Problem 1): A circular pipe girder is constructed from 80mm external diameter and 60 mm internal diameter. Three such girders are mounted vertically one at equal angles of a circular horizontal platform which the girders support. The platform is 5 m above ground level and weighs (0.1*B) KN. The platform supports an additional central load of (0.2*B) KN. The weight of the girders may not be neglected. The density of the material from which the girders are constructed is (290*B) kg/m3. Assuming that each girder supports an equal share of the load, determine the compressive stresses set up in the material of each girder: 1- At the lower point of the girder. 2- At the middle point of the girder. 3- At the upper point of the girder. Discuss the above values when the weights of the girders are neglected. Note: B = 39
Problem 1):
A circular pipe girder is constructed from 80mm external diameter and 60 mm internal diameter. Three such girders are mounted vertically one at equal angles of a circular horizontal platform which the girders support. The platform is 5 m above ground level and weighs (0.1*B) KN. The platform supports an additional central load of (0.2*B) KN. The weight of the girders may not be neglected. The density of the material from which the girders are constructed is (290*B) kg/m3. Assuming that each girder supports an equal share of the load, determine the compressive stresses set up in the material of each girder:
1- At the lower point of the girder.
2- At the middle point of the girder.
3- At the upper point of the girder.
Discuss the above values when the weights of the girders are neglected.
Note: B = 39
Problem 2):
A 20 mm diameter steel rod passes concentrically through a bronze tube (200+Q) mm long, 50 mm external diameter, and 40 mm internal diameter. The ends of the steel rod are threaded and provided with nuts and washers which are adjusted initially so that there is no end play at 25°C.
1. Assuming that there is no change in the thickness of the washers, if the stress produced in the steel is (200+Q) MN/m2 when one of the nuts is tightened, the pitch of the thread being 1 mm: Find the number of turns for the nut and stress in the bronze tube.
2. If the temperature of the steel and bronze is then raised to 40°C find the changes that will occur in the stresses in both materials.
The coefficient of linear expansion per C is 10 x10-6 for steel and 17 x10-6 for bronze. E for steel = 210 GN/m2 and, E for bronze = 100 GN/m2.
Note: Q = 39
Problem 3):
A beam ABCDE has 8 m long, has a simply supported at A and D, and AB=BC=CD=DE= 2 m, loaded with a uniformly distributed load on the 4 m span CE is 39 KN/m with 39 KN a concentrated load on C and moment on B is 39 KN.m. Draw the Shear Force and Bending Moment diagrams stating the important values and determine the maximum Bending moment value and its position.
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