Problem 1
A beam with an overhang has a T-cross section and is carrying the distributed and concentrated loads as shown.
a. Calculate the reactions and draw the shear and bending moment diagrams for the beam.
b. Calculate the deflection at Joint D and the rotation at Joint C using the virtual work method.
E=27GPa
.
c. Use SAP2000 to verify your answers for parts " a " and " b "
d. At joint B , draw the bending stress distribution along the depth of the cross-section indicating the values at critical points. What is unique about the moment at B .
e. At joint C , draw the bending and shear stress distributions along the depth of the cross-section indicating their values at critical points. What is unique about the moment and shear at C .
f. At joint C , calculate the principal stresses at a point located just below the flange.
g. Draw a sketch of the beam showing the crack pattern that you would expect to result from tensile bending and shear stresses. Show where would you provide reinforcement (no calculations).