y - axis (mm) R23 + 42 85 61 R21 89
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Using Pappus-Guldinus Theorems
Find the distance of the centroid from the X-axis
Step by step
Solved in 2 steps with 2 images
- ᴀ ꜱᴛᴇᴇʟ ꜱʜᴀꜰᴛ 2569 ᴍᴍ ʟᴏɴɢ ᴍᴜꜱᴛ ᴛʀᴀɴꜱᴍɪᴛ ᴀ ᴛᴏʀQᴜᴇ ᴏꜰ 34 ᴋɴ-ᴍ. ᴛʜᴇ ᴛᴏᴛᴀʟ ᴀɴɢʟᴇ ᴏꜰ ᴛᴡɪꜱᴛ ᴀɴᴅ ᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ꜱʜᴇᴀʀɪɴɢ ꜱᴛʀᴇꜱꜱ ᴍᴜꜱᴛ ɴᴏᴛ ᴇxᴄᴇᴇᴅ 3 ᴅᴇɢʀᴇᴇ ᴀɴᴅ 110 ᴍᴘᴀ ʀᴇꜱᴘᴇᴄᴛɪᴠᴇʟʏ. ꜰɪɴᴅ ᴛʜᴇ ᴅɪᴀᴍᴇᴛᴇʀ ᴏꜰ ᴛʜᴇ ꜱʜᴀꜰᴛ ᴛʜᴀᴛ ᴍᴇᴇᴛꜱ ᴛʜᴇʀᴇ ᴄᴏɴᴅɪᴛɪᴏɴꜱ. ᴄʜᴇᴄᴋ ʙᴀꜱᴇᴅ ᴏɴ ꜱᴛʀᴇɴɢᴛʜ ᴀɴᴅ ʀɪɢɪᴅɪᴛʏ. ᴜꜱᴇ ɢ = 78268 ᴍᴘᴀ. ᴜꜱᴇ ᴛᴡᴏ (2) ᴅᴇᴄɪᴍᴀʟ ᴘʟᴀᴄᴇꜱ.ɪɴ ᴀɴ ɪᴅᴇᴀʟ ʀᴇʜᴇᴀᴛ-ʀᴇɢᴇɴᴇʀᴀᴛɪᴠᴇ ᴄʏᴄʟᴇ, ꜱᴛᴇᴀᴍ ᴀᴛ 1 ᴋɢ/ꜱ ᴇɴᴛᴇʀꜱ ᴛʜᴇ ᴛᴜʀʙɪɴᴇ ᴀᴛ 8 ᴍᴘᴀ ᴀɴᴅ 400°ᴄ. ᴀꜰᴛᴇʀ ᴇxᴘᴀɴꜱɪᴏɴ ᴛᴏ 280°ᴄ, ᴛʜᴇ ꜱᴛᴇᴀᴍ ɪꜱ ᴡɪᴛʜᴅʀᴀᴡɴ ᴀɴᴅ ʀᴇʜᴇᴀᴛᴇᴅ ᴛᴏ 340°ᴄ. ᴇxᴛʀᴀᴄᴛɪᴏɴꜱ ꜰᴏʀ ᴏᴘᴇɴ-ꜰᴇᴇᴅᴡᴀᴛᴇʀ ʜᴇᴀᴛɪɴɢ ᴏᴄᴄᴜʀ ᴀᴛ 1.6 ᴍᴘᴀ ᴀɴᴅ 0.70 ᴍᴘᴀ ᴀɴᴅ ᴛʜᴇ ᴄᴏɴᴅᴇɴꜱᴇʀ ᴘʀᴇꜱꜱᴜʀᴇ ɪꜱ 0.005 ᴍᴘᴀ. ꜰᴏʀ ᴛʜᴇ ɪᴅᴇᴀʟ ᴄʏᴄʟᴇ:ᴀ. ᴅʀᴀᴡ ᴀ ꜱᴄʜᴇᴍᴀᴛɪᴄ ᴅɪᴀɢʀᴀᴍ ᴏꜰ ᴛʜᴇ ᴄʏᴄʟᴇ ᴅᴇꜱᴄʀɪʙᴇᴅ ɪɴ ᴛʜᴇ ᴘʀᴏʙʟᴇᴍ. ʟᴀʙᴇʟ ᴛʜᴇ ᴄᴏᴍᴘᴏɴᴇɴᴛꜱ ᴀɴᴅ ᴛʜᴇ ꜱᴛᴀᴛᴇ ᴘᴏɪɴᴛꜱ.ʙ. ᴅʀᴀᴡ ᴛʜᴇ ᴛ-ꜱ ᴅɪᴀɢʀᴀᴍ ᴏꜰ ᴛʜᴇ ᴄʏᴄʟᴇ ᴅᴇꜱᴄʀɪʙᴇᴅ ɪɴ ᴛʜᴇ ᴘʀᴏʙʟᴇᴍ. ʟᴀʙᴇʟ ᴛʜᴇ ᴄᴏʀʀᴇꜱᴘᴏɴᴅɪɴɢ ꜱᴛᴀᴛᴇ ᴘᴏɪɴᴛꜱ.ᴄ. ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴇɴᴛʜᴀʟᴘʏ ᴀᴛ ᴇᴠᴇʀʏ ᴘᴏɪɴᴛꜱ ɪɴ ᴛʜᴇ ᴄʏᴄʟᴇ.ᴅ. ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ꜰʀᴀᴄᴛɪᴏɴꜱ ᴏꜰ ᴛʜᴇ ꜱᴛᴇᴀᴍꜱ ᴇxᴛʀᴀᴄᴛᴇᴅ.ᴇ. ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ɴᴇᴛ ᴡᴏʀᴋ ᴏꜰ ᴛʜᴇ ᴄʏᴄʟᴇ ɪɴ ᴋᴡ.ꜰ. ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ɴᴇᴛ ʜᴇᴀᴛ ɪɴᴘᴜᴛ ᴛᴏ ᴛʜᴇ ᴄʏᴄʟᴇ ɪɴ ᴋᴡ.ɢ. ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴄʏᴄʟᴇ ᴛʜᴇʀᴍᴀʟ ᴇꜰꜰɪᴄɪᴇɴᴄʏ ɪɴ ᴋᴡ.ʜ. ᴄᴀʟᴄᴜʟᴀᴛᴇ ᴛʜᴇ ᴄʏᴄʟᴇ ꜱᴛᴇᴀᴍ ʀᴀᴛᴇ ɪɴ ᴋɢ/ᴋᴡʜAB, BC, CD, DE are each 2m long and the plane distance from A-D is 4m. Members are at right angles to each other. a) determine the vertical displacement at E b) determine the rotation at E E=200KN/mm^2 G= 80KN/mm^2 Iabce = constant = 25 x 10^-6 m^4 Jabce = constant = 50 x 10^-6 m^4
