Explanation Given information: The posts are made of aluminum. The modulus of elasticity of the aluminum ( E ) is 70 GPa . The length of the posts B ( L B ) is 124.7 mm . The length of the posts A and C ( L A and L C ) is 125 mm . The force is applied to the posts ( P ) is 100 kip . The cross-sectional of each post ( A ) is 400 mm 2 . The uniformly distributed load act at top and bottom of the beam ( w ) is 800 kN/m . Calculation: Convert the uniformly distributed load ( w ) to point load ( P ): P = 800 kN/m × ( 200 mm × 10 − 3 m 1 m ) = 160 kN Show the free-body diagram of joint A as in Figure 1. Refer to Figure 1. Here, F A is force of the post A , F B is force of the post B , and F C is force of the post C . Calculate the moment about point B by applying the equation of equilibrium: Sum of moments about point B is equal to 0. ∑ M B = 0 − ( F A × 100 ) + ( F C × 100 ) = 0 − 100 F A + 100 F C = 0 d ( − F A + F C ) = 0 − F A + F C = 0 F A = F C Therefore, F = F A = F C Calculate the vertical forces by applying the equation of equilibrium: Sum of vertical forces is equal to 0. ∑ F y = 0 2 F + F B − 160 = 0 2 F + F B = 160 (1) Show the geometry of the deformation diagram of the postsas in Figure 2. Refer Figure 2. Here, δ A is deformation at A and δ B is deformation at B . Calculate the forces of the posts ( F and F B ) using the deformation: δ A = δ B + 0.3 F L A A E = F B L B A E + 0.3 (2) Substitute 125 mm for L A , 124.7 mm for L B , 400 mm 2 for A , and 70 GPa for E in Equation (2). F × 125 400 × ( 70 GPa × 10 3 N/mm 2 1 GPa ) = F B × 124.7 400 × ( 70 GPa × 10 3 N/mm 2 1 GPa ) + 0.3 4.46428 × 10 − 6 F = 4.45357 × 10 − 6 F B + 0

9th Edition

ISBN: 2810014920922

Author: HIBBELER

Publisher: PEARSON

See similar textbooks

Concept explainers

Pressure Vessels

The term pressure vessel refers to a closed container that contains gas or liquid at a different pressure than environment pressure. The pressure vessels have a wide scale of applications in our day-to-day lives and other industrial places. Some common e…

Videos

Question

Chapter 4.5, Problem 4.64P

To determine

Theaverage normal stress in each post (σA, σB, and σC) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.5, Problem 4.63P

Chapter 4.5, Problem 4.65P

Students have asked these similar questions

A converging elbow (see the figure below) turns water through an angle of 135° in a vertical plane. The flow cross section diameter is 400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet, section (2). The elbow flow passage volume is 0.2 m³ between sections (1) and (2). The water volume flowrate is 0.1 m³/s and the elbow inlet and outlet pressures are 140 kPa and 90 kPa. The elbow mass is 11 kg. Calculate the (a) horizontal (x direction) and (b) vertical (z direction) anchoring forces required to hold the elbow in place. D₂- Section (1)- D₁ = 400 mm 135° 200 mm Section (2) (a) Fx= i 20809.96 N (b) Fz= i -120265 N

2: A rectangular aluminum block is loaded uniformly in three directions. The loadings are as follows:a 50 kN total resulting compressive load in the x-direction, a 200 kPa uniformly distributed tensile load in they-direction, and a 0.03 MN total resulting tensile load in the z-direction. The block has the following dimensions:L = 1 m, b = 20 cm, h = 350 mm. Use E = 70 GPa and ν = 0.25.Determine the strain in the x and y axes respectively. For the strain in the y-direction to be equal to 0, how much uniformly distributed load inthe surface of y-direction should be added? (+ for tensile, - for compressive) Answers: 5 -1.122 x10-5 / 3 decimals 6 5.102 x10-6 / 3 decimals 7 -0.357 MPa / 3 decimals

A spherical balloon with a diameter of 9 m is filled with water vapour at 200˚C and 200 kPa. Determine the mass of water in the balloon. The R value for water is 0.4615 kJ/kg∙K.

Chapter 4 Solutions

MECHANICS OF MATERIALS-TEXT

Ch. 4.2 - In each case, determine the internal normal force...Ch. 4.2 - Determine the internal normal force between...Ch. 4.2 - The post weighs 8kN/m. Determine the internal...Ch. 4.2 - The rod is subjected to an external axial force of...Ch. 4.2 - The rigid beam supports the load of 60 kN....Ch. 4.2 - The 20-mm-diameter A-36 steel rod is subjected to...Ch. 4.2 - Segments AB and CD of the assembly are solid...Ch. 4.2 - The 30-mm-diameter A992 steel rod is subjected to...Ch. 4.2 - If the 20-mm-diameter rod is made of A-36 steel...Ch. 4.2 - The 20-mm-diameter 2014-T6 aluminum rod is...

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.

Theaverage normal stress in each post ( σ A , σ B , and σ C ) .

Concept explainers

Videos

Theaverage normal stress in each post (σA, σB, and σC) .

Want to see the full answer?

Chapter 4 Solutions