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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Structures and Bending
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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
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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
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Digrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Digrams
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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.
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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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
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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
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
from Macdonald, Structure and Architecture p. 136
Bending
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Castellated Beams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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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
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Shear Forces and Bending Forces
from Schodek, Structures
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Shear and Moment Diagrams
from Schodek, Structures
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
from Schodek, Structures
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
from Schodek, Structures
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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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
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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
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Calculating shear and moment
from Schodek, Structures
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Positive & negative moments
from Schodek, Structures
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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
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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
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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
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
Load, shear and bending moment examples: distributed loads
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Shear Forces Bending StressesMoment Diagrams
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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
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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?
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Fundamental Principles of Structural DesignDepartment of Architecture
Recap Bending Stresses Shear Bending StressesBending Moment
Sizing Members: Defl ections