HW1 Hints

HW 1.1  
Angle = -36.65° (Minus means CCW), Tmax = 522.02 MPa

HW 1.2
Angle = 52.02°, Max Principal = 556.16 MPa

HW 1.3
Angle = -56.31°, Sigma2 = 18.00 ksi, Tmax = 28.50

For problems 2 and 3, you need to include Sigma3 = 0 to correctly get the
maximum shear stress.

Solving the Car Jack screw tension.

When the top of the jack is at 247.65mm high, the vertical distance between upper and lower pins in the links is 157.65mm.  So the height (H) for one of the links is half this, or 78.83mm.  The links are at a 33.72° angle that form a triangle of height 78.83mm and with a hypotenuse of 142mm.  The horizontal side (W) is 118.1mm long.

The jack sees half the weight of the front of the car or 1014.5lb of load.  We can view that load as shared equally by the two links, so one side sees 507.25lb.  This is the vertical component on each link.  The horizontal component is just W/H = 118.1/78.83 [or 1/Tan(33.72°)] times the vertical component of 507.25lb.  This equals 760.07lb.

But... the force from the lower links is also exerting that 760.07lb horizontally on the screw, to the total load on the screw is 2 x 760.07 = 1520.1lb.  To convince yourselves of this, just imagine a jack with just the two upper links and the screw - no lower links.  Then the reaction force from below would be only vertical and do nothing to stretch the screw, and then the tension on the screw would be just 760lb.