### Problem DescriptionConsider a beam with boundary conditions, loading, and cross-section as shown in the diagram. There is a compressive axial load, \( P = 5 \) kips, acting through the centroid of the cross-section in addition to the applied concentrated moment. Determine the following:(a) The normal (flexural) stress, \( \sigma \), at D due to the applied moment. (b) The normal stress, \( \sigma \), at D due to the axial load. (c) The total normal stress at D due to both the applied axial load and the applied moment.### Diagram Explanation#### Beam Diagram- The beam is supported at point A with a triangular support and at point C with a circular support. - A 5 kip axial load is applied at both ends of the beam (points A and C).- A concentrated moment of 144 k-in is applied counterclockwise at point B.- The entire beam spans 12 ft, with 5 ft from A to B and 8 ft from B to C.- Point D is located along the beam between points B and C.#### Cross-section- The cross-section of the beam at point D is shown as a rectangle.- The dimensions of the cross-section are 6 inches in width and 8 inches in height.- Point D is marked as being located central to this section with \( 2 \) inches from the right edge, indicating the location where stress is being evaluated.This setup allows for the analysis of stresses at point D under the given loading and boundary conditions.

GIVEN: *P=5 kips=5 Kips = 22.2411 kN *M=144 k-in=16.2698 kNm TO FIND: (a) The normal (flexural)…

Consider a beam with boundary conditions, loading, and cross-section given below. In addition to the applied concentrated moment, there is a compressive axial load, P = 5 kips that acts through the centroid of the cross-section. Determine the following: (a) The normal (flexural) stress, o, at D due to the applied moment. (b) The normal stress, o, (c) The total normal stress at D due to both the applied axial load and the applied at D due to the axial load moment.

Consider a beam with boundary conditions, loading, and cross-section given below. In addition to the applied concentrated moment, there is a compressive axial load, P = 5 kips that acts through the centroid of the cross-section. Determine the following: (a) The normal (flexural) stress, o, at D due to the applied moment. (b) The normal stress, o, (c) The total normal stress at D due to both the applied axial load and the applied at D due to the axial load moment.

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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Concept explainers

Combined Loading

Any functioning component, such as machine parts, structural members, pressure vessels, and so on, are all under the influence of more than one force. When anybody is under the influence of more than one force such as shear forces, bending moments, axial forces, torsion, and so on, then such body is said to be under combined loading. A very practical example of combined loading is the crankshaft of an internal combustion engine (IC engine). The crankshaft of the IC engine is under high rpm, which is caused due to the torsional forces. Due to the presence of piston, counterbalances, and internal imbalances, the crankshaft experiences lateral forces and due to the rise in temperature, the crankshaft undergoes thermal expansion, which pulls the crankshaft along the axial direction and lateral direction. The presence of unbalanced loads along the periphery of the crankshaft also induces a bending moment.

Question

### Problem Description

Consider a beam with boundary conditions, loading, and cross-section as shown in the diagram. There is a compressive axial load, \( P = 5 \) kips, acting through the centroid of the cross-section in addition to the applied concentrated moment. Determine the following:

(a) The normal (flexural) stress, \( \sigma \), at D due to the applied moment.
(b) The normal stress, \( \sigma \), at D due to the axial load.
(c) The total normal stress at D due to both the applied axial load and the applied moment.

### Diagram Explanation

#### Beam Diagram

- The beam is supported at point A with a triangular support and at point C with a circular support.
- A 5 kip axial load is applied at both ends of the beam (points A and C).
- A concentrated moment of 144 k-in is applied counterclockwise at point B.
- The entire beam spans 12 ft, with 5 ft from A to B and 8 ft from B to C.
- Point D is located along the beam between points B and C.

#### Cross-section

- The cross-section of the beam at point D is shown as a rectangle.
- The dimensions of the cross-section are 6 inches in width and 8 inches in height.
- Point D is marked as being located central to this section with \( 2 \) inches from the right edge, indicating the location where stress is being evaluated.

This setup allows for the analysis of stresses at point D under the given loading and boundary conditions.

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