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## Mechanics of Deformable Solids

by: Princess Rolfson

75

0

5

# Mechanics of Deformable Solids ME 222

Marketplace > Michigan State University > Mechanical Engineering > ME 222 > Mechanics of Deformable Solids
Princess Rolfson
MSU
GPA 3.57

Dahsin Liu

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COURSE
PROF.
Dahsin Liu
TYPE
Class Notes
PAGES
5
WORDS
KARMA
25 ?

## Popular in Mechanical Engineering

This 5 page Class Notes was uploaded by Princess Rolfson on Saturday September 19, 2015. The Class Notes belongs to ME 222 at Michigan State University taught by Dahsin Liu in Fall. Since its upload, it has received 75 views. For similar materials see /class/207530/me-222-michigan-state-university in Mechanical Engineering at Michigan State University.

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Date Created: 09/19/15
IME 222 Mechanics of Deformable Solids Lecture 17 Shearing Stress in Beams 0 Longitudinal Shear on a Beam Element of Arbitrary Shape Department of Mechanical Engineering A Loos 17391 ME 222 Mechanics of Deformable Solids Longitudinal Shear on a Beam Element of Arbitrary Shape Y We have examined the distribution of the vertical components rxy on a transverse section of a beam We now Wish to consider the horizontal components In of the stresses Extend the procedures developed in Section 62 for the determination of shear per unit length q for shear on any horizontal or vertical surface Department of Mechanical Engineering A Loos 17392 ME 222 Mechanics of Deformable Solids Longitudinal Shear on a Beam Element of Arbitrary Shape 0 Consider prismatic beam With an lPI r 1 y element de ned by the curved surface W A cwca A C l3 2 o The forces exerted on the element x F I Vertical shearing forces VC and VD I Horizontal normal forces chA and GDdA I Possible load wa I AH resultant of the internal NA longitudinal shearing forces exerted on the curved surface 11 ZFXZOZAHIO39C039D0 A t T J 0 Except for the diffelqences in C 390 integration areas this is the same result obtained before which led to Q Ax 1 17 3 AHngx Department of Mechanical Engineering A Loos IME 222 Mechanics of Deformable Solids Example 604 075 1n gtl r S 1n gt 075111 SOLUTION 075 in 0 Determine the shear force per unit length along each edge of the upper plank 0 Based on the spacing between nails determine the shear force in each nail A square box beam is constructed from four planks as shown Knowing that the spacing between nails is 15 in and the beam is subjected to a vertical shear of magnitude V 600 1b determine the shearing force in each nail Department of Mechanical Engineering A Loos 17394 IME 222 Mechanics of Deformable Solids Example 604 13in SOLUTION I q A l 075 in r0111 9 I 0 Determine the shear force per unit g T length along each edge of the upper I T plank 39 i 39 Q 6001b422in3 L 92 3g l I 2742in4 39 in L 45 in 4gti q f I E Z 111 For the upper plank edge force per unit length Q A39y O75in3inl875in 4 22in3 0 Based on the spacing between nails determine the shear force in each nail For the overall beam crosssectlon 1b 1 4 1 4 Ff 4615 175in I E451n E31n 1n 2742in4 F 8081b Department of Mechanical Engineering A Loos 17395

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