Statics: Internal Forces in Structural and Multiforce Members, Study notes of Engineering

Download Statics: Internal Forces in Structural and Multiforce Members and more Study notes Engineering in PDF only on Docsity! 1 MEM202 Engineering Mechanics - Statics MEM Chapter 8 Internal Forces in Structural Members • Axial Force and Torque in Bars and Shafts • Axial Force, Shear Force, and Bending Moments in Multiforce Members 2 MEM202 Engineering Mechanics - Statics MEM Internal Forces in A General 3-D Body 0=∑F r 0=∑F r 0=∑F r 0=∑F r 0=∑F r 5 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members Axial Forces N 10 N 10=ABF N 15=BCF N 10 N7 N5 N 8 N 7=CDF N 10 N 10 N 10 N5 N5 N 8 N 10 N 15 N 15 N7 N7 A B C D A B C D 6 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members Axial Forces N 10 N 10=ABF N 5−=BCF N 10 N 3 N 15 N 8 N 3=CDF N 10 N 10 N 10 N 15 N 15 N 8 N 10 N5− N 3 N 3 A B C D A B C DN5− 7 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members Torque mN 10 ⋅ mN 10 ⋅=ABT mN 5 ⋅−=BCT mN 10 ⋅ mN 3 ⋅ mN 15 ⋅ mN 8 ⋅ mN 3 ⋅=CDT mN 15 ⋅ mN 15 ⋅ mN 8 ⋅ mN 10 ⋅ mN5 ⋅− mN 3 ⋅ A B C D A B C DmN5 ⋅− = mN 10 ⋅ mN 10 ⋅ mN 10 ⋅ mN 3 ⋅ 10 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members F, V, and M in Multiforce Members a a ( )( ) 0500 0500 01250 =+= =−−= =+= ∑ ∑ ∑ − xaa xy xx MxM VF FF lb-ft 500 lb 500 lb 1250 xM V F x x x −= −= −= ( )( ) ( )( ) 066.38sin8.16005500 066.38sin8.1600500 066.38cos8.16001250 =+−−= =−+−= =+−= ∑ ∑ ∑ − xbb xy xx MxxM VF FF o o o x xF xV xM xF xV xM b b a a ( ) lb-ft 5000500 lb 500 lb 0 −= = = xM V F x x x lb 0.500 lb 0.1250 lb 8.1600 o66.38 b b 11 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members F, V, and M in Multiforce Members ( ) lb-ft 5000500 lb, 500 lb, 0 :105For lb-ft 500 lb, 500 lb, 1250 :50For −===≤≤ −=−=−=≤≤ xMVFx xMVFx xxx xxx x lb 1250− lb 500− lb 500 lb 1250− lb 500 lb 500− lb-ft 2500− Axial Force Shear Force Bending Moment 12 MEM202 Engineering Mechanics - Statics MEM Internal Forces in Structural Members F, V, and M in Multiforce Members lb 0770 =⇒=∑ DF FM Example 8-5 Internal forces at a-a and b-b. E D Xb Yb Mb F.B.D. for member EDF Section a-a Section b-b D