Lecture 5 - Method of Sections -
Beams
Type Lecture
Date @October 5, 2023
BEAM LOADING DIAGRAMS.pdf ARC281 Lecture 05 Method of
Materials Sections - Beams.pptx
Reviewed
Beams/Bending Elements - Shear, Bending Moment
MoS for solving beams
Shear Force and Bending Moment Diagrams
Typical Force Diagrams
Bonus Examples
Last Week:
We want things to stay still
If there are still, they are in equilibrium
If they are in equilibrium, they aren’t moving in any of the 6 degrees of freedom
We often break the problem into a 2D problem, with 3 degrees of freedom
Which means we want SFx=0, SFy=0 and SMz=0
We can use these equations to solve for the Reactions of the system that keep it in
Static Equilibrium!
We can cut sections of a truss to determine what internal axial force must keep
them in place
Lecture 5 - Method of Sections - Beams 1
, But what happens inside a beam?
Remember Bending?
A force that acts to bend a component putting one side of the part in tension and the
opposite side in compression
It is the same as tension and compression couples.
Internal Forces
If the whole is static, and part of it is static.
We can pretend cut it up to look at what it takes to part that pretend part be static, or in
Equilibrium
Lecture 5 - Method of Sections - Beams 2
, Equal and opposite forces can be written as a
moment
The Axial Forces in the top chord, bottom chord and web element of a truss, can be
written and a Shear force and a Bending Moment
Method of Section - Beam 01
Simple Span w/ Point Load at Mid-Point
Reactions:
Lecture 5 - Method of Sections - Beams 3
Beams
Type Lecture
Date @October 5, 2023
BEAM LOADING DIAGRAMS.pdf ARC281 Lecture 05 Method of
Materials Sections - Beams.pptx
Reviewed
Beams/Bending Elements - Shear, Bending Moment
MoS for solving beams
Shear Force and Bending Moment Diagrams
Typical Force Diagrams
Bonus Examples
Last Week:
We want things to stay still
If there are still, they are in equilibrium
If they are in equilibrium, they aren’t moving in any of the 6 degrees of freedom
We often break the problem into a 2D problem, with 3 degrees of freedom
Which means we want SFx=0, SFy=0 and SMz=0
We can use these equations to solve for the Reactions of the system that keep it in
Static Equilibrium!
We can cut sections of a truss to determine what internal axial force must keep
them in place
Lecture 5 - Method of Sections - Beams 1
, But what happens inside a beam?
Remember Bending?
A force that acts to bend a component putting one side of the part in tension and the
opposite side in compression
It is the same as tension and compression couples.
Internal Forces
If the whole is static, and part of it is static.
We can pretend cut it up to look at what it takes to part that pretend part be static, or in
Equilibrium
Lecture 5 - Method of Sections - Beams 2
, Equal and opposite forces can be written as a
moment
The Axial Forces in the top chord, bottom chord and web element of a truss, can be
written and a Shear force and a Bending Moment
Method of Section - Beam 01
Simple Span w/ Point Load at Mid-Point
Reactions:
Lecture 5 - Method of Sections - Beams 3
