# a beam of rectangular cross section 200mm deep and 100mm wid

a beam of rectangular cross section 200mm deep and 100mm wide .If the beam is 3m long, simply supported at either end and carries two point loads of 5kN at 1m from the left hand end and 10kN at 2m from the left hand end (a) Calculate the maximum bending moment (b) Calculate the maximum stress in the beam (c) At the point of maximum stress sketch a graph of the stress distribution through the thickness of the beam, indicating which are tensile and compressive stresses. (d) Determine the dimensions of the cross section which will minimise the maximum stress value if: � the cross sectional area of the beam can be increased by 20% � the beam section is to remain a solid rectangle � neither the breadth or depth of the beam section can be reduced below their original dimensions. Show the dimensions of the proposed beam cross section with the aid of a sketch. (e) Determine the percentage reduction of the maximum stress value when the new cross section is used.