Considering the geometric parameters shown in Fig. The formulation below accounts for the boom/ building clearance constrains ͑ C 1 ͒. This section describes the formulation in which the boom length ͑ L ͒ is expressed as a function of the main boom angle to the ground ͑ ␣ ͒.

To determine the optimum boom length of a hydraulic boom crane, the geometry of the crane is expressed using: ͑ 1 ͒ the main boom length ͑ L ͒ as a function of its angle to ground ͑ ␣ ͒, ͑ 2 ͒ the main boom length ͑ L ͒ as a function of the crane’s lifting radius ͑ R ͒, and ͑ 3 ͒ the crane’s lifting radius ͑ R ͒ as a function of the main boom angle to ground ͑ ␣ ͒. geometrical variables: main boom length L, main boom angle to ground ͑ ␣ ͒, and/or the crane’s lifting radius ͑ R ͒. Scenario 2 considers the case of a crane ͑ lattice or hydraulic ͒ equipped with a luffing jib where the building height is higher than the height of the main boom tip ͑ points T and M of Fig. Knowing that t = tan ͑ ␣ / 2 ͒, ͑ ␣ ͒ that satisfies the condition for the optimum boom length ͑ L ͒ can then be determined. Knowing all the variables involved one could solve for ͑ t ͒ by means of iterations and by subsequently ensuring that ץ 2 L / ץ ␣ 2 Ͻ 0. To select a mobile crane, contractors need to know three.

The algorithm considers the detailed geometry of each crane in its calculation, including sheave offsets ͑ C 2 and C 3 ͒ from the centerline of the main boom. Scenario 1 describes the formulation for lifts performed on the main boom only, as illustrated in Fig. Formulations for lifts performed on the luffing jib for both types of cranes ͑ lattice boom and hydraulic boom cranes ͒ can be derived in a manner similar to those described in Scenarios 2 and 3. Lifts performed on a fixed jib are considered as a special case of the general rule. Scenario 3 considers the case when the tip of the main boom is higher than the final location of the lift as shown in Fig. Scenario 2 considers the case when the building height ͑ point T 1 ͒ is higher than the height of the main boom tip ͑ point M -see Fig. Scenarios 2 and 3 describe the formulation for lifts performed on luffing jibs.

Scenario 1 describes the formulation for lifts performed on the main boom only, as shown in Fig. The evaluation is carried out for cranes either lifting on their main booms or on their jibs via three scenarios. LF C LF = Max R − C LR + R2C + TLS 11 Crane configurations that satisfy the conditions included in these two steps are evaluated for their boom and jib clearances to adjacent buildings.

Crane boom radius