(a) Explanation Given information: The elastic modulus ( E ) is 29 × 10 6 psi . The section of the beam is W 12 × 26 . Calculation: Refer Appendix C, “Properties of Rolled steel shapes”. The moment of inertia ( I ) for the given section is 204 in . 4 . Use moment area method: Show the free body diagram of the beam as in Figure 1. Determine the reaction of the support by taking moment at point B . ∑ M B = 0 − ( R A × 10 ) + [ ( 5 × 4 ) ( 4 + 4 2 ) ] + ( 8 × 4 × 4 2 ) = 0 R A = 18.4 kips Determine the reaction of the support by considering the vertical equilibrium condition: ∑ F y = 0 R A + R B = ( 5 × 4 ) + ( 8 × 4 ) R A + R B = 52 Substitute 18.4 kips for R A . R B + 18.4 = 52 R B = 33.6 kips Show the moment ( M E I ) diagram for the given loading of the beam as in Figure 2. Calculate the moment ( M 1 ) using the formula: M 1 = R A × 10 Substitute 18 .4kips for R A . M 1 = 18.4 × 10 = 184 kips ⋅ ft Calculate the ratio of M 1 E I : Ratio = M 1 E I Substitute 184 kips ⋅ ft for M 1 . M 1 E I = 184 kips ⋅ ft E I Calculate the area ( A 1 + A 2 ) due to the moment ( M 1 ) using the formula: A 1 + A 2 = 1 2 b h Here, b is the width of the triangle in area ( A 1 + A 2 ) and h is the height of the triangle in area ( A 1 + A 2 ) . Substitute 10ft for b and 184 kips ⋅ ft E I for h. A 1 + A 2 = 1 2 × 10 × ( 184 kips ⋅ ft E I ) = 920 E I kips ⋅ ft 2 Calculate the moment ( M 2 ) using the formula: M 2 = R A × 6 ft Substitute 18 .4kips for R A . M 2 = 18.4 × 6 ft =110 .4kips ⋅ ft Calculate the ratio of M 2 E I : Ratio = M 2 E I Substitute 110 .4kips ⋅ ft for M 2 . M 2 E I = 110 .4kips ⋅ ft E I Calculate the area ( A 1 ) due to the moment ( M 2 ) using the formula: A 1 = 1 2 b 1 h 1 Here, b 1 is the width of the rectangle in area ( A 1 ) and h 1 is the height of the rectangle in area ( A 1 ) . Substitute 6ft for b 1 and 110 .4kips ⋅ ft E I for h 1 . A 1 = 1 2 × 6 × ( 110 .4kips ⋅ ft E I ) = 331.2 E I kips ⋅ ft 2 Calculate the moment ( M 3 ) using the formula: M 3 = − 5 × 8 × 8 2 = − 160 kips ⋅ ft Calculate the ratio of M 3 E I : Ratio = M 3 E I Substitute − 160 kips ⋅ ft for M 3 . M 3 E I = − 160 kips ⋅ ft E I Calculate the area ( A 3 + A 4 ) due to the moment ( M 3 ) using the formula: A 3 + A 4 = 1 3 b 3 h 3 Here, b 3 is the width of the parabola in area ( A 3 + A 4 ) and h 3 is the height of the parabola in area ( A 3 + A 4 ) . Substitute 8ft for b 3 and − 160 kips ⋅ ft E I for h 3 . A 3 + A 4 = 1 3 × 8 × ( − 160 kips ⋅ ft E I ) = − 426.667 E I kips ⋅ ft 2 Calculate the moment ( M 4 ) using the formula: M 4 = − ( 5 × 4 ) 4 2 = − 40 kips ⋅ ft Calculate the ratio of M 4 E I : Ratio = M 4 E I Substitute − 40 kips ⋅ ft for M 4 (b) To determine Find the deflection ( y E ) at point C .

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 132P

(a)

To determine

Find the slope (θA) at point A.

(b)

To determine

Find the deflection (yE) at point C.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.6, Problem 131P

Chapter 9.6, Problem 133P

Students have asked these similar questions

For the beam and loading shown, determine (a) the equation of the elastic curve, (b) the slope at end A. (c) the deflection at point C. Fig. P9.35 CV B

For the beam and loading shown, determine (a) the equation of the elastic curve, (b) the deflection at the free end.

Determine the slope and deflection at D for the beam and loading shown (Fig. 8.33), knowing that the flexural rigidity of the beam is EI = 100 MN m². A 150 kN 2 m D Fig. 8.33 20 kN/m -8 m- B

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.

Find the slope ( θ A ) at point A .

Solution Summary: The author calculates the moment of inertia for the given section of the beam by considering the vertical equilibrium condition.