# 關於材料力學的一些問題

(1)A hitch-mounted bicycle rack is designed to carry up to four 135N bikes mounted on and strapped to two arms GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and is assumed to be like a cantilever beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W1 = 45 N, centered 9 in. from A [see the figure part (b)] and the rest of the rack weighs W2 = 180N, centered 480mm from A. Segment ABCDG is steel tube 50×50 mm, of thickness t=3 mm Segment BCDGH pivots about a bolt at B of diameter dB = 6 mm to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C (diameter of pin dp = 8mm) [see photo and figure part(c) ]. The overturning effect of the bikes on the rack is resisted by a force couple F‧h at BC.

(a)Find the support reactions at A for the fully loaded rack ;

(b)Find forces in the bolt at B and the pin at C.

(c)Find average shear stresses τaver in both the bolt at B and the pin at C.

(d)Find average bearing stresses σb in the bolt at B and the pin at C.

(2)A bicycle chain consists of a series of small links, each 12 mm long between the centers of the pins (see figure). You might wish to examine a bicycle chain and observe its construction. Note particularly the pins , which we will assume to have a diameter of 2.5mm.

In order to solve this problem,you must now make two measurements in a bicycle (see figure): (1) the length L to the crank arm from main axle to pedal axle, and (2) the radius R of the sprocket (the toothed wheel, sometimes called the chainring).

(a)Using your measured dimensions, calculate the tensile force T in the chain due to a force F = 800N applied to one of the pedals.

(b)Calculate the average shear stress τaver in the pins.

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• Eli
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(1) A hitch-mounted bicycle rack is designed to carry up to four 135N bikes mounted on and strapped to two arms GH [see bike loads in the figure part (a)]. The rack is attached to the vehicle at A and is assumed to be like a cantilever beam ABCDGH [figure part (b)]. The weight of fixed segment AB is W1 = 45 N, centered 9 in. from A [see the figure part (b)] and the rest of the rack weighs W2 = 180N, centered 480mm from A. Segment ABCDG is steel tube 5050 mm, of thickness t=3 mm Segment BCDGH pivots about a bolt at B of diameter dB = 6 mm to allow access to the rear of the vehicle without removing the hitch rack. When in use, the rack is secured in an upright position by a pin at C (diameter of pin dp = 8mm) [see photo and figure part(c) ]. The overturning effect of the bikes on the rack is resisted by a force couple F‧h at BC.

將一設計用以承載4部重135N自行車之(栓式或鉤式)自行車架綑綁架設於兩桿G;H( 詳見負載圖 part- a 所示 ). 車架以懸臂樑之型式(ABCDGH)與車輛(載具)連結於A( 詳見圖示 part- b ). 固定段AB之重量W1 = 45N ; 與A之中心距為 9 in(英吋)( 詳見圖示 part- b ). 車架其餘部份之重量W2 = 180N ; 與A之中心距為 480 mm. ABCDG段為50 50 mm 厚度 3 mm 之鋼管, BCDGH段以B點為一用以從車輛(載具)後側(快速)裝卸(或取下)而不用完全卸除車架之直徑 6 mm螺栓孔之軸心. 使用時, 於C處利用一 Pin(銷) 使車架成垂直狀態( 銷徑 dp = 8mm )( 詳見照片及圖示 part- c ). 致使車架上自行車傾倒之作用(力)則與BC段上之一力矩(F‧h)相抗衡.

(a)Find the support reactions at A for the fully loaded rack ;

(b)Find forces in the bolt at B and the pin at C.

(c)Find average shear stresses τaver in both the bolt at B and the pin at C.

(d)Find average bearing stresses σb in the bolt at B and the pin at C.

(a) 試求在車架完全附載情況下, A處之反作用力?

(b) 試求B處螺栓之力 ; C處 Pin (銷)之力?

(c) 試求於B處螺栓&C處 Pin (銷)之平均剪應力 τ aver?

(d) 試求於B處螺栓&C處 Pin (銷)之最大承壓應力 σ ?

2009-03-14 12:22:38 補充：

(2)A bicycle chain consists of a series of small links, each 12 mm long between the centers of the pins (see figure).

自行車鏈條由數個節距(中心距)為12mm之鏈節所組成(詳見附圖).

2009-03-14 12:23:12 補充：

You might wish to examine a bicycle chain and observe its construction. Note particularly the pins , which we will assume to have a diameter of 2.5mm.

或許你想對自行車鏈條或其結構多作觀察, 特別是針對銷(各鏈節間之連接銷)的部份, 現假設有一銷之直徑為2.5mm.

2009-03-14 12:23:53 補充：

In order to solve this problem,you must now make two measurements in a bicycle (see figure):

為了解決這問題, 必須先針對自行車做以下兩項測量(詳見附圖) :

2009-03-14 12:24:24 補充：

(1) the length L to the crank arm from main axle to pedal axle, and (2) the radius R of the sprocket (the toothed wheel, sometimes called the chainring).

(1) 長度L(腳踏軸至齒輪盤主軸<==踩踏之曲柄軸長)

(2) 飛輪之半徑R(附有齒狀之輪, 有時亦稱飛輪)

2009-03-14 12:24:43 補充：

(a)Using your measured dimensions, calculate the tensile force T in the chain due to a force F = 800N applied to one of the pedals.

(b)Calculate the average shear stress τaver in the pins.

(a) 利用所量測之尺寸(數據), 計算出在 F = 800N之條件 ; 一個踩踏作用下其鏈條承受之拉力 T = ? .

(b) 計算 Pin (銷)之平均剪應力 τ aver .

2009-03-14 12:27:11 補充：

太長了!長到超過字數限制~

自行車的專有名詞我還上網查了一下.....應該沒錯!

你參考看看吧~

Source(s): me&網路