(a) Explanation The specified increment is Δ L = 1.25 ft from the end A . Show the free-body diagram of the entire beam as in Figure 1. Determine the vertical reaction at point B by taking moment at point D . ∑ M D = 0 ( 4.8 × 5 ) × 12.5 + ( 3.2 × 10 ) × 5 − B y ( 12.5 ) = 0 300 + 160 − 12.5 B y = 0 B y = 36.8 kips Determine the vertical reaction at point D by resolving the vertical component of forces. ∑ F y = 0 − ( 4.8 × 5 ) + B y − ( 3.2 × 10 ) + D y = 0 − 24 + 36.8 − 32 + D y = 0 D y = 19.2 kips Write the equation of the load function as follows; w ( x ) = 4.8 − ( 4.8 − 3.2 ) 〈 x − 5 〉 0 = 4.8 − 1.6 〈 x − 5 〉 0 kips/ft (1) The equation for shear force as a function of load function is, w ( x ) = − d V d x Integrate the equation (1) to find V ; V = A y 〈 x − 2.5 〉 0 − ∫ w ( x ) d x = − 4.8 x + 36.8 〈 x − 2.5 〉 0 + 1.6 〈 x − 5 〉 1 kips (2) The equation for bending moment as a function of shear force is, V ( x ) = d M d x Integrate the equation (2) to find M ; M = ∫ V d x = − 4.8 x 2 2 + 36.8 〈 x − 2.5 〉 1 + 1.6 〈 x − 5 〉 2 2 = − 2.4 x 2 + 36 (b) To determine The maximum normal stress with 2% accuracy.

7th Edition

ISBN: 9780100257061

Author: BEER

Publisher: YUZU

See similar textbooks

Concept explainers

Bending Moment

In general, we can define the bending moment as the reaction induced when a certain amount of load or force is applied to an element which makes it bend.

Videos

Question

Chapter 5.4, Problem 125P

(a)

To determine

Tabulate the shear, bending moment, and maximum normal stress using the singularity function.

(b)

To determine

The maximum normal stress with 2% accuracy.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 5.4, Problem 124P

Chapter 5.5, Problem 126P

Students have asked these similar questions

Please can you help with ten attatched question?

An AISI 1018 steel ball with 1.100-in diameter is used as a roller between a flat plate made from 2024 T3 aluminum and a flat table surface made from ASTM No. 30 gray cast iron. Determine the maximum amount of weight that can be stacked on the aluminum plate without exceeding a maximum shear stress of 19.00 kpsi in any of the three pieces. Assume the figure given below, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. 1.0 0.8 Ratio of stress to Pmax 0.4 90 0.6 στ Tmax 0.2 0.5a a 1.5a 2a 2.5a За Distance from contact surface The maximum amount of weight that can be stacked on the aluminum plate is lbf.

A carbon steel ball with 27.00-mm diameter is pressed together with an aluminum ball with a 36.00-mm diameter by a force of 11.00 N. Determine the maximum shear stress and the depth at which it will occur for the aluminum ball. Assume the figure given below, which is based on a typical Poisson's ratio of 0.3, is applicable to estimate the depth at which the maximum shear stress occurs for these materials. 1.0 0.8 Ratio of stress to Pma 9 0.6 στ 24 0.4 Tmax 0.2 0 0.5a a 1.5a Z 2a 2.5a За Distance from contact surface The maximum shear stress is determined to be MPa. The depth in the aluminum ball at which the maximum shear stress will occur is determined to be [ mm.

Chapter 5 Solutions

EBK MECHANICS OF MATERIALS

Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.1 through 5.6 For the beam and loading shown,...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.7 and 5.8 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...Ch. 5.1 - 5.9 and 5.10 Draw the shear and bending-moment...

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.

Tabulate the shear, bending moment, and maximum normal stress using the singularity function.

Solution Summary: The author analyzes the shear, bending moment, and maximum normal stress using the singularity function.

Concept explainers

Videos

Tabulate the shear, bending moment, and maximum normal stress using the singularity function.

The maximum normal stress with 2% accuracy.

Want to see the full answer?

Chapter 5 Solutions