Tutorial Sheet 2

# Tutorial Sheet 2 - Imperial College of Science, Technology...

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Sheet 2 Page 1 Imperial College of Science, Technology & Medicine Department of Aeronautics Second Year Structural Mechanics and Dynamics II Tutorial Sheet 2 Section a – Theory Development 1. The principle of virtual forces, in the form of the unit load method, gives the displacement as ε σ = V dV r If only end load is considered, this can be expressed as = = bars of . no 1 i i i i i i A E L N N r and if only bending is considered, it can be expressed as () = = bars of . no 1 i L 0 i i i i dz I E z M z M r i From the general expression of the unit load method, show that if both effects are taken into account the deflection is ( ) ( ) = = + = bars of . no 1 i L 0 i i i i bars of . no 1 i i i i i i dz I E z M z M A E L N N r i provided that the xy-axes are located at the centre of area of the cross-section of the beam. For the simple angle beam shown in figure 1, show that the displacement r, corresponding to the force R, arises almost entirely from the bending component if the beams are slender. L L R Figure 1

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Sheet 2 Page 2 Section b – Tutorial Problems 2. The statically indeterminate river bridge structure of figure 1a has to be repaired whilst it is still in place and still loaded. The repair requires disconnecting member 27 at joint 7 and member 38 at joint 8. The resulting structure is then statically determinate and is loaded as shown. Determine the forces in all of the members.
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## This note was uploaded on 03/24/2010 for the course AE A.213 taught by Professor S.pinhoandm.aliabadi during the Winter '09 term at Imperial College.

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Tutorial Sheet 2 - Imperial College of Science, Technology...

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