Taken from the web

Taken from TAM251 Lecture Notes - L7S3

**Reference pages have a broken link image here**

Taken from the web

, as well as a bending moment.

The distribution of normal and shearing stresses satisfies:**Reference pages have a broken link image here**

Guessed based on context clues and lecture slides

Taken from TAM251 Lecture Notes - L7S6-7

Average shear stress is given by

Shear stress at a specific point is given by

- \( V \) : shear force
- \( Q \) : First area moment of inertia of cut section ( \( Q = \Sigma yA \) )
- \( I \) : Second area moment of inertia of whole section
- \( t \) : beam thickness

****Expandable Derivation****

Taken from the web

**(A)** An element of width \( dx \) in a bending beam has a FBD of the bending moment stress distribution.

**(B)** An element distance \( y \) away from the neutral axis has a FBD of the bending moment stress distribution For this element to be in equilibrium, \( \tau_{xy} \) must be present.

**(C)** Simplified FBD. The width of this element is \( t(y) \).

****End Derivation****

Taken from TAM251 Lecture Notes - L7S8

or

****Expandable Derivation****

****End Derivation****

Maximum shear stress occurs at the Neutral axis

**Reference pages have a broken link image here**

Taken from TAM251 Lecture Notes - L7S10

The neutral axis of an I-beam is the center. To find the I, use the parallel axis theorem. When determining the stress distribution, break the beam up into sub-sections of constant thickness for easier calculations. The stress distribution is a discontinuous parabola.

BSM: section feels a little light as is, could benefit from a few extra figures, equations, and/or commentary on how to do shear flow calculations.

Taken from the web

Built-up beams are beams that have been put together with either an adhesive (glue, epoxy, etc) or fasteners (nails, bolts, etc). Calculating **Shear flow** allows for determining how much adhesive or how often a fastener is needed.

****Expandable Derivation****

****End Derivation****

Taken from TAM251 Lecture Notes - L7S13

Adhesives supply resistance along the length of the contacting parts. Determine the minimum shear strength at these contacting/weak points using the shear stress equation.

Fasteners supply resistance at fixed intervals. Use the shear flow formula to analyze the beam.

**Reference pages have a broken link image here x2**

**Reference pages have a broken link image here**

**Reference pages have a broken link image here**