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The solid shaft is supported by journal bearings at A and B that exert force components online in the x and z directions. Knowing that Tall = 6 ksi, determine the smallest permissi- ble diameter of shaft AB. F= 200 lb 8 in. 4 in. 8 in. 4 in. F, 250 lb 4 in. F₂ = 50 lb 8 in. 4 in. BE

The solid shaft is supported by journal bearings at A and B that exert force components online in the x and z directions. Knowing that Tall = 6 ksi, determine the smallest permissi- ble diameter of shaft AB. F= 200 lb 8 in. 4 in. 8 in. 4 in. F, 250 lb 4 in. F₂ = 50 lb 8 in. 4 in. BE

Structural Analysis
Structural Analysis
6th Edition
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:KASSIMALI, Aslam.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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**Problem Statement:** 1. The solid shaft is supported by journal bearings at A and B that exert force components online in the x and z directions. Knowing that \(\tau_{\text{all}} = 6 \, \text{ksi}\), determine the smallest permissible diameter of shaft AB. **Illustration Description:** The diagram shows a solid shaft with two gears and two journal bearings. The first gear is positioned closer to point C and the second gear closer to point E. The following details are annotated on the diagram: - **Point A (bearing):** Located between points C and E. - **Point B (bearing):** Located near end E of the shaft. - **Gear at C:** Exerts a force \( F_x = 200 \, \text{lb} \) on the shaft. This gear is 4 inches from point A. - **Gear between A and B:** Exerts a vertical force \( F_z = 50 \, \text{lb} \) on the shaft, shown 8 inches from the gear at C. - **Gear at E:** Exerts a force \( F_x = 250 \, \text{lb} \) on the shaft. This gear is also 4 inches from point B, which is at the extreme right end near point E. The shaft consists of: - A section from C to A measuring 4 inches. - A section from A to another gear measuring 8 inches. - A section from the gear to B measuring another 8 inches. - A section from B to E measuring 4 inches. **Objective:** Calculate the smallest permissible diameter of shaft AB that can withstand the given forces without exceeding the allowed shear stress of \(6 \, \text{ksi}\).
Transcribed Image Text:**Problem Statement:** 1. The solid shaft is supported by journal bearings at A and B that exert force components online in the x and z directions. Knowing that \(\tau_{\text{all}} = 6 \, \text{ksi}\), determine the smallest permissible diameter of shaft AB. **Illustration Description:** The diagram shows a solid shaft with two gears and two journal bearings. The first gear is positioned closer to point C and the second gear closer to point E. The following details are annotated on the diagram: - **Point A (bearing):** Located between points C and E. - **Point B (bearing):** Located near end E of the shaft. - **Gear at C:** Exerts a force \( F_x = 200 \, \text{lb} \) on the shaft. This gear is 4 inches from point A. - **Gear between A and B:** Exerts a vertical force \( F_z = 50 \, \text{lb} \) on the shaft, shown 8 inches from the gear at C. - **Gear at E:** Exerts a force \( F_x = 250 \, \text{lb} \) on the shaft. This gear is also 4 inches from point B, which is at the extreme right end near point E. The shaft consists of: - A section from C to A measuring 4 inches. - A section from A to another gear measuring 8 inches. - A section from the gear to B measuring another 8 inches. - A section from B to E measuring 4 inches. **Objective:** Calculate the smallest permissible diameter of shaft AB that can withstand the given forces without exceeding the allowed shear stress of \(6 \, \text{ksi}\).
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