Paul Thompson
April 13, 2024
The Relieving Chambers
Inside the Great Pyramid is the King’s Chamber made of close-fitting granite blocks. This chamber has a flat ceiling made from a number of large granite beams that span from one wall to the other. This is the first time a flat ceiling was used in a pyramid. Typically, the roofs are gabled meaning they are like a normal house roof where the two sides are at an angle and meet in the center. A single beam that spans across a room tends to sag in the middle and this tries to stretch the rock on the bottom side. Rock can take a lot of compressive stress but tends to fail in tension.
Above the ceiling are five levels of rock that have been the subject of speculation for years. They have been called the five “relieving chambers” because it has been thought that they protected the King’s Chamber from all the weight of the rock above. In fact, it doesn’t do a thing to protect anything. Above the highest chamber is a traditional gabled roof that does support the weight above it. The relieving chambers are isolated from the surrounding rock and stand by themselves under their own weight.
I have determined that the Egyptians probably used the framework of rock beams to press down on the ends of the ceiling beams. Essentially, this clamps the beam against the top of the two walls that are opposite one another. Although there are four walls in the chamber, it is important to note we are talking about the walls on either end of the beams. That would be the north and south walls. A normal beam set on top of two opposite walls will sag slightly in the center and the ends will kick up in the air slightly. This is called a simply supported beam and is the weakest way to use them, having the most sag and the greatest stress (the underside, halfway across).
If one were to clamp the beams to the top of the wall, the deflection is reduced to one fifth and the stress goes down to one third. That is because pushing the ends down causes the beam to bend upwards near the ends and it still sags in the middle but much less (see picture). The deflection and stress in the upward direction is equal to the deflection and stress in the downward direction.
The stack of blocks is freestanding within the pyramid, presumably, so they know how much weight is applied. If it were tied into the main structure, it would be hard to predict the actual force being applied.
Whether or not the Egyptians knew, mathematically, that the stress could be cut to a third, they could have determined by experiment that clamping the ends would have an outsized benefit. Despite this, the beams in the pyramid have developed cracks. But the cracks happened near the walls rather than at the midpoint of the beams. That shows the stress has been rearranged or it would have cracked in the middle.
Picture of the relieving chambers
Figure 1 King's Chamber
This shows the rocks pressing down on top of the ceiling beam. Note the gabled roof at the top is not touching the stack of rocks. It supports the rest of the pyramid overhead.
drawing showing how clamping ends reduces sag
Figure 2 Relieving chambers
The left picture shows an exaggerated sag of a simply supported beam. The right side shows the stack of beams bearing down on the ends of the ceiling beam. It shows the exaggerated shape a beam takes when clamped flat on the ends. The beam tends to bow upwards then downwards then upwards again. The amount of deflection upwards equals the deflection down so it splits the stress in two directions where neither direction is excessive. If the Egyptians had access to large bolts, the beam could have been held flat with bolts instead of a tower of rock.
video showing how clamping ends of beam will raise center
April 13, 2024
The Relieving Chambers
Inside the Great Pyramid is the King’s Chamber made of close-fitting granite blocks. This chamber has a flat ceiling made from a number of large granite beams that span from one wall to the other. This is the first time a flat ceiling was used in a pyramid. Typically, the roofs are gabled meaning they are like a normal house roof where the two sides are at an angle and meet in the center. A single beam that spans across a room tends to sag in the middle and this tries to stretch the rock on the bottom side. Rock can take a lot of compressive stress but tends to fail in tension.
Above the ceiling are five levels of rock that have been the subject of speculation for years. They have been called the five “relieving chambers” because it has been thought that they protected the King’s Chamber from all the weight of the rock above. In fact, it doesn’t do a thing to protect anything. Above the highest chamber is a traditional gabled roof that does support the weight above it. The relieving chambers are isolated from the surrounding rock and stand by themselves under their own weight.
I have determined that the Egyptians probably used the framework of rock beams to press down on the ends of the ceiling beams. Essentially, this clamps the beam against the top of the two walls that are opposite one another. Although there are four walls in the chamber, it is important to note we are talking about the walls on either end of the beams. That would be the north and south walls. A normal beam set on top of two opposite walls will sag slightly in the center and the ends will kick up in the air slightly. This is called a simply supported beam and is the weakest way to use them, having the most sag and the greatest stress (the underside, halfway across).
If one were to clamp the beams to the top of the wall, the deflection is reduced to one fifth and the stress goes down to one third. That is because pushing the ends down causes the beam to bend upwards near the ends and it still sags in the middle but much less (see picture). The deflection and stress in the upward direction is equal to the deflection and stress in the downward direction.
The stack of blocks is freestanding within the pyramid, presumably, so they know how much weight is applied. If it were tied into the main structure, it would be hard to predict the actual force being applied.
Whether or not the Egyptians knew, mathematically, that the stress could be cut to a third, they could have determined by experiment that clamping the ends would have an outsized benefit. Despite this, the beams in the pyramid have developed cracks. But the cracks happened near the walls rather than at the midpoint of the beams. That shows the stress has been rearranged or it would have cracked in the middle.
Picture of the relieving chambers
Figure 1 King's Chamber
This shows the rocks pressing down on top of the ceiling beam. Note the gabled roof at the top is not touching the stack of rocks. It supports the rest of the pyramid overhead.
drawing showing how clamping ends reduces sag
Figure 2 Relieving chambers
The left picture shows an exaggerated sag of a simply supported beam. The right side shows the stack of beams bearing down on the ends of the ceiling beam. It shows the exaggerated shape a beam takes when clamped flat on the ends. The beam tends to bow upwards then downwards then upwards again. The amount of deflection upwards equals the deflection down so it splits the stress in two directions where neither direction is excessive. If the Egyptians had access to large bolts, the beam could have been held flat with bolts instead of a tower of rock.
video showing how clamping ends of beam will raise center