Explanation Given information: Consider the assembly consists of three simply supported beams. The bottom of the top beam rests on the top two beams. The value of EI is constant. The uniform load applied on the beam is 3 kN m . Calculation: Show the forces acting in the beam AB as shown in Figure 1. Refer to Figure 1. Consider the reaction at the points G and H are denoted by R . The deflection at the point G due to the loading is denoted by δ a . Consider the reactions at the supports A and B are denoted by A y and B y . The loading in the beam is symmetrical. Then, Calculate the reaction A y and B y as follows: A y = B y = ( Total load on the beam 2 ) = ( 3 × 6 − R − R 2 ) = ( 18 − 2 R 2 ) = 9 − R Show the loading on the beam AB as shown in Figure 2. Refer Figure 2. Show the deflection at the point G of the beam AB as follows: δ a ′ = δ a = δ 1 + δ 2 + δ 3 (1) Show the expression for δ 1 as follows: δ 1 = w x 24 E I ( x 3 − 2 L x 2 + L 3 ) Substitute 3 kN m for w, L 3 for x . δ 1 = 3 × ( L 3 ) 24 E I [ ( L 3 ) 3 − 2 L ( L 3 ) 2 + L 3 ] Substitute 8 m for L. δ 1 = 3 × ( 8 3 ) 24 E I [ ( 8 3 ) 3 − 2 × 8 ( 8 3 ) 2 + 8 3 ] = 8 24 E I [ 18.9629 − 113.777 + 512 ] = 139.062 E I ( ↓ ) Show the expression for δ 2 as follows: δ 2 = P b x 6 E I L ( L 2 − b 2 − x 2 ) Substitute R for P, L 3 for x , and L 3 for b. δ 2 = R ( L 3 ) ( L 3 ) 6 E I L ( L 2 − ( L 3 ) 2 − ( L 3 ) 2 ) = R ( L 2 9 ) 6 E I L ( L 2 − 2 L 2 9 ) = R L 2 54 E I L ( 9 L 2 − 2 L 2 9 ) = R L 2 54 E I L ( 7 L 2 9 ) Substitute 8 m for L. δ 2 = R ( 8 ) 2 54 E I ( 8 ) ( 7 × 8 2 9 ) = 3 , 584 R 486 E I = 7

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Concept explainers

Buckling of columns

The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

Videos

Question

Chapter 12.9, Problem 12.132P

To determine

The vertical reaction at the supports.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.9, Problem 12.131P

Chapter 12, Problem 12.133RP

Students have asked these similar questions

Mini project You are an engineer working for a power systems company responsible for ensuring grid stability. Your team has recently observed low-frequency oscillations in the system following disturbances such as load changes, faults, and switching operations. These oscillations have led to voltage instability, frequency deviations, and, in severe cases, system blackouts. A task force has been formed to address this issue, and you have been assigned a critical role in developing a damping control strategy. Your objective is to analyze system performance, propose engineering solutions, and compare the effects of different damping approaches. Answer the following questions 1. Identify the Engineering Problem: - What is the fundamental issue affecting power grid stability? - How do low-frequency oscillations impact the system's reliability? - What parameters indicate system instability? 2. Assess the Current Status Using Equations and Calculations: - Given the characteristic roots of the…

H.W 4: The beam shown below is subjected to the distributed loading of w=120 kN/m. Determine the principal stresses in the beam at point P, which lies at the top of the web. Neglect the size of the fillets and stress concentrations at this point. I=67.4×10-6 m4. 15 mm w=120 kN/m B 0.3 m 2 200 mm A 10 rim 15 mm 175 mm

A 3 m x 5 m section of wall of the cold room is not insulated, and the temperature at the outer surface of this section is measured to be 7°C. The temperature of the outside room is 30°C, and the combined convection and radiation heat transfer coefficient at the surface of the outer wall is 10 W/m2°C. It is proposed to insulate this section of the furnace wall with glass wool insulation (k = 0.038 W/m°C) in order to reduce the heat transfer by 90%. Assuming the outer surface temperature of the cold room wall section still remains at about 7°C, determine the thickness of the insulation that needs to be used.

Chapter 12 Solutions

Mechanics of Materials

Ch. 12.2 - In each case, determine the internal bending...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope and deflection of end A of the...Ch. 12.2 - Determine the slope of end A of the cantilevered...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the maximum deflection of the simply...Ch. 12.2 - Determine the slope of the simply supported beam...Ch. 12.2 - An L2 steel strap having a thickness of 0.125 in....Ch. 12.2 - The L2 steel blade of the band saw wraps around...Ch. 12.2 - A picture is taken of a man performing a pole...

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.