Explanation Calculation: Show the free body diagram of the beam as in Figure 1. Calculate the vertical reaction at point A by taking moment about point B . ∑ M B = 0 − R A L + P × ( L 4 + L 4 ) − P × ( L 4 ) = 0 − R A L + P L 2 − P L 4 = 0 R A = P L 4 L R A = P 4 Calculate the vertical reaction at point B by resolving the vertical component of forces. ∑ F y = 0 P 4 − P + P + R B = 0 R B = − P 4 Calculate the moment due to the reaction at A : M 1 = P 4 × L 2 = P L 8 Calculate the M 1 E I value; Substitute P L 8 for M 1 . M 1 E I = P L 8 E I = P L 8 E I Show the M 1 E I diagram in below Figure 2. Calculate the area ( a ) using the relation: A 1 = 1 2 ( L A D ) ( M 1 E I ) Substitute L 2 for L A D and ( P L 8 E I ) for ( M 1 E I ) . A 1 = 1 2 ( L 2 ) ( P L 8 E I ) = P L 2 32 E I Calculate the moment due to the point load: M 2 = ( P 4 × ( L 2 + L 4 ) ) − ( P × L 4 ) = − P L 16 E I Calculate the M 2 E I value; Substitute − P L 16 E I for M 2 . M 2 E I = − P L 16 E I E I = − P L 16 E I Show the ( M 2 E I ) diagram in below Figure 3. Calculate the position of point of contra flexure as below: P 4 ( L 2 + x ) − P × x = 0 P L 8 + P x 4 − P x = 0 P L 8 − 3 P x 4 = 0 − 3 P x 4 = − P L 8 x = P L 8 × 4 3 P x = L 6 Calculate the area ( A 2 ) using the relation: A 2 = 1 2 ( x ) ( M 1 E I ) Substitute L 6 for x and P L 8 E I for ( M 1 E I ) . A 2 = 1 2 ( L 6 ) ( P L 8 E I ) = P L 2 96 E I Calculate the area ( A 3 ) using the relation: A 3 = 1 2 ( L D E − x ) ( M 2 E I ) Substitute L 6 for x and − P L 16 E I for ( M 2 E I ) . A 3 = 1 2 ( L 4 − L 6 ) ( − P L 16 E I ) = − P L 2 384 E I Calculate the moment due to reaction at point B: M 3 = − P 4 × L 4 = − P L 16 Calculate the M 3 E I value; Substitute − P L 16 for M 3 . ( M 3 E I ) = − P L 16 E I = − P L 16 E I Show the ( M 3 E I ) diagram in below Figure 4. Calculate the area ( A 4 ) using the relation: A 4 = 1 2 ( L E B ) ( M 3 E I ) Substitute ( L 4 ) for L E B and − P L 16 E I for ( M 3 E I ) . A 4 = 1 2 ( L 4 ) ( − P L 16 E I ) = − P L 2 128 E I Calculate the tangential deviation of B with respect to A using the relation: t B / A = A 1 ( ( 1 3 × L A D ) + L D E + L E B ) + A 2 ( 2 3 x + ( L D E − x ) + L E B ) + A 3 ( 1 3 ( L D E − x ) + L E B ) + A 4 ( 2 3 L E B ) Substitute P L 2 32 E I for A 1 , P L 2 96 E I for A 2 , ( − P L 2 384 E I ) for A 3 , ( − P L 2 128 E I ) for A 4 , ( L 6 ) for x , ( L 2 ) for L A D , ( L 4 ) for L D E , and ( L 4 ) for L E B

7th Edition

ISBN: 8220102804487

Author: BEER

Publisher: YUZU

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 141P

To determine

The magnitude (yK) and location of the largest downward deflection (xK).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.6, Problem 140P

Chapter 9.6, Problem 142P

Students have asked these similar questions

15 mm DA 100 mm 50 mm Assuming the load applied P 80 kN. Determine the maximum stress in the bar shown assuming the diameter of the whole A is DA = 25 mm.

use engineering economic tables, show full solution

Do not use chatgpt. I need quick handwritten solution.

Chapter 9 Solutions

EBK MECHANICS OF MATERIALS

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.

The magnitude ( y K ) and location of the largest downward deflection ( x K ) .

Solution Summary: The author calculates the vertical reaction at point A by taking moment about point B.

Concept explainers

Videos

The magnitude (yK) and location of the largest downward deflection (xK).

Want to see the full answer?

Chapter 9 Solutions