facts Flashcards
reactions for pin
2
reactions for roller
1
reactions for fixed end
3
Point moments will show up in ________ but not in _______ diagrams.
bending moment, shear force
What is the sign convention of sagging?
positive
What is the sign convention of hogging?
Negative
A beam is subjected to sagging. Where is the compression and tension?
tension on bottom of curve, compression on top of curve
What is the bending moment at an internal support e.g. pin?
0
Where will the point of zero shear be?
at the maximum bending moment
How do point loads and moments represent themselves in shear force and bending diagrams?
PL: vertical shift in SF, cause change in BM
PM: vertical shift in BM, not present in SF
What 3 things should be checked for after completing a SF and BM diagram?
reference co-ordinate system, value labels, dimensions
What should always be the first step in approaching a problem?
Verifying determinancy
Describe the changes in fibre length to the sections below when a beam is subjected to a bending moment
a. neutral axis
b. tension fibres
c. compressive fibres
a. no change
b. elongate
c. shorten
What are 4 major assumptions of truss analysis?
The members only connect at the nodes
Members have negligible weight
The pins (at the nodes) are frictionless
The loads are only present at the nodes
What is the sign convention for tensile stress/ strains vs compressive stresses/ strains?
tensile = +ve, compressive = -ve
What two methods would be used to locate POCs?
similar triangles or polynomials/ polynomial solving
The area under the SF diagram is equal to ______. Hence it can also be said that the BM is the result of __________ the SF diagram.
the change in bending moment, integrating
If the SF diagram is first order, what order will the BM be?
second
The SF diagram is linear, what will the BM diagram look like?
third order curve
How should internal support calculations be approached?
deduce as much information as possible about reactions and then split the element into two parts along the pin
List the 3 most common types of external supports
roller, pin, fixed end
list the 2 most common types of internal support
roller, pin
what order line does a UDL produce?
2nd order (linear)
what order line does a point load produce?
1st order, parallel lines with vertical shifts
How do you locate a POC?
Take moments about the point using an unknown variable x from the distance and let this moment = 0
How do you find the location of a point of zero shear?
equate forces either side of point to zero and solve for the unknown distance (usually occurs in UDLs)
What units are moment of inertia in?
mm^4 or m^4
If in doubt about units for length, force or large prefixes: _____________________.
Revert to SI units e.g. metres, newtons and other non-prefixed terms
BE CAREFUL with squared units (e.g. square the power of 10 you are changing by too)
How many values of z are there for a section?
2 (assuming the top and bottom parts are different - divided at the neutral axis)
Should you choose the minimum and or maximum z value in subsequent calculations stress/ moment capacity calculations?
minimum
To include a point moment in calculations, does it need to be multiplied by the distance from the point being analysed?
No
When drawing Bending moment diagrams of 3rd order (and upwards), how should the concavity be determined?
Positively if sagging and negatively for hogging as a starting point
also consider if gradient of shear force/ bending moment should be 0 or not
Tensile stresses and strains are _____ since they cause elongation. Likewise _______________ are ___________.
positive, compressive stresses and strains, negatige since they shorten
How many members (maximum) can be cut in the method of sections?
3
What are the 4 different types of failure under tension?
Brittle (direct split), Shear (diagonal split), ductile cup and cone (extruded section of smaller diameter stretched) and complete ductile (pulled into two “triangle” shaped 3D sections
A greater moment if inertia or second moment of area along one axis than the other indicates _________.
The section will be more resistant to bending along that axis
