bending stress

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Structures and Bending

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Digrams

Author: Iano, Joseph.Location: Sidney Sussex College LibraryClassmark: BXO IJ Ian

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Digrams

500 kN 500 kN

A

1

D

C

B2

3

4200 kN 200 kN 200 kN 300 kN

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Digrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Digrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Beams subject to lateral load carry loads by bending. Structures that carry loads in bending are generally less structurally effi cient than funicular structures, but they are extremely useful for variable loads, and are ubiquitous throughout structural design and architecture. The most effi cient beams follow the moment diagram of the internal forces.

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

External forces vs. internal forces

RRbRa

4.9 kN 4.9 kN4.9 kN

RbRa

4.9 kN 4.9 kN4.9 kN

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Axial stress vs. bending stress

RbRa

4.9 kN 4.9 kN4.9 kN

RbRa

4.9 kN 4.9 kN4.9 kN

RbRa

4.9 kN 4.9 kN4.9 kN

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

from Macdonald, Structure and Architecture p. 136

Bending

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Castellated Beams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Shear Forces

Forces in a structure that cause two parts of a member to slide past one another

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Shear Forces and Bending Forces

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Shear and Moment Diagrams

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Bending, shear and moment: further reading

Understanding Structures, Derek Seward Chapter 7 p 120-133

Structures for Architects, Bryan J.B. Gauld Chapter 3 p 30-49

The Structural Basis of Architecture, Sandaker and Eggen Chapter 4 p 80-92

Shaping Structures:Statics, Zalewski and Allen Chapter 9 p 218-219

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Calculating bending moments

from Zalewski and Allen, Shaping Structures

The bending moment at any vertical section through a structural element is the summation of moments about a point on the axis of the element at that section of all the forces and reactions that act to the left of it. M = R

LxL - P

1x1 - P

2x2

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Calculating shear and moment

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Positive & negative moments

from Schodek, Structures

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

from Schodek, Structures

Moment diagrams and defl ected shape

Moment diagram ‘points’ in direction of defl ection

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

from Schodek, Structures

Moment diagrams and defl ected shape

Moment diagram drawn on tension side of beam

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Load, shear and bending moment examples: point loads

Drawing shear diagrams • determine beam reactions • ‘walk’ pencil along the beam • pencil moves up and down with the loads • diagram must ‘close at each end of the beam

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Load, shear and bending moment examples: distributed loads

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Shear Forces Bending StressesMoment Diagrams

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Stresses Shear Bending StressesBending Moment

Sizing Members: Bending Stress

σ = Μy / I

The stress in the extreme fi bers of a beam subjected to bending.

from Macdonald, Structure and Architecture p. 136

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Stresses Shear Bending StressesBending Moment

Sizing Members: Bending Stress example

The maximum bending moment in a laminated timber beam is 7 kNm. The allowable stress for the beam is 10 MPa in tension or compression. What is the cross-section of the beam if we don’t want it to be more than 30 cm deep?

Is this a good shape? Why or Why not? What can we do for greater structural effi ciency?

Fundamental Principles of Structural DesignDepartment of Architecture

Recap Bending Stresses Shear Bending StressesBending Moment

Sizing Members: Defl ections