A 6 times 10 inch timber beam is reinforced by bolting two s

A 6 times 10 inch timber beam is reinforced by bolting two steel straps to its sides as shown. Given: the modulus of elasticity of the wood is 1.50 times 106 psi, and the modulus of the steel is 30.0 times 10^6 psi. If the cross-section supports a horizontal moment resultant of 200 kip-in in the orientation shown, determine a) the maximum tension and compression stress in the wood and b) the maximum and minimum stresses in the steel. Required: For full credit as part of your work you must show a sketch of the transformed cross-section, and how it is used to compute the location of the centroid and the moment of inertia of the transformed moment of inertia. (These are sometimes called the \'modulus-weighted centroid\' and the \'modulus-weighted moment of inertia.)

Solution

Changeover of fixtures on a machine takes 35 minutes. Following changeover an average of 5 parts must be produced and discarded before correct sitting is achieved. The machine cycle time for each part is 2 minutes and the materials cost is $1.50. The labour cost for a skilled set up person is $45 per hour while the machine operator is paid $30 per hour. Current batch size is 50. Suppose the set up time can be reduced so that the operator can perform the changeover and on average only two parts are required before correct setting is achieved, what should be the new set up time so that a batch size of 20 could be produced with only 90% of the current cost per unit? The cost per unit is the total of material cost, labour of set up and labour cost of running the machine.