R 72 362 18 2 1 a 0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview:   THESE 3 SCHEMATICS REPRESENT STRUCTURES SUBJECTED TO COMBINED LOADINGS •  METHOD OF SOLUTION INVOLVES SUPERPOSITION PRINCIPLE ☞  TRUE IF… STRESSES AND STRAINS ARE PROPORTIONAL TO THE APPLIED LOAD (i.e., the material obey’s Hooke’s law) ☞AND ALSO IF…Stresses and strains due to one load must not be affected by presence of other loads. 4/3/13 M. Mello/Georgia Tech Aerospace 20 METHOD OF ANALYSIS (ILLUSTRATION BY EXAMPLE) EXAMPLE 1: CanNlever beam subjected to a torque T and bending load P applied at the free end of the bar STEP 1: Select points in structure where stresses and strains are to be determined ☞ in this case point A (on top) and point B (on side) are selected which are part of the same cross secNon ☞ we will also discuss points C and D in due course 4/3/13 M. Mello/Georgia Tech Aerospace 21 CanJlever beam subjected to combined torsion and bending (cont.) Stress resultants at a cross secNon STEP 2: Determine the stress resultants at the cross secNon i.e., an axial force, a twisNng moment, a bending moment, and/or a shear force •  In this case the stress resultants acNng at the cross secNon are: ☞ twisNng moment T (given) Calculated by applying rudimentary staNcs but ☞ bending moment M=Pb IntuiNvely obvious and so no analysis required In this case ☞ shear force V=P 4/3/13 M. Mello/Georgia Tech Aerospace 22 CanJlever beam subjected to combined torsion and bending (cont.) A ⌧1 B T ⌧1 Shear stress due to twisNng torque T STEP 3: Calculate the normal and shear stress at the selected points ☞ Consider the effect of each stress resultant, one at a Nme ☞ step 3a: stress due to the twisNng moment T: Tr 2T ⇡r4 ⌧1 = where: I p = and so, ⌧1 = 3 Ip ⇡r 2 4/3/13 M. Mello/Georgia Tech Aerospace 23 CanJlever beam subjected to combined torsion and bending (cont.) P y A Use right hand rule: fingers Curl in direcNon of bending, thumb points in direcNon of A M < 0 M= - Pb B M x Bending stress at point A due to bending M STEP 3 (conNnued): Calculate the normal and shear stress at the selected points ☞ step 3b: stress due to the bending moment M: A 4/3/13 = My ⇡r4 where: I = and so,...
View Full Document

This note was uploaded on 09/19/2013 for the course CEE 3001 taught by Professor Zhu during the Spring '09 term at Georgia Institute of Technology.

Ask a homework question - tutors are online