A beam extends over a span of 9.5 m and an overhang (cantilever) to the right of the right support of 4.0 m (that is, the total length of the beam is 13.5 m.) The beam supports a service dead load of 18 t/m that does not include self-weight, and a service live load of 7 t/m. Assume the connections between the beam and the supports are simple pins or rollers. Prepare your work according to the following steps: 1. Draw the shear (Vu) and bending moment (Mu) envelopes for the beam, ignoring self- weight. Note that there will be a maximum positive and a maximum negative moment. 2. Use the larger of the two maximum moments to determine the required dimensions for a reinforcement ratio around 0.85 of the maximum. Select the dimensions such that the effective depth (d) is approximately 1.3 times the width. Use multiples of 5 cm for h and b. Using these dimensions, select the reinforcement required at two locations: for the maximum positive and the maximum negative moment. 3. Repeat using the smaller of the two maximum moments to determine the required dimensions for a reinforcement ratio around the maximum. Select the dimensions such that the effective depth is approximately 1.3 times the width. Use multiples of 5 cm for h and b. Select the reinforcement required at two locations using these dimensions: for the maximum positive and the maximum negative moment. Note that the beam must be doubly reinforced to support the larger moment. 4. Present your design using side views, sections, and details as appropriate. 5. If self-weight is to be included, draw the shear and bending moment diagrams and repeat the beam design for the larger maximum moment. Again, determine the required dimensions for a reinforcement ratio around the maximum, and select the dimensions such that the effective depth is approximately 1.3 times the width. Use multiples of 5 cm for h and b. Select the reinforcement required at two locations using these dimensions: for the maximum positive and the maximum negative moment. 6. Repeat the design of the beam for the maximum moment only, including self-weight. This time use the dimensions obtained in step five, however, with b - h of step five, and h = b of step five. Note that the beam probably must be doubly reinforced. 7. If the beam has b= 80 cm, h=110 cm, and is reinforced with 11 0 28 bars at midspan and 9 28 above the right support with 10 stirrups, determine the maximum distributed service live load the beam can support. The beam supports a service dead load of 4 t/m that does not include self-weigh. Prepare a short report to explain your findings and conclusions. The soundness of your work, organization, and quality of your drawings will make up your final grade for this homework. Use fe' =28 MPa, fy = 420 MPa, Yconcrete = 24 kN/m.