LECTURE+36+COE-3001-A

# LECTURE 36 COE-3001-A

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . Mello/Georgia Tech Aerospace qa3 ( ✓B ) 1 = 6EI 20 Appendix G- 1: case 4 ☞ “Point load (P) contribu=on to deﬂec=on P L3 P L2 ( B )2 = ( ✓B ) 2 = and angle of rota=on at end B” 3EI 2EI ☞ Combine individual solu=ons B = ( B ) 1 + ( B )2 AND (✓B ) = (✓B )1 + (✓B )2 qa3 P L3 qa3 P L2 (4L a) + ( ✓B ) = + B= 24EI 3EI 6EI 2EI 4/9/13 M. Mello/Georgia Tech Aerospace 21 EXAMPLE 8- 7 Problem: Can=lever beam supports a uniform load intensity q ac=ng over the right- hand half of the beam. The beam has length L and constant ﬂexural rigidity EI. Determine: 1.  Deﬂec=on δB at the free end of the beam 2.  angle of rota=on ΘB at the free end of the beam SOLUTION: Take alterna=ve approach this =me and demonstrate the method of integra=ng a concentrated load solu=on across the distance over which the load intensity q is applied (x=- L/2 to x=L) ☞ consult consult Appendix G- 1 case 5 point load (P) contribu=on at the free end. 4/9/13 M. Mello/Georgia Tech Aerospace 22 EXAMPLE 8- 7: Appendix G- 1: case 4 ☞ replace P by qdx AND replace a with x d B (qdx)(x2 ) = (3L 6EI (qdx)(x2 ) d✓B = 2EI 4/9/13 x) resul=ng diﬀeren=al deﬂec=on at the free end due to qdx at x resul=ng diﬀeren=al angle of rota=on at the free end due to qdx at x M. Mello/Georgia Tech Aerospace 23 EXAMPLE 8- 7 (ﬁnish) ☞ Now integrate each diﬀeren=al expression from (x=- L/2 to x=L) in order to capture the cumula=ve eﬀect of the load intensity distribu=on (q) on the deﬂec=on and angle of rota=on at the free end of the beam (qdx)(x2 ) (qdx)(x2 ) dB= (3L x) d✓B = 6EI 2EI ZL ZL q q ✓B = x2 (3L x)dx x2 dx B= 6EI L/2 2EI L/2 L 7qL3 q x4 3 ✓B = xL B= 48EI 6EI 4 L/2 41qL4 B= 384EI ☞ We could have easily used case 3 of Appendix G- 1 and obtained the same answer without this integra=on procedure. ☞ Integra=on procedure is useful when we don’t have the tabulated solu=on for a distribu=on q(x). This example demonstrates and validates an alterna=ve approach. 4/9/13 M. Mello/Georgia Tech Aerospace 24 EXAMPLE 8- 8 Problem: Compound beam has a roller support at A, an internal hinge at B, and a ﬁxed support at C. Segment AB has length (a) and segment BC has length (b). A Concentrated load (P) acts...
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