- ᴀ 39.37-ᴄᴍ x 55.85-ᴄᴍ, 327-ʀᴘᴍ, 16-ᴄʏʟɪɴᴅᴇʀ, 4-ꜱᴛʀᴏᴋᴇ, ꜱɪɴɢʟᴇ-ᴀᴄᴛɪɴɢ ꜱᴛᴀᴛɪᴏɴᴀʀʏ ᴅɪᴇꜱᴇʟ ᴇɴɢɪɴᴇ ɪꜱ ᴄᴏɴɴᴇᴄᴛᴇᴅ ᴛᴏ ᴀ 3125- ᴋᴠᴀ (0.80 ᴘᴏᴡᴇʀ ꜰᴀᴄᴛᴏʀ) ɢᴇɴᴇʀᴀᴛᴏʀ. ᴛʜᴇ ᴇɴɢɪɴᴇ ᴀʟꜱᴏ ᴅʀɪᴠᴇꜱ ᴀ 30-ᴋᴡ ᴇxᴄɪᴛᴇʀ. ᴀɴ ᴇxᴄɪᴛᴇʀ ɪꜱ ᴀ ꜱᴍᴀʟʟ ɢᴇɴᴇʀᴀᴛᴏʀ, ᴍᴏᴜɴᴛᴇᴅ ᴏɴ ᴛʜᴇ ꜱᴀᴍᴇ ꜱʜᴀꜰᴛ ᴀꜱ ᴛʜᴇ ᴍᴀɪɴ ɢᴇɴᴇʀᴀᴛᴏʀ, ᴡʜɪᴄʜ ᴘʀᴏᴅᴜᴄᴇꜱ ᴅᴄ ᴘᴏᴡᴇʀ ꜰᴏʀ ᴛʜᴇ ᴍᴀɪɴ ɢᴇɴᴇʀᴀᴛᴏʀ ꜰɪᴇʟᴅ ᴡɪɴᴅɪɴɢ. ᴀꜱꜱᴜᴍɪɴɢ ᴀɴ ᴏᴠᴇʀᴀʟʟ ɢᴇɴᴇʀᴀᴛᴏʀ ᴇꜰꜰɪᴄɪᴇɴᴄʏ ᴏꜰ 92%, ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ʙʀᴀᴋᴇ ᴍᴇᴀɴ ᴇꜰꜰᴇᴄᴛɪᴠᴇ ᴘʀᴇꜱꜱᴜʀᴇ ɪɴ ᴋᴘᴀ.The rod BD is made of material with G1= 33 GPa has a diameter 46 mm is bonded to the tube CA at point B, the tube made of material with G2=56 GPa has an outer diameter 97 mm and wall thickness of 8 mm. If T1=1268 N.m and T2=2282 N.m, answer the following questions: The polar moment of inertia of the rod BD is The polar moment of inertia of the tube CA is The maximum shear stress of the rod BD is The maximum shear stress of the tube CA is The maximum shear stress of the assembly is The angle of twist between D and B is The angle of twist between C and A is The angle of twist at D is The angle of twist between C and B is The reaction at point A isl-length steel with a diameter at the wide end twice the diameter at the narrow end determine the x and y coordinates of the center of mass of the rod in terms of l. (steel material density is constant).
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