### Problem Statement**a) Simply Supported Beam Scenario:**A steel 4 X 4 X 0.25-inch square tube (moment of inertia \(I = 8.215 \, \text{in}^4\)) is used as a simply supported beam. A 100-pound weight is dropped from a height of 24 inches onto the beam at mid-span. The task is to determine the maximum stress in the beam. The modulus of elasticity \(E\) is given as \(29 \times 10^6 \, \text{psi}\).**Accompanying Diagram:**- A simply supported beam with fixed ends.- A 100 lb weight is shown being dropped from a height of 24 inches exactly at the mid-span.- The beam spans a distance of 8 feet.**b) Beam with Spring Supports Scenario:**Instead of fixed supports, the beam is supported by springs at both ends. Calculate the maximum stress in the beam when the 100-pound weight is dropped from a height of 24 inches, using the same beam properties as in part a).**Accompanying Diagram:**- A beam with spring supports instead of fixed ends.- The springs have a stiffness of \(k = 200 \, \text{lb/in}\).- The same 100 lb weight is shown being dropped from a height of 24 inches at mid-span.- The beam also spans a distance of 8 feet.The two diagrams depict different support conditions for the beam, each affecting how the beam will respond when the weight is applied.### ObjectiveCalculate and compare the maximum stress experienced by the beam under each scenario using the given conditions and properties.

For the solution refer below images.

a) A steel 4 X 4X 0.25-inch square tube (moment of inertia I = 8.215 inª) is used as a simply supported beam. A 100-pound weight is dropped from a height of 24 inches onto the beam at mid- span. Find the maximum stress in the beam. Use E = 29 X 106 psi. k = 200 lb/in 8 ft TIIMIT 100 lb b) Instead of fixed supports, the beam is supported by springs at both ends. Find the maximum stress in the beam when the 100-pound weight is dropped from a height of 24 inches (same beam properties as in part a). 24 in 100 lb 8 ft 24 in k = 200 lb/in

a) A steel 4 X 4X 0.25-inch square tube (moment of inertia I = 8.215 inª) is used as a simply supported beam. A 100-pound weight is dropped from a height of 24 inches onto the beam at mid- span. Find the maximum stress in the beam. Use E = 29 X 106 psi. k = 200 lb/in 8 ft TIIMIT 100 lb b) Instead of fixed supports, the beam is supported by springs at both ends. Find the maximum stress in the beam when the 100-pound weight is dropped from a height of 24 inches (same beam properties as in part a). 24 in 100 lb 8 ft 24 in k = 200 lb/in

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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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 Statement

**a) Simply Supported Beam Scenario:**

A steel 4 X 4 X 0.25-inch square tube (moment of inertia \(I = 8.215 \, \text{in}^4\)) is used as a simply supported beam. A 100-pound weight is dropped from a height of 24 inches onto the beam at mid-span. The task is to determine the maximum stress in the beam. The modulus of elasticity \(E\) is given as \(29 \times 10^6 \, \text{psi}\).

**Accompanying Diagram:**

- A simply supported beam with fixed ends.
- A 100 lb weight is shown being dropped from a height of 24 inches exactly at the mid-span.
- The beam spans a distance of 8 feet.

**b) Beam with Spring Supports Scenario:**

Instead of fixed supports, the beam is supported by springs at both ends. Calculate the maximum stress in the beam when the 100-pound weight is dropped from a height of 24 inches, using the same beam properties as in part a).

**Accompanying Diagram:**

- A beam with spring supports instead of fixed ends.
- The springs have a stiffness of \(k = 200 \, \text{lb/in}\).
- The same 100 lb weight is shown being dropped from a height of 24 inches at mid-span.
- The beam also spans a distance of 8 feet.

The two diagrams depict different support conditions for the beam, each affecting how the beam will respond when the weight is applied.

### Objective

Calculate and compare the maximum stress experienced by the beam under each scenario using the given conditions and properties.

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