In the textbook it says dp= 0.5 in, ab= 1 1/8 in, and lastly bs= 1 5/16 in. Im n
ID: 1842833 • Letter: I
Question
In the textbook it says dp= 0.5 in, ab= 1 1/8 in, and lastly bs= 1 5/16 in. Im not sure what the last abbreviation is meant for. I'm assuming it's for the tube but I'm not sure.
4.33 A hitch for an automobile is to be designed for pulling a maximum load of 3600 lb. A solid square bar fits into a square tube and is held in place by a pin, as shown in Figure P4.33. The allowable axial stress in the bar is 6 ksi, the allowable shear stress in the pin is 10 ksi, and the allowable axial stress in the steel tube is 12 ksi. To the nearest n., determine the minimum cross-sectional dimensions of the pin, the bar, and 16 the tube. (Hint: The pin is in double shear.) Square Tube Pin Square Barr Figure P4.33Explanation / Answer
The pin is in double shear. Thus per shear surface the load =3600/2=1800lb. For an allowable shear stress of 10ksi,results in area diameter of the pin = SQRT(4/*(1800/10000))= 0.478". Rounded to the next available 1/16" size, it becomes 0.5". Now that the bar must be able to accommodate the pin of 0.5", First for the given load of 3600 bar axial load, and allowable stress of 6ksi , we get minum required area as 3600/6000= 0.6 in2 or 0.774" Square. But 0.774" Square is not suitable for drilling 0.5" hole. After accomodating the hole the area left is 0.387 square incheaes, means allowable stress will exceed. hence we shall increase the size of the bar to 1.125" . The stress after accomodating 0.5" thru hole is 3600/(1.125^2-0.5*1.125)=3600(1.2656-0.5625)=3600/0.703= 5120 psi is acceptable. (with 1 1/16 bar, stress slighly exceed alloable value. hence selected 1.125" Now select a tube whose cross cetional area meets the minimum specified stress. Allowable stress is 12ksi, Area required is 3600/12000= 0.3 in2. Selecting size of 1.25 with 0.065" has required sectional area but fail to accommodate 1.125" solid bar. Hence forced to lookf 1.375" tube with 0.065" (16 gage) wall thickenss . My guess for 'bs' is bar steel.