UNIVERSITY of PLYMOUTH

 

MECH115: Engineering Science 1

 

Tutorial examples: - Bending                                                  [Use g = 9.81 m/sē where required]

 

 

  1. For each of the following cross-sections find the position of neutral axis above the base (in cm), and the second moment of area (in cm4 ) about the neutral axis. All dimensions are in cm. It is suggested that you use a spreadsheet.

[(a) 4.80 cm, 422.65 cm4; (b) 3.93 cm, 251.49 cm4; (c) 5.68 cm, 702.84 cm4]

 

           (a)                                             (b)                                                     (c)

 

 

  1. For each of the above sections find the tensile and compressive stresses induced when each is subject to a bending moment of 24 kNm. Assume tension on the base.  [(a) -352.1, 272.6 MN/m2; (b) -579.3, 375 MN/m2; (c) -250.0, 194.0 MN/m2 ]



  1. A pure bending moment of 200 Nm is applied to a fibre glass fishing rod. The diameter of the rod is 26mm.  If Young's modulus for glass fibre is 20GN/mē. Find the bend radius. [2.243 m ]



  1. Floor boards made of wood must not deflect more than a certain amount when stood on.
    If joists are spaced at 400mm intervals, find the thickness of floor boards required if the deflection in the middle is to be 1mm when subject to a uniform bending moment of 64Nm. The width of the floor board is 120mm. Wood has a Young's modulus of  16GN/mē. Hint: find the radius of curvature.   [ 25 mm]

 

 

  1. For each of the beam loadings shown below, draw the shear force and bending moment diagram:

 

 

 

 


(a)

 

 

 

 

 

 

 

 


           

 

(b)

 

 

 

 

 

 

 

 


            (c)

 

 

 

 

 

 

 


            (d)

 

 

 

 

 

 

 

  1. In order to enable an engine of mass 450 kg to be lifted out of a car, a DIY enthusiast is considering fitting a RSJ into his double garage. The span would be 6m, and the engine would be lifted at the mid-point. If the allowable stress for mild steel is 80 MN/m2, find a suitable RSJ from BS 4.   [Z required = 83 cm3 ]

 

 

 

 

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