Situation
A simply supported steel beam spans 9 m. It carries a uniformly distributed load of 10 kN/m, beam weight already included.

Given Beam Properties:
Area = 8,530 mm2
Depth = 306 mm
Flange Width = 204 mm
Flange Thickness = 14.6 mm
Moment of Inertia, Ix = 145 × 106 mm4
Modulus of Elasticity, E = 200 GPa

1.   What is the maximum flexural stress (MPa) in the beam?

A.   107 C.   142
B.   54 D.   71

2.   To prevent excessive deflection, the beam is propped at midspan using a pipe column. Find the resulting axial stress (MPa) in the column

Given Column Properties:
Outside Diameter = 200 mm
Thickness = 10 mm
Height, H = 4 m
Modulus of Elasticity, E = 200 GPa
A.   4.7 C.   18.8
B.   9.4 D.   2.8

3.   How much is the maximum bending stress (MPa) in the propped beam?

A.   26.7 C.   15.0
B.   17.8 D.   35.6

 

Situation
A 12-m pole is fixed at its base and is subjected to uniform lateral load of 600 N/m. The pole is made-up of hollow steel tube 273 mm in outside diameter and 9 mm thick.
1.   Calculate the maximum shear stress (MPa).

A.   0.96 C.   1.39
B.   1.93 D.   0.69

2.   Calculate the maximum tensile stress (MPa).

A.   96.0 C.   60.9
B.   69.0 D.   90.6

3.   Calculate the force (kN) required at the free end to restrain the displacement.

A.   2.7 C.   27
B.   7.2 D.   72

 

Sum of Areas of Infinite Number of Squares

Problem
The side of a square is 10 m. A second square is formed by joining, in the proper order, the midpoints of the sides of the first square. A third square is formed by joining the midpoints of the second square, and so on. Find the sum of the areas of all the squares if the process will continue indefinitely.
 

Sum of Areas of Equilateral Triangles Inscribed in Circles

Problem
An equilateral triangle is inscribed within a circle whose diameter is 12 cm. In this triangle a circle is inscribed; and in this circle, another equilateral triangle is inscribed; and so on indefinitely. Find the sum of the areas of all the triangles.