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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,...
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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.
 Spring '09
 ZHU

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