Solid Mechanics: Shear Force and Bending Moment

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

For a simply supported beam subjected to a uniformly distributed load (UDL), where does the maximum bending moment typically occur?

  • At a quarter of the span from either support
  • At the point of maximum shear force
  • At one of the supports
  • At the mid-span of the beam (correct)

What type of support primarily resists both vertical and horizontal forces, but does not resist moment?

  • Roller Support
  • Fixed Support
  • Simple Support
  • Hinge Support (correct)

Under what loading condition is a beam considered to be in a state of 'pure bending'?

  • When the shear force is maximum along the beam.
  • When the bending moment is zero along the beam.
  • When the bending moment varies linearly along the beam.
  • When the shear force is zero along the section of the beam. (correct)

What is a primary characteristic of a cantilever beam?

<p>It is fixed at one end and free at the other. (B)</p> Signup and view all the answers

What is the definition of a Uniformly Varying Load (UVL)?

<p>A load that increases or decreases linearly along the length of a beam. (D)</p> Signup and view all the answers

What does a positive shear force in a beam signify, based on standard sign conventions?

<p>The resultant of forces to the left of the section is upward. (C)</p> Signup and view all the answers

Which type of bending moment causes 'sagging' in a beam?

<p>A positive bending moment. (B)</p> Signup and view all the answers

What is a key characteristic of a 'fixed' beam?

<p>It has both translational and rotational restraint at the supports. (A)</p> Signup and view all the answers

How Shear Force (SF) and Bending Moment (BM) vary with respect to beam length?

<p>SF and BM vary depending on the type and position of the loads. (C)</p> Signup and view all the answers

Consider a simply supported beam with a single concentrated load at its mid-span. What is the shape of its bending moment diagram?

<p>Triangular. (C)</p> Signup and view all the answers

A beam is subjected to a uniformly distributed load (UDL) along its entire length. Which statement accurately describes the shear force diagram?

<p>It varies linearly from one support to the other. (C)</p> Signup and view all the answers

What is the bending moment at the free end of a cantilever beam?

<p>Zero (A)</p> Signup and view all the answers

A continuous beam is best described as which of the following?

<p>A beam extending over more than two supports. (D)</p> Signup and view all the answers

For a uniformly varying load (UVL) on a beam, how does the shear force typically vary?

<p>Quadratically (C)</p> Signup and view all the answers

What is the term for the bending moment that causes a beam to curve downwards?

<p>Hogging (B)</p> Signup and view all the answers

If a simply supported beam has a point load (W) at a distance 'a' from support A and 'b' from support B, what is the reaction at support A?

<p>Wb/L (B)</p> Signup and view all the answers

A beam is supported in such a way that it extends beyond one or both of its supports. What type of beam is this?

<p>Overhanging beam (C)</p> Signup and view all the answers

In shear force diagrams, what does a sudden vertical jump indicate?

<p>A point load (B)</p> Signup and view all the answers

How is the bending moment related to the shear force?

<p>The shear force is the derivative of the bending moment. (A)</p> Signup and view all the answers

For a simply supported beam with a uniformly distributed load (w) over its entire length (L), what is the maximum bending moment?

<p>$wL^2/8$ (D)</p> Signup and view all the answers

A bending moment diagram is drawn for a simply supported beam under a central point load. What does the slope of the bending moment diagram represent?

<p>Shear force (B)</p> Signup and view all the answers

Which of the following is true for a 'roller' support?

<p>It resists only vertical forces. (D)</p> Signup and view all the answers

What is the effect of an overhanging section on the bending moment diagram of a beam?

<p>It can introduce negative bending moments. (B)</p> Signup and view all the answers

A beam is subjected to a combination of point loads and a uniformly distributed load (UDL). Which of the following statements is generally true?

<p>The shear force diagram will consist of both straight and curved lines. (D)</p> Signup and view all the answers

At which point is the bending moment generally considered to be zero in a simply supported beam?

<p>Supports (C)</p> Signup and view all the answers

For a uniformly varying load (UVL) increasing from zero at one end to maximum at the other end of a simply supported beam, where would you expect the maximum bending moment to occur?

<p>Somewhere between the mid-span and the end with maximum load (C)</p> Signup and view all the answers

What is a 'point of contraflexure' in a bending moment diagram?

<p>The point where bending moment changes sign. (D)</p> Signup and view all the answers

A cantilever beam is subjected to a point load at its free end. How does the bending moment vary along the length of the beam?

<p>It increases linearly from the free end to the fixed end (A)</p> Signup and view all the answers

What is the primary purpose of drawing shear force and bending moment diagrams?

<p>To visually represent the internal forces and moments in a beam under load. (A)</p> Signup and view all the answers

For a beam with only uniformly distributed load, at which point shear force will be zero?

<p>Mid point of the beam. (D)</p> Signup and view all the answers

A simply supported beam of length L carries a concentrated load W at the center. What is the bending moment at the center?

<p>WL/4 (A)</p> Signup and view all the answers

What type of beam is supported on more than two supports?

<p>Continous beam (D)</p> Signup and view all the answers

What indicates hogging in the bending moment diagram?

