Maximum Flexural Stress

Support Added at the Midspan of Simple Beam to Prevent Excessive Deflection

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 = 4 m
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

 

Stresses of Hollow Circular Tube Used as a Pole

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

 

Strength of Temporary Earth Retaining Wall Made from Wooden Planks

Situation
A temporary earth retaining wall consists of wooden plank driven vertically into the ground. The wall is designed to resist 2.4 m height of soil.

Given the following:
Cross-sectional dimensions of the plank = 300 mm wide × 75 mm thick
Allowable bending stress of the plank = 10.4 MPa
Allowable shear stress of the plank = 0.8 MPa
Unit weight of retained soil = 17.3 kN/m3
Active earth pressure coefficient = 1/3

1.   Calculate the maximum flexural stress.

A.   12.7 MPa C.   8.6 MPa
B.   14.2 MPa D.   10.1 MPa

2.   Calculate the maximum shear stress.

A.   1.11 MPa C.   0.99 MPa
B.   0.33 MPa D.   0.77 MPa

3.   Calculate the minimum thickness of the plank to prevent failure.

A.   90 mm C.   110 mm
B.   80 mm D.   100 mm

Problem 1003 | Maximum stresses in wood and steel of composite beam

Problem 1003
A simply supported beam 4 m long has the cross section shown in Fig. P-1002. It carries a uniformly distributed load of 20 kN/m over the middle half of the span. If n = 15, compute the maximum stresses in the wood and the steel.
 

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