Question

Part C - Maximum shear flow in the channel

Determine the maximum shear flow, qmax

, experienced by the channel.

Express your answer to five significant figures and include the appropriate units.

Review Learning Goal: To determine the maximum shear flow in a thin-walled member that is subjected to a vertical shear force. As shown, a channel is subjected to a vertical shear force of V = 90.0 kN and has dimensions b = 60.0 mm , e = 300.0 mm, and d = 200.0 mm Line NA represents the neutral axis of the cross section with respect to the y axis and point represents the centroid of the cross section. (Figure 1) Once the neutral axis has been determined for the given cross section, the largest moment of area A' about this axis can be determined. Determine the moment of area, Qmax, of area A' shown in the figure. (Figure 2) Express your answer to five significant figures and include the appropriate units. View Available Hint(s) Qmax = 1.1408x106mm Submit Previous Answers Correct Part C-Maximum shear flow in the channel Determine the maximum shear flow, Qmax, experienced by the channel Express your answer to five significant figures and include the appropriate units. View Available Hint(s) Figure 1 of 2 > H ? N * d 9max = 114 I b mm 12 Submit Previous Answers N * Incorrect; Try Again; 2 attempts remaining h Provide Feedback Next >

Answer 1

Solution: Shear flow (q) = txt aris off shear stress > where ti the thickness at Here t = qb= 2x 60 - 120 mm > so 1st you have to find shear stress at N-A (ie. Maximum shear stress) Voman TNA =łmune = Inst Vomune Hence shear flow = IMA So to find IMA 1st finel position of Neutral areis. ܐܐ 200mm 60mm j=165 mm So assuming top fibre N- 300 man Ke es reference fibre 1955mm Al It fomm Tk comm ca 200x60 x 30 + 2 x 300 xbox *(60+150) qwx 60+ 2x300x60 - g = 165mm from top - Now find IMA , about neutral are is INA = It teI z 2 2) INA = 200 x 603 12 +960 xbox(165-301272x box360 + 2x60 x 300 x(195-150) 2INA = 56502 x106mm 12

- Omare (above on on below meu prolaris), about = moment of area neutral anis » Omare = 2 xbox 195x195 = 2281560 mm 3 2 v omax » So shear flow (2) mare INA 3 qon go XI CVO NX 2281500 mm 565.2 x 106mo man mms Imere = 363.296 N mm So Чталх = 363.30 mm