MT-1620 al.2002 Figure 15.8 Representation of joints, skins, and shear flows in cross-section of box beam 5 Look at the equilibrium of joint(1 Figure 15.9 Representation of skins and stringer and associated loads and shear flows at ioint(1 skin stringer d sP skin Paul A Lagace @2001 Unit 15
MIT - 16.20 Fall, 2002 Figure 15.8 Representation of joints, skins, and shear flows in cross-section of box beam Figure 15.9 Look at the equilibrium of joint 1 Representation of skins and stringer and associated loads and shear flows at joint 1 stringer skin skin : Paul A. Lagace © 2001 Unit 15 - 11
MT-1620 al.2002 Notes The stringer only carries axial load The skin carries only shear flow The shear flow at the "end" of the skin(where it is cut must be the same as at the edge(the cross-section cut). This is due to equilibrium Apply equilibrium:∑7-0 P+lP + -dx +la, dx-g dx =lO dx dP →q1-q6 dx More generally note that Paul A Lagace @2001 Unit 15-12
MIT - 16.20 Fall, 2002 Notes: • The stringer only carries axial load • The skin carries only shear flow •� The shear flow at the “end” of the skin (where it is “cut”) must be the same as at the edge (the cross-section cut). This is due to equilibrium (σxy = σyx) • Apply equilibrium: ∑Fx = 0 dP ⇒ − P + P + dx + q1 dx − q6 dx = 0 dx dP ⇒ q1 − q6 = − dx More generally note that: Paul A. Lagace © 2001 Unit 15 - 12
MT-1620 1. Angle that skin comes into joint doesn' t matter since q along aml 2002 edge is always in x-direction Figure 15.10 Representation of skins at joint coming in at any angle 2. Stringer alone gives dp as its contribution Figure 15.11 Representation of stringer isolated at joint dp Paul A Lagace @2001 Unit 15-13
MIT - 16.20 Fall, 2002 1. Angle that skin comes into joint doesn’t matter since q along edge is always in x-direction Figure 15.10 Representation of skins at joint coming in at any angle 2. Stringer alone gives dP as its contribution dx Figure 15.11 Representation of stringer isolated at joint Paul A. Lagace © 2001 Unit 15 - 13
MT-1620 Fall 2002 3. If shear flows into joint, its contributions is in the negative x direction; if shear flows" out of' joint, its contribution is in the positive x-direction Figure 15. 12 Representation of shear flowing(left) into and (right)out of joint X Adding all this up in +lqu=0 dx dx Use this in general Paul A Lagace @2001 Unit 15-14
MIT - 16.20 Fall, 2002 3. If shear flows “into” joint, its contributions is in the negative xdirection; if shear flows “out of” joint, its contribution is in the positive x-direction Figure 15.12 Representation of shear flowing (left) into and (right) out of joint Adding all this up: dP − qin + qout = 0 dx dP ⇒ qout − qin = − dx Use this in general Paul A. Lagace © 2001 Unit 15 - 14
MT-1620 al.2002 For a more complicated joint, use superposition Figure 15 13 Representation of joint with multiple skins >Need an expression for P--start with P=NAO differentiating dP do ax x o since are considering stringers with a uniform cross-section Most general case A Joint Equilibr x Paul A Lagace @2001 Unit 15-15
MIT - 16.20 Fall, 2002 For a more complicated joint, use superposition Figure 15.13 Representation of joint with multiple skins --> Need an expression for P -- start with: P = Aσ xx differentiating: dP A dσ xx + σ d A ⇒ = xx d x d x d x = 0 since are considering stringers with a uniform cross-section Most general case: qout − qin = − A dσ xx Joint Equilibrium d x Paul A. Lagace © 2001 Unit 15 - 15