Random Steps of a Drunk Man: Probability of Escaping the Cliff

Problem
From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?

A.   2/27 C.   4/27
B.   107/243 D.   1/2

 

Problem 917 | Combined Axial and Bending

Problem 917
For the structure in Problem 916, calculate the maximum compressive stress in bar ABC if its cross section is 200 mm square.
 

916-fbd-member-abc.gif

 

Problem 916 | Combined Axial and Bending

Problem 916
For the structure shown in Figure P-916 is hinged to fixed supports at A and E. Compute the maximum compressive stress developed in bar BDE if its cross section is 200 mm square. Neglect the weights of the members.
 

916-given-structural-assembly.gif

 

Problem 915 | Combined Axial and Bending

Problem 915
For the structure in Problem 914, compute the maximum tensile stress developed in bar CB.
 

914-two-bar-structure.gif

 

Problem 914 | Combined Axial and Bending

Problem 914
The structure shown in Figure P-914 is hinged to fixed is hinged to fixed supports at A and C. Assume that the pin connections at A, B, and C are frictionless. The bars are each 4 in. by 4 in. in section. Compute the maximum compressive stress developed in bar AD.
 

914-two-bar-structure.gif

 

Problem 913 | Combined Axial and Bending

Problem 913
Solve Problem 912 if P = 6 kips and F = 10 kips.
 

912-rectangular-link.gif

 

Inner Circle Reading of the Double Vernier of a Transit

Problem
Figure P-SF01 is a double vernier of a transit and the dashed line indicate the two sets of coincident lines. What is the reading of the inner circle?
 

01-008-vernier-circle-reading.gif

 

A.   175° 42' C.   184° 18'
B.   193° 8' D.   181° 3'

 

Problem 912 | Combined Axial and Bending

Problem 912
Compute the stresses at A and B on the link loaded as shown in Figure P-912 if P = 9000 lb and F = 3000 lb.
 

912-rectangular-link.gif

 

Problem 911 | Combined Axial and Bending

Problem 911
A concrete dam has the profile shown in Figure P-911. If the density of concrete is 2400 kg/m3 and that of water is 1000 kg/m3, determine the maximum compressive stress at section m-n if the depth of the water behind the dam is h = 15 m.
 

911-gravity-dam.gif

 

Length of Parabolic Sag Curve with Given Change in Grade Per Station

Problem
A grade of -5% is followed by a grade of 1%, the grades intersecting at the vertex (Sta. 10 + 060). The change of grade is restricted to 0.4% in 20 m. Compute the length of the vertical parabolic sag curve in meters.

A.   360 m C.   300 m
B.   320 m D.   340 m

 

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