at point C due to the given point loads (i.e., do not consider the self-weight deflection), if the beam is a W18x35, bent about its strong axis. Note: be careful about units (advice: work in kips and inches. Also, see the online examples; working in inconsistent units can get very messy, so the best advice is to work in consistent units, from the beginning).

2. INDETERMINATE FRAME. Solve the horizontal and vertical reaction components at A and D and plot the moment diagram

for the beam and columns (on the compression side), determining all local min and max values. Given: the beam-column connections are rigid, A and D are pinned foundations. The story height is 20 ft and the span length is 50 ft. the uniform load is 1 kip/ft, the beams and columns have EI=100000 kip-ft2

STEPS:

1. Remove a redundant at D by converting the pin into a roller. Use virtual work to determine the horizontal movement of roller D, due to the applied loading.

2. Determine the horizontal displacement at point D due to this one kip load at point D.

10’ 10’ 10’

15 kips 10 kips

A B C D

50 ft

20 ft

w = 1 kip/ft

A

B C

D

50 ft

20 ft

w = 1 kip/ft

A

B C

D

50 ft

A

B C

D 1 kip

IN CLASS EXAMPLE: COMPUTE

HORIZONTAL DEFLECTION AT C

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)

CE311 Fall 2017 Lesson 39: Virtual Work for Indeterminate Frames (and Beams)