(a) Explanation Given information: The section of the cantilever beam ABC is W 130 × 23.8 The young’s modulus ( E ) of steel is 200 GPa . Calculation: Show the free body diagram of the beam as in Figure 1. Calculate the moment due to the reaction at B as below: M 1 = R B × L A B Here, L A B is length of the beam. Substitute 1.8 m for L A B . M 1 = R B × 1.8 = 1.8 R B Calculate the M 1 E I value: Substitute 1.8 R B for M 1 . ( M 1 E I ) = 1.8 R B E I Show the ( M 1 E I ) diagram in below Figure 2. Calculate the area ( A 1 ) using the relation: A 1 = 1 2 ( L A B ) ( M 1 E I ) Substitute 1.8 m for L A B and 1.8 R B E I for ( M 1 E I ) . A 1 = 1 2 ( 1.8 ) ( 1.8 R B E I ) = 1.62 R B E I (1) Calculate the moment ( M 2 ) due the point load: M 2 = − 20 × ( L A B + L B C ) Here, L B C is length of the beam. Substitute 1.8 m for L A B and 1.2 m for L B C . M 2 = − 20 × ( 1.8 + 1.2 ) = − 60 kN ⋅ m Calculate the ( M 2 E I ) value: Substitute − 60 kN ⋅ m for M 2 . ( M 2 E I ) = − 60 E I Show the ( M 2 E I ) diagram in below Figure 3. Calculate the area ( A 2 ) using the relation: A 2 = 1 2 ( L A B + L B C ) ( M 2 E I ) Substitute 1.8 m for L A B , 1.2 m for L B C , and ( − 60 E I ) for ( M 2 E I ) . A 2 = 1 2 ( 1.8 + 1.2 ) ( − 60 E I ) = − 90 E I Refer Appendix C “Properties of rolled steel shape (SI units)” for moment of inertia of section W 130 × 23.8 and the value is 8.91 × 10 6 mm 4 . Calculate the value ( EI ): Substitute 200 GPa for E and 8.91 × 10 6 mm 4 for I . E I = ( 200 GPa × 1 , 000 , 000 kN/m 2 1 GPa ) × ( 8.91 × 10 6 mm 4 × 1 m 4 1 , 000 4 mm 4 ) = 1 , 782 kN ⋅ m 2 Express the tangential deviation equation of C with respect to A : t C / A = A 1 ( ( 2 3 L A B ) + L B C ) + A 2 ( 2 3 ( L A B + L B C ) ) Equate the above equation to zero. 0 = A 1 ( ( 2 3 L A B ) + L B C ) + A 2 ( 2 3 ( L A B + L B C ) ) (2). Substitute 1.62 R B E I for A 1 , − 90 E I for A 2 , 1 , 782 kN ⋅ m 2 for EI , 1 (b) To determine The final value of the reaction ( R B ) at point B .

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

Videos

Question

Chapter 9.6, Problem 153P

(a)

To determine

Find how much point B should be raised to return point C to tits original position.

(b)

To determine

The final value of the reaction (RB) at point B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.6, Problem 152P

Chapter 9.6, Problem 154P

Students have asked these similar questions

a 300n girl and an 400n boy stand on a 16m platform supported by posts A and B. The platform itself weighs 200N. What are the forces exerted by the supports on the platform?

C A cylindrical piece of steel 38 mm (1½ in.) in diameter is to be quenched in moderately agi- tated oil. Surface and center hardnesses must be at least 50 and 40 HRC, respectively. Which of the following alloys satisfy these requirements: 1040, 5140, 4340, 4140, and 8640? Justify your choice(s).

Using the isothermal transformation diagram for a 1.13 wt% C steel alloy (Figure 10.39), determine the final microstructure (in terms of just the microconstituents present) of a small specimen that has been subjected to the following time-temperature treatments. In each case assume that the specimen begins at 920°C (1690°F) and that it has been held at this temperature long enough to have achieved a complete and homogeneous austenitic structure. (a) Rapidly cool to 250°C (480°F), hold for 103 s, then quench to room temperature. (b) Rapidly cool to 775°C (1430°F), hold for 500 s, then quench to room temperature. (c) Rapidly cool to 400°C (750°F), hold for 500 s, then quench to room temperature. (d) Rapidly cool to 700°C (1290°F), hold at this temperature for 105 s, then quench to room temperature. (e) Rapidly cool to 650°C (1200°F), hold at this temperature for 3 s, rapidly cool to 400°C (750°F), hold for 25 s, then quench to room temperature. (f) Rapidly cool to 350°C (660°F), hold for…

Chapter 9 Solutions

Mechanics of Materials, 7th Edition

Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - In the following problems assume that the flexural...Ch. 9.2 - 9.1 through 9.4 For the loading shown, determine...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - 9.5 and 9.6 For the cantilever beam and loading...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - For the beam and loading shown, determine (a) the...Ch. 9.2 - Knowing that beam .AB is a W10 33 rolled shape...Ch. 9.2 - Knowing that beam AB is an S200 34 roiled shape...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Find how much point B should be raised to return point C to tits original position.

Solution Summary: The author explains how to calculate the moment due to the reaction at B.

Concept explainers

Videos

Find how much point B should be raised to return point C to tits original position.

The final value of the reaction (RB) at point B.

Want to see the full answer?

Chapter 9 Solutions