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LECTURE+33+COE-3001-A

# Loads 4313 m mellogeorgia tech aerospace

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Unformatted text preview: I 4 ( P b) r i.e., A = ⇡ r4 /4 A = Mr ⇡ r 4 /4 M. Mello/Georgia Tech Aerospace A = 4P b ⇡r3 24 CanJlever beam subjected to combined torsion and bending (cont.) A P B V = P V = P ⌧2 Shear stress at B due to twisNng shear force V STEP 3 (conNnued): Calculate the normal and shear stress at the selected points A ☞ step 3c: Determine the shear stress due to the shear force V: ⌧2 = 4V 3A ⌧2 = 4V 3⇡ r2 B Recall: For bending of a cylindrical shap the shear stress formula only applies along the neutral axis (where the shear stress happens to be maximum) 4/3/13 M. Mello/Georgia Tech Aerospace 25 CanJlever beam subjected to combined torsion and bending (cont.) STEP 4: Combine the individual stresses to obtain the resultant stresses: ☞ Note that we will only consider plane stress problems ⌧1 B T ⌧1 Shear stress due torque T 4/3/13 A A A + A B M + B V = P Bending stress at point A due to bending M M. Mello/Georgia Tech Aerospace ⌧2 shear stress at point B due to shear force V 26 CanJlever beam subjected to combined torsion and bending (cont.) STEP 4: Combine the individual stresses to obtain the resultant stresses: ☞ Obtain the stresses acNng a stress element at the point ☞  The enNre problem is then reduced to a Mohr’s circle analysis of the resultant stresses! Stress element at point A ☞ Stress element at point B ☞ 4/3/13 M. Mello/Georgia Tech Aerospace 27 CanJlever beam subjected to combined torsion and bending (cont.) STEP 5: DETERMINE THE PRINCIPAL STRESES AND MAXIMUM SHEAR STRESS AT THE SELECTED POINTS ☞ APPLY STRESS- TRANSFORMATION EQUATIONS ☞ OR USE MOHR’S CIRCLE ☞ IF REQUIRED, CONSIDER OTHER INCLINED PLANES STEP 6: USE HOOKE’S LAW TO OBTAIN STRAINS AT THESE POINTS 4/3/13 M. Mello/Georgia Tech Aerospace 28 CanJlever beam subjected to combined torsion and bending (cont.) STEP 7: SELECT ADDITONAL POINTS AND REPEAT THE PROCESS. ☞ IF THE OBJECTIVE IS TO DETERMINE THE LARGEST STRESSES… ☞ THEN, CRITICAL POINTS MAY BE SELECTED AT CROSS SECTIONS WHERE THE STRESS RESULTANTS HAVE THEIR LARGEST VALUES ☞ LIKE POINTS C AND D AT THE SUPPORT WHERE THE BENDING MOMENT IS MAXIMUM 4/3/13 M. Mello/Georgia Tech Aerospace 29...
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