Shear and Bending Moment in Beams
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Questions and Answers

For Mmax, Q = ______

0

Peaks in a bending moment diagram frequently occur at concentrated loads or supports where the slope of the bending moment diagram is zero.

False (B)

What should be considered in order to determine the maximum bending moment?

All sections of the beam should be considered.

Define the point of contraflexure.

<p>Point of contraflexure is a point on the beam where the Bending Moment changes from sagging to hogging or hogging to sagging.</p> Signup and view all the answers

What is the bending moment at the point of contraflexure?

<p>ZERO</p> Signup and view all the answers

For the beam shown, the sum of moments (ΣΜ) at A is:

<p>80 Nm (C)</p> Signup and view all the answers

For the beam with UDL loading as shown, the bending moment at A due to the UDL is:

<p>w(x^2)/2 N/m (C)</p> Signup and view all the answers

For the propped cantilever shown, the bending moment at A due to the UDL is:

<p>40 kNm (D)</p> Signup and view all the answers

For the propped cantilever loaded as shown, the bending moment at A is:

<p>0 kNm (D)</p> Signup and view all the answers

Which of the following is true regarding the Point of Contraflexure?

<p>All of the above. (D)</p> Signup and view all the answers

Flashcards

Shear Force

Internal force acting tangent to a section of a beam.

Bending Moment

Internal moment that resists bending caused by external loads.

Calculate Shear Force

Shear force calculation at different points along the beam's length.

Shear Force Diagram (SFD)

Diagram representing how the shear force varies along the length of a beam.

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Calculate Bending Moment

Calculation of internal moments acting on different sections of the beam.

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Bending Moment Diagram (BMD)

Diagram showing the variation of bending moment along the beam's length.

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Point of Contraflexure

The point where bending moment changes sign (from sagging to hogging or vice versa).

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Point of Inflexion

A.k.a. Point of Contraflexure.

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Maximum Bending Moment Condition

The bending moment is a maximum where shear force is zero.

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Zero Shear Force Location

Locate where the shear force changes sign or crosses the x-axis.

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Calculate Max Bending Moment

Calculate the bending moment at the point of zero shear force.

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Combined Loading

Beam subjected to both distributed and concentrated loads.

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Uniformly Distributed Load (UDL)

Loads spread evenly over a length.

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Concentrated Load

A single force acting at a specific point.

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Free Body Diagram (FBD)

Diagram showing all external forces and moments acting on a body.

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Support Reactions

Forces exerted by supports on a beam.

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Simply Supported Beam

Beam supported at both ends.

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Cantilever Beam

Beam fixed at one end and free at the other.

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Sum of Moments (∑M)

Sum of moments about any point must be zero for static equilibrium.

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Sum of Vertical Forces (∑Fv)

Sum of vertical forces must be zero for static equilibrium.

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Fixed Support

A fixed support resists both force and moment.

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Pinned Support

A pinned support resists forces but allows rotation.

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Roller Support

A roller support resists force in one direction, allows movement in the perpendicular direction and allows rotation.

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Bending Moment UDL Formula

M = -w(x^2)/2

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Propped Cantilever

A cantilever beam supported at one end.

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Sagging

Bending from above (smiling).

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Hogging

Bending from below (frowning).

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Continuous Beam

A beam supported at multiple points.

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Bending Moment Peaks

Peaks in BMD diagrams occur most often.

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Beam sections

Consider all parts to determine MMax.

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Study Notes

  • Shear force and bending moment are studied in beams with combined loading.
  • Shear forces are calculated at different sections of a beam.
  • Shear force diagrams are constructed for beams with different types of loads.
  • Bending moment is understood in beams with combined loading.
  • Bending moment is calculated at different locations of a beam.
  • Bending moment diagrams are constructed for beams with different types of loads.
  • The point of contraflexure (or inflexion) is calculated.
  • The condition for maximum bending moment in beams is understood.
  • Bending moment is maximum where the shear force is zero.
  • The location of zero shear force is determined.
  • The maximum bending moment is calculated.

Condition for Maximum Bending Moment

  • For maximum bending moment, the shear force Q = 0.
  • Zero shear force corresponds to peak values of bending moment.
  • Peaks in the bending moment diagram frequently occur at concentrated loads or supports where the slope of the bending moment diagram is not zero.
  • All beam sections should be considered to determine the maximum bending moment.

Point of Contraflexure (or Point of Inflexion)

  • Point of contraflexure: point on the beam where the bending moment changes from sagging to hogging or vice versa.
  • Bending moment is zero at the point of contraflexure.
  • The point of contraflexure is also called the point of inflexion.

Combined Loading

  • The beam is subjected to uniformly distributed loads and concentrated loads.
  • Shear force and bending moments at salient points must be calculated.
  • This is necessary because the shear force and bending moment change at each concentrated load.

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Description

Study of shear force and bending moment in beams, including calculations and diagram construction under combined loading. Understand the point of contraflexure and the condition for maximum bending moment, where shear force is zero. Determine the location of zero shear force to calculate maximum bending moment.

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