<p>Negative Bending Moment (A)</p> Signup and view all the answers

For a simply supported beam with a uniformly distributed load, the shear force diagram is?

<p>Triangle (A)</p> Signup and view all the answers

Shear force is defined as?

<p>Sum of all vertical forces (B)</p> Signup and view all the answers

Which of these is true about bending moment at a hinge?

<p>Always Zero (B)</p> Signup and view all the answers

Choose the correct formula for the relation betwen maximum bending moment (M), the shear force (V), and distributed load (w).

<p>$w = d^2M/dx^2$ (C)</p> Signup and view all the answers

Identify the correct unit for Bending Moment.

<p>N-m (A)</p> Signup and view all the answers

How does the Uniformly Varying Load (UVL) impact the shear force in a beam?

<p>The Shear force varies parabolically. (C)</p> Signup and view all the answers

Flashcards

SF and BM Diagrams

Diagrams showing the variation of Shear Force (SF) and Bending Moment (BM) along the length of a beam.

Cantilever Beam

A beam fixed at one end and free at the other.

Simply Supported Beam

A beam supported at both ends.

Overhanging Beam

A beam extending beyond one or both of its supports.

Signup and view all the flashcards

Continuous Beam

A beam supported by multiple supports along its length.

Signup and view all the flashcards

Fixed Beam

A beam with both ends rigidly fixed or restrained.

Signup and view all the flashcards

Point Load

A concentrated force acting at a single point on the beam.

Signup and view all the flashcards

Uniformly Distributed Load (UDL)

A load distributed evenly over a length of the beam.

Signup and view all the flashcards

Uniformly Varying Load (UVL)

A load that varies linearly along the length of the beam.

Signup and view all the flashcards

Positive Shear Force

Shear force is considered positive if total forces to the left of the section is upward.

Signup and view all the flashcards

Sagging

Bending moment causing concavity upwards.

Signup and view all the flashcards

Hogging

Bending moment causing concavity downwards.

Signup and view all the flashcards

Pure Bending

A condition where shear forces are zero and bending moment is constant.

Signup and view all the flashcards

Study Notes

  • MEC201 Solid Mechanics Unit 4 focuses on Shear Force and Bending Moment.
  • Diagrams help understand the variation of Shear Force (SF) and Bending Moment (BM) along the length of a beam.

Types of Beams

  • Cantilever: Fixed at one end and free at the other.
  • Simply Supported: Supported at both ends.
  • Overhanging: Extends beyond its supports on one or both ends.
  • Fixed: Restrained against rotation and displacement at both ends.
  • Continuous: Supported at more than two points.

Types of Loads

  • Point Load: A concentrated load acting at a single point, measured in Newtons (N).
  • Uniformly Distributed Load (UDL): A load distributed evenly across a length, measured in N/m.
  • Uniformly Varying Load (UVL): A load that varies linearly along the length.

Sign Conventions for Shear Force

  • Shear force is positive if the resultant force to the left of the section is upward.

Sign Conventions for Bending Moment

  • Sagging: Positive bending moment that tends to bend the beam upwards.
  • Hogging: Negative bending moment that tends to bend the beam downwards.
  • Clockwise moment on the left-hand side is positive.
  • Anticlockwise moment on the left-hand side is negative.

Pure Bending

  • Shear forces should be zero on any cross-section perpendicular to the longitudinal axis of the beam
  • The beam experiences a constant bending moment

Shear Force and Bending Moment Diagrams for a Cantilever Beam with Point Loads

  • Shows an applied force W at point B
  • Shear Force Diagram (SFD) is positive and constant along the beam.
  • Bending Moment Diagram (BMD) starts at zero at the free end and increases linearly to -WL at the fixed end.
  • Example: 1600N at A, 300N at B, 500N at C, and 80N at D.

Shear Force and Bending Moment Diagrams for a Cantilever Beam with Uniformly Distributed Load (UDL)

  • UDL is measured as w N/m along length L
  • The Shear Force Diagram (SFD) increases linearly from zero at the free end to wL at the fixed end
  • The Bending Moment Diagram (BMD) is parabolic, increasing from zero at the free end to -wL²/2 at the fixed end

Shear Force and Bending Moment Diagrams for a Cantilever Beam with Uniformly Varying Load (UVL)

  • Load varies from zero to a maximum value (w) along the length (L).
  • Max SF is = wL /2.
  • Max BM = wL^2 / 6.

Simply Supported Beam Analysis:

  • Determine Reaction Forces: Start by finding the reaction forces at the supports.
  • Moment Calculation: Calculate the bending moment at specific points.
  • A simply supported beam is subjected to loads W1 and W2.

Alternative Method to Find Reaction Forces:

  • The reaction force at A (RA) = (W x b) / (a + b)
  • The reaction force at B (RB) = (W x a) / (a + b), where a and b are the distances from the load to the supports.
  • Total load = wxl, where w is the load per unit length

Key Moments at Point A:

  • -W x a + RB x l = 0
  • RB = (W * a) / l
  • RA = (W * b) / l

Determining the location of zero shear force:

  • Set up an equation and solve for x to determine to point of 0 shear force where x = sqrt (l^2/3)

Overhanging beam

  • Bending moment is zero at points C, L and E

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Related Documents

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser