(a) Explanation Assumption: Apply the sign convention for calculating the equations of equilibrium as below: For the horizontal forces equilibrium condition, take the force acting towards right side as positive ( → + ) and the force acting towards left side as negative ( ← − ) . For the vertical forces equilibrium condition, take the upward force as positive ( ↑ + ) and downward force as negative ( ↓ − ) . For moment equilibrium condition, take the clockwise moment as negative and counter clockwise moment as positive. Apply the following sign convention for calculating the bending moment at any section x-x while approaching from the left hand side. Take clockwise moment as positive and anticlockwise moment as negative Apply the following sign convention for calculating the shear force at any section x-x while approaching from the left hand side. Take downward force as negative and upward force as positive. Calculation: Show the free-body diagram of the beam as in Figure 1. Find the magnitude of the upward reaction by resolving the vertical component of forces. ∑ F y = 0 − ( 8 × 1.5 ) − ( 8 × 1.5 ) + ( w g × 6 ) = 0 w g = 4 kN/m Consider a section x from left end of the beam. Section AC ( 0 ≤ x < 1.5 m ) : Show the free body diagram of the section as in Figure 2. Find the shear force at the section by resolving the vertical component of forces. ∑ F y = 0 4 × x − 8 × x − V + 0 V = − 4 x (1) Find the bending moment at the section by taking moment about the section. ∑ M x = 0 M − 4 × x × x 2 + 8 × x × x 2 = 0 M − 2 x 2 + 4 x 2 = 0 M = − 2 x 2 (2) When x = 0 ; Substitute 0 for x in Equation (1); V = − 4 ( 0 ) = 0 Substitute 0 for x in Equation (2). M = − 2 ( 0 ) 2 = 0 When x = 1.5 m ; Substitute 1.5 m for x Equation (1); V = − 4 ( 1.5 ) = − 6 kN Substitute 1.5 m for x in Equation (2). M = − 2 ( 1.5 ) 2 = − 4.5 kN-m Section CD ( 1.5 m < x < 4.5 m ) : Show the free body diagram of the section as in Figure 3. Find the shear force at the section by resolving the vertical component of forces. ∑ F y = 0 4 × x − 8 × 1.5 − V = 0 4 x − 12 − V = 0 V = 4 x − 12 (3) Find the bending moment at the section by taking moment about the section. ∑ M x = 0 − 4 × x × x 2 + 8 × 1.5 × ( x − 1.5 2 ) + M = 0 − 2 x 2 + 12 ( x − 0.75 ) + M = 0 M = 2 x 2 − 12 ( x − 0.75 ) (4) When x = 1.5 m ; Substitute 1.5 m for x in Equation (3). V = 4 ( 1 (b) To determine Find the maximum absolute values of the shear force and bending moment.

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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 7.2, Problem 7.48P

(a)

To determine

Draw the shear force and bending moment diagrams.

(b)

To determine

Find the maximum absolute values of the shear force and bending moment.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 7.2, Problem 7.47P

Chapter 7.2, Problem 7.49P

Students have asked these similar questions

A crude oil of specific gravity0.85 flows upward at a volumetric rate of flow of 70litres per second through a vertical venturimeter,with an inlet diameter of 250 mm and a throat diameter of 150mm. The coefficient of discharge of venturimeter is 0.96. The vertical differences betwecen the pressure toppings is 350mm. i) Draw a well labeled diagram to represent the above in formation i) If the two pressure gauges are connected at the tapings such that they are positioned at the levels of their corresponding tapping points, determine the difference of readings in N/CM² of the two pressure gauges ii) If a mercury differential manometer is connected in place of pressure gauges, to the tappings such that the connecting tube up to mercury are filled with oil determine the difference in the level of mercury column.

Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You

Can you solve it analytically using laplace transforms and with Matlab code as well please. Thank You.

Chapter 7 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 7.1 - Prob. 7.1P Ch. 7.1 - Prob. 7.2P Ch. 7.1 - 7.3 Determine the internal forces at point J when...Ch. 7.1 - Prob. 7.4P Ch. 7.1 - Prob. 7.5P Ch. 7.1 - Prob. 7.6P Ch. 7.1 - An archer aiming at a target is pulling with a...Ch. 7.1 - For the bow of Prob. 7.7, determine the magnitude...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - A semicircular rod is loaded as shown. Determine...

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.