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Calculation Example – Section Modulus S
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A simple beam pinned at two ends is loaded as shown in the figure. Calculate the required section modulus S if σallow =1500 ΚΝ/m2, L =24 m, P =2000 KN, and q = 400 KN/m.

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Calculation Example – Friction
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The friction coefficient is c1=0.2 between two bodies A,B. The friction coefficient is c2=0.18 between body B and the ground. If mass mA=0.5kgr and mB=1kgr , what is the minimum force P so that the two bodies start sliding?(we consider that there is no friction at the rope).

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Calculation Example – Simple harmonic vibration part 2
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A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation

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Calculation Example – Simple harmonic vibration part1
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A single point with mass m is vibrating harmonically. The displacement x from point of balance is governed by the differential equation

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Calculation Example – Critical load.
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A solid rod has a diameter of 20 mm and is 600 mm long. It is made of a material that can be modeled by the stress–strain diagram shown in the figure below. If it is used as a pin-supported column, determine the critical load.

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Calculation Example – Minimum allowable Diameter.
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Determine the minimum diameter of the rod. The axial tensile force is P=10KN. The allowable stresses in tension and shear is 100MPa and 40MPa.

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Calculation Example – Member Diagram.
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Determine the diagrams for moment and shear for the following pinned at two ends beam. Total length 9m. EI constant. Units KN,m.