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A crane is a type of machine mainly used to lift, lower, and horizontally move heavy objects. It is immensely useful in construction works. In this problem, we will be analyzing a type of crane called a luffing crane. Cable 6 m 10000 N 20000 N Main mast Figure 1: a typical luffing crane As illustrated in fig. 1, a luffing crane typically consists of a main mast, a jib, a gantry and a counterweight. The jib and the gantry are always perpendicular, but the jib can vary in angle with the horizontal line. In this problem, however, we will consider it fixed at 30°. The counterweight is pulling directly downward on the end of the gantry, which is also connected to the end of the jib by a cable. In reality, the main mast and jib are made of multiple short columns and beams welded together into a compound structure. For this problem, however, we will assume that the mast and jib are each made of a single constant cross-section steel. The steel has E = 210 GPa, Sy = 400 MPa, and Sut = 550 MPa. In this problem, the main mast is 10 m long, the jib is 20 m long, and the gantry is 6 m long. The counterweight weighs 20000 N. The angle 0 = 30°. The maximum weight that the crane can lift is 10000 N. The safety factors of the mast and the jib are 2 and 3, respectively. The jib can be considered fixed to the mast, while the mast base is fixed to the ground and free to move at the top. Determine the required section modulus Zmast and Zjib and moments of inertia Imast and Ijib of the mast and the jib. Ignore fatigue and stress concentration factors. You may assume that the mast, jib, and gantry are weightless. 30⁰ Gantry www 30⁰ 10 m 20 m Jib

A crane is a type of machine mainly used to lift, lower, and horizontally move heavy objects. It is immensely useful in construction works. In this problem, we will be analyzing a type of crane called a luffing crane. Cable 6 m 10000 N 20000 N Main mast Figure 1: a typical luffing crane As illustrated in fig. 1, a luffing crane typically consists of a main mast, a jib, a gantry and a counterweight. The jib and the gantry are always perpendicular, but the jib can vary in angle with the horizontal line. In this problem, however, we will consider it fixed at 30°. The counterweight is pulling directly downward on the end of the gantry, which is also connected to the end of the jib by a cable. In reality, the main mast and jib are made of multiple short columns and beams welded together into a compound structure. For this problem, however, we will assume that the mast and jib are each made of a single constant cross-section steel. The steel has E = 210 GPa, Sy = 400 MPa, and Sut = 550 MPa. In this problem, the main mast is 10 m long, the jib is 20 m long, and the gantry is 6 m long. The counterweight weighs 20000 N. The angle 0 = 30°. The maximum weight that the crane can lift is 10000 N. The safety factors of the mast and the jib are 2 and 3, respectively. The jib can be considered fixed to the mast, while the mast base is fixed to the ground and free to move at the top. Determine the required section modulus Zmast and Zjib and moments of inertia Imast and Ijib of the mast and the jib. Ignore fatigue and stress concentration factors. You may assume that the mast, jib, and gantry are weightless. 30⁰ Gantry www 30⁰ 10 m 20 m Jib

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A crane is a type of machine mainly used to lift, lower, and horizontally move heavy objects. It is immensely useful in construction works. In this problem, we will be analyzing a type of crane called a luffing crane. Cable WESTI 20 m 6 m 10000 N 20000 N Main mast Figure 1: a typical luffing crane As illustrated in fig. 1, a luffing crane typically consists of a main mast, a jib, a gantry and a counterweight. The jib and the gantry are always perpendicular, but the jib can vary in angle with the horizontal line. In this problem, however, we will consider it fixed at 30°. The counterweight is pulling directly downward on the end of the gantry, which is also connected to the end of the jib by a cable. In reality, the main mast and jib are made of multiple short columns and beams welded together into a compound structure. For this problem, however, we will assume that the mast and jib are each made of a single constant cross-section steel. The steel has E = 210 GPa, Sy = 400 MPa, and Sut = 550 MPa. In this problem, the main mast is 10 m long, the jib is 20 m long, and the gantry is 6 m long. The counterweight weighs 20000 N. The angle 0 = 30°. The maximum weight that the crane can lift is 10000 N. The safety factors of the mast and the jib are 2 and 3, respectively. The jib can be considered fixed to the mast, while the mast base is fixed to the ground and free to move at the top. Determine the required section modulus Zmast and Zjib and moments of inertia Imast and Ijib of the mast and the jib. Ignore fatigue and stress concentration factors. You may assume that the mast, jib, and gantry are weightless. 30⁰ Gantry 30⁰ 10 m Jib
Transcribed Image Text:A crane is a type of machine mainly used to lift, lower, and horizontally move heavy objects. It is immensely useful in construction works. In this problem, we will be analyzing a type of crane called a luffing crane. Cable WESTI 20 m 6 m 10000 N 20000 N Main mast Figure 1: a typical luffing crane As illustrated in fig. 1, a luffing crane typically consists of a main mast, a jib, a gantry and a counterweight. The jib and the gantry are always perpendicular, but the jib can vary in angle with the horizontal line. In this problem, however, we will consider it fixed at 30°. The counterweight is pulling directly downward on the end of the gantry, which is also connected to the end of the jib by a cable. In reality, the main mast and jib are made of multiple short columns and beams welded together into a compound structure. For this problem, however, we will assume that the mast and jib are each made of a single constant cross-section steel. The steel has E = 210 GPa, Sy = 400 MPa, and Sut = 550 MPa. In this problem, the main mast is 10 m long, the jib is 20 m long, and the gantry is 6 m long. The counterweight weighs 20000 N. The angle 0 = 30°. The maximum weight that the crane can lift is 10000 N. The safety factors of the mast and the jib are 2 and 3, respectively. The jib can be considered fixed to the mast, while the mast base is fixed to the ground and free to move at the top. Determine the required section modulus Zmast and Zjib and moments of inertia Imast and Ijib of the mast and the jib. Ignore fatigue and stress concentration factors. You may assume that the mast, jib, and gantry are weightless. 30⁰ Gantry 30⁰ 10 m Jib
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