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CE311 FALL 2017 Lesson 36 – Influence Lines II “You may beat me, but you will not outwork me” – Dan Gable 1 LESSON 36 – INFLUENCE LINES II Monday, November 20, 2017 LESSON OBJECTIVES 1. Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, subjected to loads that can move (e.g., distributed live loads, etc.) Supplementary Reading: Found on the Online Version of this handout. Homework (Do not hand in). 0. Use Muller-Breslau to construct the influence lines for the reaction at B, the shear at C, and the moment at C. Then, determine the range of reactions at B, the maximum positive moment at C, the maximum negative moment at C, and the maximum shear magnitude at C. Given: uniform dead load of 0.5 kip/ft, uniform live load of 1 kip/ft, and a single live concentrated load of 10 kips. B is a pin support, while A is a roller support. 0. Draw the maximum moment envelopes (i.e., positive and negative) neatly and to scale for the beam shown, indicating all values, using a 2ft-interval. Given: 1.0 kip/ft distributed dead load 2.0 kip/ft distributed live load A single 10 kip moving point load Beam is a reinforced concrete beam (relevant to problem 3). 0. Draw the previous beam, showing the locations for which positive (bottom) and negative (top) reinforcing steel are needed. Note: Reinforced Concrete beams need steel reinforcement on the tension side, only (this will be covered in detail in a subsequent lesson). 1 The irony of this statement is that Dan Gable was known as “the man who never lost.” In 1970, he was famous and on the cover of Sports Illustrated because of his remarkable story: in nearly 300 wrestling matches in high school and in college, he had never lost. Not once. Not ever. With a collegiate record of 181-0, ABC’s Wide World of Sports focused the nation’s attention on Dan Gable, as he met Larry Owings in the NCAA finals, his senior year. Incredibly, Gable lost (meanwhile, the only claim to fame for Larry Owings is that he is the answer to the trivia question, “who is the only man to beat Dan Gable?”). Then he got really motivated. He trained for the 1972 Olympics at 4am because he “couldn’t sleep knowing that, somewhere, the Russians were training.” He won the 1972 Olympic gold medal while never even giving up a point. He celebrated winning the gold medal by immediately going for a 5-mile run. His coaching career was even more dominant than his wrestling career. In 21 years of coaching the Iowa Hawkeyes, he won 21 Big10 titles and 16 National Championships (including 9 in a row, a feat unmatched in any college sport). In the state of Iowa, a common expression is, “Michael Jordan is the Dan Gable of Basketball.” Internationally, he was so famous that A Des Moines newspaper reporter once wore an Iowa hat to a Russian village during the Cold War, in the mountains near the Siberian border, where an American had never been. A young man stepped out of the crowd, pointed toward the hat and said one of the few English words he knew: "Gable." 4 ft. 2 ft. 6 ft.

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Page 1: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

“You may beat me, but you will not outwork me” – Dan Gable1 LESSON 36 – INFLUENCE LINES II

Monday, November 20, 2017 LESSON OBJECTIVES

1. Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, subjected to loads that can move (e.g., distributed live

loads, etc.) Supplementary Reading: Found on the Online Version of this handout. Homework (Do not hand in).

0. Use Muller-Breslau to construct the influence lines for the reaction at B, the shear at C, and the moment at C. Then, determine the range of reactions at B, the maximum positive moment at C, the maximum negative moment at C, and the maximum shear magnitude at C. Given: uniform dead load of 0.5 kip/ft, uniform live load of 1 kip/ft, and a single live concentrated load of 10 kips. B is a pin support, while A is a roller support.

0. Draw the maximum moment envelopes (i.e., positive and negative) neatly and to scale for the beam shown, indicating all

values, using a 2ft-interval. Given:

1.0 kip/ft distributed dead load 2.0 kip/ft distributed live load A single 10 kip moving point load Beam is a reinforced concrete beam (relevant to problem 3).

0. Draw the previous beam, showing the locations for which positive (bottom) and negative (top) reinforcing steel are needed. Note: Reinforced Concrete beams need steel reinforcement on the tension side, only (this will be covered in detail in a subsequent lesson).

1 The irony of this statement is that Dan Gable was known as “the man who never lost.” In 1970, he was famous and on the cover of Sports Illustrated because of his remarkable story: in nearly 300 wrestling matches in high school and in college, he had never lost. Not once. Not ever. With a collegiate record of 181-0, ABC’s Wide World of Sports focused the nation’s attention on Dan Gable, as he met Larry Owings in the NCAA finals, his senior year. Incredibly, Gable lost (meanwhile, the only claim to fame for Larry Owings is that he is the answer to the trivia question, “who is the only man to beat Dan Gable?”). Then he got really motivated. He trained for the 1972 Olympics at 4am because he “couldn’t sleep knowing that, somewhere, the Russians were training.” He won the 1972 Olympic gold medal while never even giving up a point. He celebrated winning the gold medal by immediately going for a 5-mile run. His coaching career was even more dominant than his wrestling career. In 21 years of coaching the Iowa Hawkeyes, he won 21 Big10 titles and 16 National Championships (including 9 in a row, a feat unmatched in any college sport). In the state of Iowa, a common expression is, “Michael Jordan is the Dan Gable of Basketball.” Internationally, he was so famous that A Des Moines newspaper reporter once wore an Iowa hat to a Russian village during the Cold War, in the mountains near the Siberian border, where an American had never been. A young man stepped out of the crowd, pointed toward the hat and said one of the few English words he knew: "Gable."

4 ft. 2 ft. 6 ft.

Page 2: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 3: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 4: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 5: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 6: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 7: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 8: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II

Page 9: 4 ft. 6 ft. 2 ft. - Sites at Lafayette · Construct influence lines using the Muller-Breslau Principle. 2. Construct maximum moment envelopes for determinate beams, ... uniform dead

CE311 FALL 2017 Lesson 36 – Influence Lines II


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