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radiant; bright.
smiling brightly; cheerful.
any of various relatively long pieces of metal, wood, stone, etc., manufactured or shaped especially for use as rigid members or parts of structures or machines.
Building Trades. a horizontal bearing member, as a joist or lintel.
Engineering. a rigid member or structure supported at each end, subject to bending stresses from a direction perpendicular to its length.
Nautical.

a horizontal structural member, usually transverse, for supporting the decks and flats of a vessel.
the extreme width of a vessel.
the shank of an anchor.

Aeronautics. the direction perpendicular to the plane of symmetry of an aircraft and outward from the side.
the widest part.
Slang. the measure across both hips or buttocks:
broad in the beam.
Machinery.

walking beam.
(in a loom) a roller or cylinder on which the warp is wound before weaving.
a similar cylinder on which cloth is wound as it is woven.

the crossbar of a balance, from the ends of which the scales or pans are suspended.
a ray of light:
The sun shed its beams upon the vineyard.
a group of nearly parallel rays.
Radio, Aeronautics. a signal transmitted along a narrow course, used to guide pilots through darkness, bad weather, etc.
Electronics. a narrow stream of electrons, as that emitted from the electron gun of a cathode ray tube.
the angle at which a microphone or loudspeaker functions best.
the cone-shaped range of effective use of a microphone or loudspeaker.
Citizens Band Radio Slang. beam antenna.
a gleam; suggestion:
a beam of hope.
a radiant smile.
the principal stem of the antler of a deer.
to emit in or as in beams or rays.
Radio. to transmit (a signal) in a particular direction.
Radio and Television. to direct (a program, commercial message, etc.) to a predetermined audience.
to emit beams, as of light.
to smile radiantly or happily.
beam in, Citizens Band Radio Slang. to be received under optimum conditions; be heard loud and clear:
They told me I was really beaming in.
fly the beam, Radio, Aeronautics. (of an aircraft) to be guided by a beam.
off the beam,

not on the course indicated by a radio beam.
Informal. wrong; incorrect:
The pollsters were off the beam again for the last presidential election.

on the beam,

on the course indicated by a radio beam, as an airplane.
Nautical. at right angles to the keel.
Informal. proceeding well; correct; exact:
Their research is right on the beam and the results should be very valuable.

Contemporary Examples

There’s something very poignant about the photographs of a beaming Hillary Clinton in India.
Why I Don’t Envy Hillary Reihan Salam July 19, 2009

After the chat, The Daily Beast caught up with a beaming Jessica Alba on her way to dinner.
Ralph Lauren: ‘Tastemaker and Lifesaver’ Lizzie Crocker October 24, 2011

I found myself chatting with an older woman that was beaming from ear to ear.
‘When the Garden Was Eden’: Why New York City Needs the Knicks Now More Than Ever Robert Silverman April 18, 2014

As a modest new royal, the beaming bride covered up with a white angora bolero cardigan.
Dress No. 2! The Daily Beast April 28, 2011

Lugging her trophy, the bawling girl wobbled down the ramp into the arms of her beaming family and boyfriend.
‘The Land of the Permanent Wave’ Is Bud Shrake’s Classic Take on ‘60s Texas Edwin Shrake February 1, 2014

Historical Examples

“I’m so glad you came,” she said with great cordiality, seating herself near the other and beaming on her.
Miss Pat at Artemis Lodge Pemberton Ginther

Camille Doucet received me with a beaming expression on his face.
My Double Life Sarah Bernhardt

Late one afternoon he drove up to the house in Avenue Louise, and when Dorothy came downstairs for the drive her face was beaming.
Castle Craneycrow George Barr McCutcheon

But he had accomplished his purpose, for the Indian was won over and beaming with pleasure.
Murder Point Coningsby Dawson

And Gordon Lowndes stood erect in his place, fanning himself with the unpaid-for programmes, and beaming upon all the house.
Young Blood E. W. Hornung

noun
a long thick straight-sided piece of wood, metal, concrete, etc, esp one used as a horizontal structural member
any rigid member or structure that is loaded transversely
the breadth of a ship or boat taken at its widest part, usually amidships
a ray or column of light, as from a beacon
a broad smile
one of the two cylindrical rollers on a loom, one of which holds the warp threads before weaving, the other the finished work
the main stem of a deer’s antler from which the smaller branches grow
the central shaft of a plough to which all the main parts are attached
a narrow unidirectional flow of electromagnetic radiation or particles: a beam of light, an electron beam
the horizontal centrally pivoted bar in a balance
(informal) the width of the hips (esp in the phrase broad in the beam)
a beam in one’s eye, a fault or grave error greater in oneself than in another person
off beam, off the beam

not following a radio beam to maintain a course
(informal) wrong, mistaken, or irrelevant

on the beam

following a radio beam to maintain a course
(nautical) opposite the beam of a vessel; abeam
(informal) correct, relevant, or appropriate

verb
to send out or radiate (rays of light)
(transitive) to divert or aim (a radio signal or broadcast, light, etc) in a certain direction: to beam a programme to Tokyo
to pass (data, esp business card details, etc) from one hand-held computer to another by means of infrared beams
(intransitive) to smile broadly with pleasure or satisfaction
n.

Old English beam originally “living tree,” but by late 10c. also “rafter, post, ship’s timber,” from Proto-Germanic *baumaz (cf. Old Norse baðmr, Old Frisian bam “tree, gallows, beam,” Middle Dutch boom, Old High German boum, German Baum “tree,” Gothic bagms), perhaps from PIE verb root *bheue- “to grow” (see be). The shift from *-au- to -ea- is regular in Old English.

Meaning “ray of light” developed in Old English, probably because it was used by Bede to render Latin columna lucis, the Biblical “pillar of fire.” Nautical sense of “one of the horizontal transverse timbers holding a ship together” is from early 13c., hence “greatest breadth of a ship,” and slang broad in the beam “wide-hipped” (of persons). To be on the beam (1941) was originally an aviator’s term for “to follow the course indicated by a radio beam.”
v.

“emit rays of light,” early 15c., from beam (n.) in the “ray of light” sense. Sense of “to smile radiantly” is from 1804; that of “to direct radio transmissions” is from 1927. Related: Beamed; beaming.
biology, electronics, aesthetics, and mechanics (robotics)

occurs in the Authorized Version as the rendering of various Hebrew words. In 1 Sam. 17:7, it means a weaver’s frame or principal beam; in Hab. 2:11, a crossbeam or girder; 2 Kings 6:2, 5, a cross-piece or rafter of a house; 1 Kings 7:6, an architectural ornament as a projecting step or moulding; Ezek. 41:25, a thick plank. In the New Testament the word occurs only in Matt. 7:3, 4, 5, and Luke 6:41, 42, where it means (Gr. dokos) a large piece of wood used for building purposes, as contrasted with “mote” (Gr. karphos), a small piece or mere splinter. “Mote” and “beam” became proverbial for little and great faults.

see:

broad in the beam
off the beam